SINGHANIA UNIVERSITY '

B. TECH- pn-<:.1---"'J;~ -· MATHIVIATICS

UNIT 1

Asymptotes, Curvature, Multiple point and Curve tracing

UNIT 2

Partial differentiation, Maxima and Minima

UNIT 3

Length of plane curve, Volumes and surface of solid of

revolution, Double and Triple integrals, Gamma and Beta

function

Unit 4

Differential equation of first order and first degree, Linear

differential equation with constant coefficients

Unit 5

Linear differential equation of second order

SINGHANIA UNIVERSITY

diploma -1 sem

MATHMATICS

UNIT 1

Asymptotes, Curvature, Multiple point and Curve tracing

UNIT 2

Partial differentiation, Maxima and Minima

UNIT 3

Length of plane curve, Volumes and surface of solid of

revolution , Double and Triple integrals , Gamma and Beta

function

Unit 4

Differential equation of first order and first degree, Linear

differential equation with constant coefficients

Unit 5

Linear differential equation of second order

I

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(Contents J Chapters

UNITS-I

1. Sphere

2. Cone

3. Cylinder

UNITS-II

4. Matrices

I UNITS-III

5. Vector Func~ions of a Real Variable, their Derivatives and Scalar and Vector Fields

6. Integration of Vectors

7. Integral Theorems

UNITS-IV

8. Velocity and Acceleration

9. Rectilinear Motion in a Resisting Medium

I UNITS-V I 10. Series Solutions of Second Order Linear

Differential Equations

11. Partial Differential Equations of First Order

0 Appendix-A

0 Appendix-B

0 Model Question Papers-I, II

DOD

Page No.

1.1 - 1.34

2.1 - 2.16

3.1 - 3.12

4.1 - 4.50

5.1 - 5.58

6.1 - 6.36

7.1 7.54

8.1 - 8.24

9.1 - 9.24

10.1 - 10.34

11.1 - 1 J .43

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BCA-103

Time: 3 hours

MATHEMATICS

External Marks: 80 Internal Marks: 20

Note: Examiner v.-111 be required to set NINE questions in all. Question Number 1 will consist of roral 8 parts (short-answer cype questions) covering the encire syllabus and \\ill carry 16 marks. In addition ro the compulsory question there will be four units i.e. Unit- I to Unit-IV. E"\am.iner u,'ill ser two questions from each Unit of the syllabus and each guesrion will carry 16 marks. Smdent will be required to attempt FIV't questions in all. Question Number 1 will be compulsory. In addition ro compulsory question, student v..ill have to attempt four more questions selecting one question from each Unit.

UNIT I SETS: Sets, Subsets, Equal Sets Universal Sets, Finite and Infinite Sets, Operation on Sets, Union, Intersection and Complements of Sets, Cartesian Product, Cardinality of Set, Simple Applications. DETERMINANTS: Definition, Minors, Cofactors, Properties of Detenninants, Applications of determinants in finding area of triangle, Solving a system of linear equations. MATRICES: Definition, Types of Matrices, Addition, Subtraction, Scalar Multiplication and Multiplication of Matrices, Adjoint, Inverse, solving system of linear equation Cramer's Rule.

UNIT II RELATIONS Al'il) FlJNCTIONS: Properties of Relations, Equivalence Relation, Partial Order Relation Function: Domain and Range, Onto, Into and One to One Functions, Composite and lnverse Functions. · LIMITS & CONTINUITY: Limit at a Point, Properties of Limit, Computation of Limits of Various Types of Functions, Continuity of a functior, at a Point, Continuity Over an Interval, Sum, product and quotient of continuous functions, lntennediate Value Theorem. Type of Discominuities.

UNIT Ill DIFFERENTIATION: Derivative of a function, Derivatives of Sum, Differences, Product & Quotient of functions, Derivatives of polynomial, trigonometric, exponential, logarithmic, inverse trigonometric and implicit functions, Logarithmic Differentiatioh, Chain Rule and differentiation by substitution.

UNIT IV INTEGRATION: Indefinite Integrals, Methods of Integration by Substitution, By Parts, Partial Fractions, Integration of Algebraic and Transcendental Functions, Reduction Formulae for simple and Trigonometric FLmctions, Definite Integral as Limit of Sum, Fundamental Theorem of Integral Calculus, Evaluation of definite integrals by substitution, using properties of definite integral,

SUGGESTED READINGS I. C.L.Liu: Elements of Discrete Mathematics, McGraw Hill. 2. Lipschutz, Seymour: Discrete Mathematics, Schaum's Series 3. Babu Ram: Discrete Mathematics, Vinayek Publishers, New Delhi. 4. Trembley, J.P & R. Manohar: Discrete Mathematical Structure with Application

to Computer Science, TMH. S. Kenneth H. Rosen: Discrete Mathematics and its applications, TMH. 6. Doerr Alan & Levasseur Kenneth: Applied Discrete Structures for Computer

Science, Galgotia Pub. Pvt. Ltd. 7. Gersting: Mathematical Structure for Computer Science, WH Freeman &

Macmillan. 8. Hopcroft J.E, Ullman J.D.: Introduction to Automata theory, Languages and

Computation, Narosa Publishing House, New Delhi.

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t .'.LGEBRA & TRIGONOMETRY ...... :li~·~ i(i.

ALGEBRA b,·; '" It:-~ Section ~ I (3 Questions) ~-·'"'· ~~~ Syrn.m.etric, Skew-symmetrices, Hermitian and Skew-Hermitian matrices. Elementary oper:.:r:ions O!:l

:::ar.rices. Inverse of a matri-..:::. Linear independence of row and column matrices. Row rank, colunm rank

..,..,d r:mk of a matr.!x. Equivalence of colmnn and row ~-1J..!r.s. Eigenvalues. e.igen vectors and the characteristic

equarion of a maL.--i.--..:::. Cayley Harni..iron theore....-n and its use .in finding inverse of a mat:ri.'r. Applications of

i9, fi? ~-.~. =:2.-tticcs m a sys~e:-::l of li..'"le:t:: (bot..l::. homogene':)US and non-ho::nogene:::ms) egu.r~ti.cr::s. Theorems on ccr::.sis:ez.c;;-Sg:· - - lin . ~ ::-~ a system ot ear equations.

It:. Section • II (2 Questions)

~ "Rdarior:s b~t'w·ecn the roots ~r::C cocffic.i.cnts of general polynomial equation m one: -;--az.i.ablc:.

~ .. ~-:1sformation of equations. Descarte's rule of signs. Solution of cubic equations (Ca:rdan method) and

~ -· 3-:quddiatic equation.; (Des carte's an.d Ferari ~,feillods).

if Section · III (3 Questions) !-" -&,:

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~.1app.ings. Equivalence relations and partitions. Congruence moduio n.

Definition of a group with ex<Unples and simple properties. Subgroups. Generation of groups. Cyclic

;r::•.J.ps. Coset dccompo.sition. Lagrange's theorem and its consequences. Fermars and Euler's theorem.

H-o.r:aomorplN.sm and Isomorphism. :Normal subgroups. Quotient groups. The fundamental theorem of .:::Cr:::wmorphism. Permutation groups. Even and odd permutations. The alternating groups A

11• Cayley's

G:e:::rem. Introciucnon ro rings, Subrings, integral do:mains and fields. Characteristic of a ring.

TRIGONOMETRY

~ Section - IV (2 Questions)

t- Del'vioivre's theorem and its applications. Direct and inverse circular and hyperbolic function-s .

.:..ogarithm of a complex quantity. Expansion of trigonometrica1 functions. Gregory's Series. SurnmzciD.u oi ~ene~.

Note: The examiner is requested to set ten questions in all selecting guesrions section wise as indicate;:! in. th-e.

syll;.bus. The ca..-:;didate 1s ::<eqcired to .;::ttempr E>-;ce questions selecting atkast: one question from e.;t6

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B.A.IRSc. I (Paper II) CALCULUS AND ORDINARY DIFFERENTIAL EQUATIONS

Section I (2 Questions)

Successive differentiation. Leibnitz theorem. Maclaurin and Taylor series expansions. Asymptotes. Curvature. Tests for concavity and convexity. Points of inflexion. Multiple points, Tracing of curves in Cartesian and polar coordinates.

Section II (3 Questions)

Reduction formulae. Quadrature. Rectification. Volumes and surfaces of solids of revolution.--· -

Section III (3 Questions)

~ Exact ctifr€rential equations. First orde;·-hlgher degree equations solvable for x, y, p. Clairaut's form and singular solutions. Geometrical meaning of a differential equation. Orthogonal trajectories. Linear differenti5'r~quations with constant coefficients .... Homcgeneou$ linear ordiJ:¥~rY differential equations, Total differential equations. · · ''· . -:·-

Section IV (2 Questions)

Linear differential equations of second order. Transformation- of the equation by chang-· ing the ·dependent variable/the independent variable, reduction of order. Method of variation of parameters and unknown coefficients. Ordinary simultaneous differential equations.

Note. The examiner is requested to set ten questions in all selecting questions sectionwise as indicated in the syllabus. The candidate is ~equired t-o attempt five questions selecting at least one ques­tion from each section.

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B.A./B.Sc. I - PAPER lli

(n:CTORANAL YSIS AND GEOMETRY :.. ., £ f': S,e~on I ( 2 Questions)

Vector Analysis

-'!'::or t Scalar and vector product of three vectors. Product of four vectors. Reciprocal vectors. Vector

f~nnanon. Gradient, Divergence and Cud.

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f' Section II ('2 Questions) n -~ £; -~n. Theorems of Gauss. Green, Stokes and problems based on these

fl• Geometry

~Section Ill ( 3 Questions)

f; General equation of second degree. Tracing of conics. System of conics. Confocal conics. Polar f:;:~tion of a conic.

b· 5ection IV ( 3 Questions) f General corucoids. Paraboloids. Plane Sections of Conicotds. Generating lines. Confocal Conicoirls.

t'' lkJoccion of Second Degree Equation. Sphere, Cone, Cylinder

~1· ~ - --------~::.;._~ Sate : The examiner IS requested to set ten questions in all, selecttng questtons sect1onwise as mdicated /~ ~---• in the syllabus. The candidate is required to attempt five questions selecting atleast one question

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B.A./B.Sc. PART II

PAPER I

BM 201A- ADVANCED CALCULUS

Definition of a sequence. Theorems on limits of sequences. Bounded and monotonic sequences. 'C"u·Chjr's convergence criterion: Sequential continuity. Properties of continuous functions. Uniform

... :ontinuity. Series of non-negative terms. Comparison tests. Cauchy's integral test Ratio tests. Raabe's, bgatithmic, de Morgan and Bertrand's tests, Gauss t~st.Alternating series. Leibnitz's theorem ... 1\.bsolute

· m:i conditional convergence.

Mean:,alue theorems and their geometrical interpretations. Darbou.x's intermediate value theorem .fur derivatives. Taylor's theorem with various forms of remainders. · -._ •

Limit and continuity of functions of two variables. Partialranfereotiarioo. Change <:>f.~blei, 'C!::cler's theorem on homogeneous fu?ctions. Taylor's theorem for fu;nctions of two v~~~es)~~~~~f.- ~--·

!\fa-, minima and saddle points of functions of two variables. Lagrange's multiplier iriei:&q'f~ ~:':• . . -~

;c~aitn: - III (2 Questions) /

Envelopes. Evolutes. Indeterminate forms.

- IV (2 Questions)

... ?;,ta and Gamma functions. Double and triple integrals. Dir:ichlets integrals. Change of order of ~~rna on in double integrals.

The e.'";:amine.r is requested to set ten questions in all selecting questions secrionwise as indicated in the syllabus. The candidate is required to attempt five questions selecting 3tleast one question from each section.

.B.A./JliS!', PAWL:II PAPER II- . -: "'::"i'.; ~ ,, f . ~--- ''·-

Section- I (2 Questions) · . . . ··-·· . ;. • . .·. ;_ .

. Series solutions of differentiaiequations: £~:!~method, Bessel, Legendre 'f'id·f:i,~ge~tjjc equat!On& Bessel,. Legendre and Hypergeometnc funcbons and thett properttes - ~onvergence, i:eCUJ'tence and 'genei.ring:iioi!ariions Ottliogonolity c>f· Bessel functi:ot.J~ -ami L:egcm~:j'io'lj<h<i~ :'n":.::·<f ,;·( · ·

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• ··~rial Geometry - C~s with torsio,;; pru;cipal normal, osculating circle; bino$U, Sen:et - Fre!lei:fu$j,ii!ire, M'&S~f centte.of curvatu.re, sp#ericai·~iifre, surfaces, enV<;lop~ edge of regreS,ion, , · fonttii/hd,'{Jl''inagnirudes of the first ordeL · "~

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I SYLLABUS I

B.A./B.Sc. PART II

PAPER III

BM 203A - MECHANICS

Conditions of equilibrium of Coplanar forces. Virtual work in two-dimensions. Proof of principle of virtual work and its converse for coplanar forces. Forces which may be omitted in forming the equation of virtual work.

Section - II (2 Que•tions)

Forces in three dimensions. Stable and unstable equilibrium.

Section - III (3 Questions)

Velocities and accelerations alpog radial_and trans..ve....-se_ directions, and alo?g tangential and normal _Qirec~~~s.-Sitr>ple1u.r1Jlo11fc motion. Elastic strings. --- . ···

Motion on smooth and rough plane curves. M,Qtipn in_a_resisting medium. Motion of particles of ~~ngmass.

Section - IV (2 Questions)

S:entral Orbits. Kepler's laws of motion.

Motion of a particle in three dimensions. Acceleration in terms of different coordinate system$.

Note: The examiner is requested to set ten qu~stions in all selecting questions sectionv;>ise as indicated in the

syllabus. The candidate is required to attempt five questions selecting adeast one question from each section.

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... 1:1.sc. Part-Ill, Syllabus (i) One major experiment (ii) 'Hvo minor experiments (iii) Record of Practical Work

"- (iv)Oralll:st (Viva-Voce) ~Paper I: Analysis ·

Real-Analysis

15 MarY..s - 20 Marks

7 Marl:i 8 Mart!>

Unit-1 : Riemann inrcgral, Integrability of cOntinuous and monotonic functions. The fundamentcll theorem of int~gral calculus, mean value theoreni.s of integral calculus. Improper Integrals and their convergence,· Comparison tests, Abel's an~ Dirichlcr~s tests. FruUani's imegral. Integral as a function of a parameter.

· Unit-11: Continuity, derivability and intergrability o( an integral of a function of a parameter. Partial derivation and differentiability of real valued functions of two variables.

C01nplex Analysis

Unit-lii : Complex numbers as ordered pairs. Geometric reprcscn~ution of complex numbers. Stereographic projection. Cominuity and differentiability of corpplcx fuhctions. Analytic functions. Cauchy-Ricman equations. H~rmbnic functions. Metf.iC Spaces ·

Unit-TV: Definition and example of mctr!c SPf!CCs. Neighbourhoods. Limit point, interior points, open and closed set~ Closure and interior, 'Boundary points. Subsp~ce ·_ of a metric space. Cauchy sequences, completeness. ·

Unit-V: Continuous (t,mctions. Uniform conlinuity. Isomerry·and h·omomorphism, Eguival~nt matrks. · ·

~Paper H: Abstract Algebra . .

Unft-I: Group-Automorphisms, inner automoq~hism, Automorphism groups and their computations. Conjugacy relations. Norma!iser, Counting Principle and the class · equation of finite group. Center for g:oup of prime order.

Unit-IJ : Normal Subgroups. Quotient groups. The fundamenral . .th.corcm o( homomorphism, Permutation groups. Even and odd·permutarions. Cayley's theorem.

Unit-III : Ring theory-Ring homomorph-ism, Ideals arid Quotient-Rings ... Euclidean rings. Plynomial firigs. Polynomi~ls over' the Rational field, Definition and cxamptes of vector spaces. Subspaces. Sum ~nd direct sum ofsubspaccs. Ljnear. span Linear dependance, [ndependance and their basic prqpcrlies.

UnH-IV : Basis, finite dimensional vector spaceS: Existence t_heorem for bases. Invariance of the number of clements of a basis set. Dimension, Existence ·of complementary_subspace of a subspace of-finite dimc;nsional vector space. J?imension · of sums of subspaces. Quotient space and its dim~nsion. Linear transformations and their representation as matrices. 'f'!le Algebra of linear t~an.Sformaiions. The rank nullity theorem.

Unit-V: Inner product spaces'-Cauchy Schwarz inequality. Orthogqna! vectors, OrthogOnal Complements. Orthonormal sets and -bases, Hessel's inequality for P!lite dil'nef!sional spaces. _Gramschmidt orthogonalization process. Paper HI: Any one of the folliJwing· papers

(i) Programming inC and Numerical Analysis Unit-1: Programmer's model of a computer. Algorithms. Flow ch3rts. Data" types.

Arithmetic 8nd input/output instructions. Decisions Control structu_rcs. Decision statements. Logical ami Conditional operators. Loop case control structures.

· Unit-II :. Functions. Recursions·, PreprocesorS. Arrays. Puppcting · Ot strings. Structures pointers. flie formatting.

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B.Sc. Part-Ill, Syllabus 15

Unit-Ill : Solution of Equations : Bisection, Secant, Regular falsi,· NewlOn's Method. Roots of Polynomials. Interpolation. Lagranges.and }!C"rmite interpolation, Divider! Differences, Difference Schemes, Interpolation. Formu!ns using Differences. NtJmericnl Differentiation

Unit-TV : Numerical Quadrature :-NeWton-Cote's Fo;mu/as Gauss Qiladra:urc, Formulas. Chebychev's Formulas. Linear equati_ons. Direct. methods of solving systems ~f linear equations (Gauss Elimination, LU decompo~ition, Cholesky Decorriposition) interactive Methot:ls (Jacobi, Gat,~ss Seidal, R<.~laXation Methods).

Unit-V : Ordinary Differenti<'~l_ Equations. Euler mcthod.f Single-step methods, Ru"nge-lwtta's m.:!thods. Multi-aep methods, Milne·Simpson" method, MC:thods based on numerical integration, ·MI.Ihods ~ased on Numerical differentiation, Boundary Value Problems, Eign value }lroblems.

. ~i) Discrete MathematicS Unlt-1 :Sets and Proposition~-Cardinality, MathematiCal Inductions. Principle ot

lnclusi6n and excluslion. Computabitity and-... Formal . Languages~Ordercd · .se~s. Languages. Phrase Structure Grammers. Types of Gr·arnmers and Umguages.

Unit-11 :·Pcrmu_fationS, Combin"arionS and disc;rcte pi-obability. Unit-in: Rel<ltions and f:unetions: Binary-relationst_Equiva\cnce H.e!ntions and

partitions. Partial order relations and tattices. Chains and AmichJins-Pigcon Hole. Principt.e.

Unit-IV : Graph and planr.r Graphs-Basic "Ierminology. Mulligraphs. Weighted Graphs~ Paths and Circuits. Shortest paths. Eulirian Paths and Circuits. 1tavel!ing ·

_ salesmab problem. Planar Graphs. U9lt-V : lloo\iean Algeb~as-Latticcs and Algebraic struclrucs. Duality.

Distrit\l.ltive and complemented Lalliccs. Boolean Lauices and Boolean Algebras. llooleah · Functions. and l?.xpre:Ssions;. Propositional calculus. Design and lmplcn_)cntation of Digital Networks-SwitChing Circuits.

.\ (iii) DHTerential Geometry nnd Terisor Caiculus Unit~~ : Local Theory of Curvcs~Spacc curves. Examples. Planer curves. elices.

Serret-F~~nct apparatUs. Exis_t_ence of space curVes. InVolutes' and evolutCs of curves. Local Theory of Surfaces-Pan~metric patches on surface. First Fundamental form and arc length. Normal Curvature. ·

U~I~·II: a·eodesic Curvature and Gauss formi.Jta, Shape operator Lp of a surface at a poi_QL- Vector field along a cuJ_"V~. Second a_nd third fundamentl:ll forms of a surface. Weierig~rten ~ap. Principal curVatures .0-aUssian· Curv~ture. Mean and normat curvatures.

Urii~~III: Global the<!lry of surfaces-Geddesic Coordinate pathccs. Gauss-Bonner fOrmU:Iae. Euter characteristic of a surface:.

u~·lt~IV : Elements of general Riemannian Geometry-Concepts of manifolds and examp!~s. Riemannian metric. "Thnsor fields. Covarient· diffcrentialion Syrilmctry--properti~s of curvature tensor. ·

Unit-V: ('..oncepts of affine connc:.:tion. Christoffel symbols. Curvature and Thrtion tensors.': Riemannian metric. and afftine connection Geodesic and norm' a! coordinates, rund,fJm6nt.ai Theorem of Riemannian Geometry.

(iv} Probability T.heory and Optitftiz:ition

l-.robahility Theory: Uuit-1 : Notion of probability : Random experiment,_ ~mpiC space, axiom of

probability, elementary prQperties of probability, ._e:qually likely outcome proble.ms. Handom variable~; : '"Concept, cumulative distribution functiOn, discrcate a.n~

M .A./.!\l.Sc.(.Pre,·ious) lVf'athcmntics E xa rn inalion

Sthernt~ of E.xamiu:.tr.inn : Annua~ Sthemc~ Note: l)upc1·s I to V tlt'l' t'rlmpul:-;ory·

Pap('t·- .1: /\dvnncc<l Ab-stn)C.t Algchn1

'';"cachi;1g ~ {) HtHU'S p~r \\-1.'.\.'-k

Examination: CfHnmou fm Rt');1lll:~r!i\otH:oUcgi~t1f' C;uuhd:ttt\"

3 Hrs. dur:1tiou

Noit•:

Thi~ r:Jt't'l' is divided lnw FiVE Unit~. TWO que,<;! ions '1.\"ili h~ SCi from ta-.h Unii. c~ndiJ.:ncs are required lo anempt FiVE qu{"SfiO!lS in all .laking ONE quest inn frcm cad1 -Unit AH·questions CIU'T")-' e_qual marks.

Direct product of group:-: {E:-:-:emal nnd Jnt<"mn\). fso:norphism iht'·('rcm:>- D!:w1c•nd i.~O:UOJ}"I!lbm theort:m, HutleTl1y LC'l1llll:t, Conjugate dasscs {E.':duding r·;.:~OU)JS.}. C•)mmutawrs., Derived suhg,wu_ps. Nmmal :-;erics ;mrl Solt·ab!e group-s. Composi:.i.:.;:t scrks. ReJim?Jnt.nt rhcan:m and .lordan-Hold-.:r ~h~tJn:m f0r !nitniit' gn~ups.

liuit2:

Eu:jide.m:rings. 'Moduks. Subm\Jciuks._ Qu<llic::n module~ Dirc:cl !>Ums und lvlodu!e Hummno-rphism.s, Genel"ation qfmt)dwles. Cyclic nHY.:hlie .. <:. Linc::.:.r tr.msinrmarim: of \'CdN space-s. Dual spaces. l.'!u~d ha~is and Otcir proper:ies. Dwll mar,'). Am;il:ila!OL

F.idC thoory- E:-.:lcnsion Jk-ids.. A1g:t::bmlc and Transt:cmknial -C\!Gn$ions. gt:pnr<~t:k <mJ ins""P~rnble e.;:tt".n:::ions. 1\1mm~! e-Y.tensi{lns. Splilling fidrlt-. Ci-<Jl!)l!< ·111cory .. -Uv.:: dcrncnt·c ,,f G,aloi~•-th::-,ory. A_uwnwrphi<:0.1 of eK\cn:-.ion.s. Fund<:ment:\i 1hc-orem of Gu!ni;;; ;ht:nry. :;;olutioo.s o[ polynomial equ<JtJons by radicals rmd ln;;olv<~bili1y nf t;ent.~ral equa\i1m o!' dtpet· five by radical:-..

~-~~-~-·----------------------------

Unit 4:

Mmric.-e~ of a lincnr maps. :Odarricc~ oftornp(}sltiml n1aps. Matric.e~ ofdualmnp, Eiget> \'illucs. Eigen \'(.".('.ll)rs. RanJ.·. and l>1ullity of linear mnrs •md m:llriccs. Jm'tTlib!c m::ltric.es~ Similar matrices, .Dctcrminams of m<~.trices and it$ compuwtions. Characleristic polynomial and eigen t•alucs. ·

Unit 5:

Rt".Jl inner pmducl-spt~ce, Scbwarizs inequality. Orthogonality. Bessel's ·inequality. Adjoint. Self adjoint linear U1:1nsfonnat.i(lhS and matrice.s, OU10gonal linear transfurmati:m1 1md ma:Irices. Principal Axis Theorem.

Pupe.r ~ fl: Real Analysis and Topology

Teaching: 6 Hour!' pc1· Week EX11miuathm; Cmnrnon for Rcgnhn·/Non-colle~iai"C Candidalc~

3 Hrs. durnlion Mnx. Marks J 0(1

i\nte :

ll;is p:1per is divitled into-FIVE Units. TWO qucstinn.s tvill be scr from each Unit. CandidAtes arc required 10 attempt Ff·'\'"£ questions in a·u tnking O)'JE question from e<tc!J

U;'i:.. AJI question~ carr.v equ3.1 marks.

fJnil I:

/I.Jgcbrn and algebras of sets. Algebras gcnc~ted by :1 c:lass of ~;ulJ.<;el~. Horel sets. Lebcsgut" measure of sen; of real numbers. Mcasurahility and Mca:-urc of<! sc.t Existenc-e ofNon-mcasurablc sets... Mt:as:umbk fuJlCtions. l~ca.'!i~:flti(ln of Hfl11·ncgativ..~ mcnsur.~hle. ftmdion as limit of an inc-rc:-t.<>ir.g sequence -of simpk functions, St111c1ure of mc.:~surablc functions. Convergen;;r in JneJtsure. Egoroffs theorem.

Unif 2:

9/c:icrstras:;'g theorem Gn the ::~ppmxlmatirm ~Jf continuou!> functi0n by poly.rw:ni:.l.is. L::hesg.ue in1Cf:,'T~i ofbotmded mcr~slmJh1e func-tions. Lche.sgu::- theorem on flu: pa:-;.->,1&~~ 1.;~

the timit under the .integral sign for bounzkd mzasurable func{i;_l\lS. Summahk fun~::~~m:r-. Space of square surnmnb.!c funclions. Fourier ~.!ric-!' :md cocftk.ic-11\.s, Par.scvaf't: id:!JJj;;y, Rie...,,:-Fi:;her T'heorc.m.

Uni1 :\;

1-r--hc~:,·;;lJc int•!{~':'~~J.it;;.• !-'r; ·nt,,t::lhini's ~lv:nrerr.. L:--tp<c~~t--s. i·rnldt:r~Minkowski incqualitie: . Cvrnp;ctencss of U'-:<paces. Topt)loglcnl spacCs, Subspares. Oper, sets._ Clt>scci scl". Neighbourhood system, R:se~: and suh-hnscs.

Cnit 4:

CN1tinuous mappine:. and Hol!'!t'O!llOrphism, Nets., Fi!~ers. Scpar:11ion axio:!l5 (1'<'. Tr. T::. T_:. T4), Product nnd Quotlem :;:pat".c.".

Unit 5:

Cnmpact anrllocaHy cnmpac1 spax~"- 7 ychonn-ff~ nne point' compaciification. Connct-lcd and l..oc:lily connected spaces, Continulty and Cl)nnech.dn.ess and Compactness.

P:1pcr- J'f-1: HjffcreutiaJ £qu:lHons

T caC'hing ~ () Jlouno pr.r Wed;. Exa:nina1lnn: Comnwn f,>r HcguJ:tr!Non-c:oUe-giatt~ 0Hldid<th\"

3 Urs. tlurntion The.ory J1 ~pc.r

Nol\":

This pr>;··t.~r is divide-..1 intn FI~·-'E 1 ;nil:-;. T\VO (!!lCstion'" .,.,.; l\ he sc< .fr0m c;Kh Unii. c~ndid:::HC.S are require-d 1{,' UHl"-mpt F!VE quesllom in aU \~klng O'KE qJ..t(!!'<i<m fn•J'l: eac-h L'nit. /\11 quest10ns t:.<Jrry C"qu~il m.:u-ks.

1 l

NonMline<rr ordiJJary different i:1! equations of particular fom1s. Riccnti's equation ·Grncnll SQlution and the sDiutiOil whe11 one. twp-or three p."L'1icub: solutions urc k:n0wr .. Total Di1Tcrcntial equalion::;. Pan in/ differential equati~:.•n:; ofsccrtnd o:·dcnvith valiohlc c.o· cfiidcni._c:- Monge's l!lethQd.

Uuil 2:

Clr1:<~~ifjcaiirm flflinear p.:!rtinl dilferc.iJ\i.'ll equation pfscc()nd ord~·r. C.1.ud1;<~ prohkm. Me: hod ofscparaiino of vo;·\ablcs. l..aplr:!ce. Wa<'t:.TlJti {iiffu~:~ion e-quation->. Ca;lOilh::.J!

fon11.~. Linear homoge-neous b~mndury \'<J)u~: problems. Eigcn values and eigtn funditm:>. S!rum-Lim:vilk·- h(rundm·y va!t1c problc:ms. Orthogonality of cigcn fun('ti(•ns. Reality of eig_en values.

·unil 3:

Calculus of variation . Functionals, \' ari:ruicm of a fimctiona! nnd iL'- properties. VnriaUon::t.! p:-vblcm~ with fn:t:d boundari-e~, Euler"!>- cgwuion. E~:·trcmals. hmdicnal d::pcndcll! on scvcml unktl(!\.._.IJ function~ and their -fin:1 ordc:r dcrivntivt·.s, Ptlll~-tio-nals dC'.pcndclll on higher order -tbrivntives. -Fwicciomils d~pendcn1 on the function of marl' liHm one-independent \-;uiahlc-. V:.triational problems in pnrmm:::.tri(~ fonn. Series solution of a second ordc:- Jjncar diffe.rcn!inl equation ncar u regnhJrisin&-rul~r rx1lni C\1t:i1wd of Frobe-niu:c:) with special reference W Gnuss hypergeorndric·cquation and Lcgcndn:'s r:quruion.

linir 4:

Gauss h~·pcrgc:-omt:i.ri<· fnn:;t;tm <md ils Jlrf:lf'"'..:J1ie!". lnl!?tzml n~prcscnl;.~tion. Un~ar transfnnnation fonnuias, Coni1gUous: funrlioa relations. Diffcrr.ntiation formulae, Lille:lr rebtion betwee-,n the solutions of Gaus.." hypt·rgoo:netric equntion. Kummer'~ confluent h.'-fX"t£'X'll1Ctric functinn and i1s pr0perties. Jmegrni ;epresenr::~tion. K llnmJer':-.: i1rsi ;:mn.~fomrmion. J .. egendrc ruhn(.lmia!!' and .functlotls P11(:x"J and Q1,(x).

Unir5:

Bessel tUncti0n.<; Jt,(x), Hcm1i1e polynomials HnCx1. L.1guerre nnd Associ:Jted Laguerre pol~·nnmiDis,

J1 aJ>t~!·- IV: l)iflf>.renrial Gt•(Hlldry

m~---------------------------------------------------------

•

Teaching:(, Hours per Wt-.cf; Examinntion : Cummon fnr J{t .. ,!:U1ar/Nrm~.r<!llq~i;l'1l' Cundirlaie~

3 Hrs. duration M:n:. Mark" 100

h'otc:

This pap~r-is div-idd itno FIVE Units. T\liO qucs!ions wifl be set from e-ach Unit Crutdidates are reqt1ircd tu attempt FIVE qlJeslions ir: a!l raking O~}j qucSlion frrm-: e:-J.cl'i UniL ldl qucsliom cnrry ti:'-l.}ual murk;;;_

lJnH 1;

Thteory of {".urvc-s- Space cur~·cs. Tangetl.ei. c(lfllar"l·of-ctlrYC and. surface. Oswlaiir.g. p-lane, Priril.:-ipal Jlonnal rmd BinorrmiL Cun·atun:. Torsion, St.'t"re!-Fre-n~t's fonnula.-. Gsc.ulaiing_ circle and Osculating_spherc. Existence and Uniquenss theorems, Bcrtrr.:1td 2.11rn;•s, Involute, Evo-lu(cs.Conoids, 1nficxion::~1 t&'1£.C"llls. Singular point~.hldicalr~~:

f:swe:'lop, Edge of regression. Ruk-d :>urfac..e. Dc"elopabtc surfa<;e, T.u1.gent plane tn a rule-d surfnce .. :Nece.•,sary and sufflcit~nt conditioa tha1·a surfwx~ ~=f O shouJd repn.:sern a devdopable ::urface. Metric or-a su:Jace~Fi~-t!'>e~.:ond and third fundamc.nta! fmm.•:;.fundamelital mag_nitud~ of some important snrfit-::es. (),ihog-onf!l rmje-ciorie.s. normal c-urvmure. Meunier;~ ihcorc:m •. Unit 3:

t'ricipa! direction$ and Principal curvature:s. Fit"$1 cmvmure. !\·le-an curvmure. G~\J~inn curvature. UmhiHQO. P...:-1diu;; of c-urv<:~rure of W\"\i normal seciinr. m <111 wuh-di..:: on z "­f[x.y). Radius of etlr'-'ature of a g)-veil-section ti1rough any poim en z."" ft:-.:.y). Lines{'{ curvature, Pr-incipal radii. Helation !){';\ween fundamentai fOrm$. / ... symptolic lines. Diffhcnilal equatinn of an a:;ymploiic "iiuc.-Curvah:rr and "TO:·sion of an asymptmic: lint":. Geodesics. DiffcrelJ!ial c-.qua\lon of l.l geod•:sic, Sjn;;ic differt-Jlli:1! equation nfa gewle-&ic. Gcode;;:c on<~ sur! ace of revolution, G~l):.icsk Cun·s.l\lft'. a."ld Torsion. fhws-s~Honw:~ ThC-(lX!Tj.

Vnit 4:

./

Gauss's formulae. G.nJss's characledstic cquntic.'n, Weingarten equations. Mainnrdi· o--.dav..i eqn::Jtions. Fundnnicnt::1l ('Xist..~ce tiicmcm for Sllrf:}GC.S. Parallel sur.fllt.X:'$".

Oaul';sia..:l tilld mean r.urwl!Ur'C' for<\ pm-.-dk!l surface, Bonm·f'.s the-.or:.'!rn on parallel surfaces. Tensor Analysis-- Kront·~.:ker delia. C.111travarinni and Covarimn tensors. ~:ymmcttic tensors, QuCl1iel11 law of tc.rl~>Pn>. Rclati-\'e. tcnsoc 'Riemannian space. J\1etri('_ tcnsN. Jndic.ator. Pennutation symhoJ:.; and Permutation tensors.

Unit 5:

Christo-ffel Fymbols and th-:!ir p1opt:nics. CoYm1nnt di/Tcnmtiation of ft.:ns:rrs. Ricci's !.llcorc-rn. lnuinsic- dcrh'ati\'C. (lc:r!de:;ics. Differentiai cmmtion -of zcodesic. Gcodr.!lic coordi;talcs, Field of pa.r.<~!lc! \'CCIQiS, Reimann·Christo.fitJ tensor--and iu propcnics. Co\'ariant Cl,Jr\-'Uturc lcrL<~or, Einstein space. Bia-nc-hi'!' .identity. Einstci:11ensor. Flat~· spacr. Isotropic poinL Schur':; theon.·-nL

V·.tpc:r- V: M<·dtanic~

'fl';H'.hing: 6 Houl's pc1· Week Ex~mliuation ; Common for Rc-gular-J~on-cQIIcginie Candidates

Nntt':

This paper ls divided int0 FIVE UniL<;. TV/0 qu<~stio.us will be sc: from e:nch Uni1. Candida.1es:-nre rcquiied ln <Jt!cmp! FIVE que-stions in aJ! ulklng ONE qucsl.inn from cnch Unil. AH questions carry <"qual marks ..

IJnil I:

D'Aiembert's principle. The gcnc.mJ equations or motion of a rigid body. Motion of c.cntrc­ofioertia and motion relative to centre of inertia. t>.·lotion ahQui a fixed axis. llle Cflmpound pendulum, Centre. of pe:rcu~sion. Motion of a rigid ll0dy in t\'-'0 dimt·.nsiom under finite and impulsive f(·lrccs.

Unit 2:

MoliN\ in thre<> di1m·:r:::i:m::- ~'-'ith t'l:'fet'~';tKt' 10 FAdc;-'s Cy!i~r:n_\~:\ and g"'"u:ne~··k·;; \:qWJ:ti(}n;;., !v1o;in~1 'J!idc: >10 i ,;-:_'1.":':. Nbtior, umir:-;- intpuL"--1·,-~ f1)nx·~- Cc•;:~t:rv~:kn , .. '-''StJentunJ (JinC;l; :;c1d ar!gL:b:·:1 ~tllG e;1e-rg:· fn:- i"':r<itr~ <18 wcl! ;!~ imjwbiv.~ ffwc~_-s

Unil ~:

Lng~~:lgc\ equation:; i(x ht>li):J{}J1liWS dynamic-al system, Energy C(jlWliO:l ro:· COJJSt:rvll!ih; fitld. Sm<dl {'::=~:illatwns, MotionLmdcr inuuisJve fO:ces. \-1otio:J ,-;fJ lop. 1.-ktmifl<Jl;';:> Gq•mticm;, (l"!" ;:;,,-to!\ (";ftr:lS!'::Y::i.i{;;~ a;'::•~·::·gy. -jJ;.Unifton·s prl;it:i[>it: F!Dd ;.cincit•lt oflc&'i: acilun.

[nlt 4:

Kitll.'.nl.<~:-it:> ofidt>.uf tluid. [Jtgr<mt~e's and -Et:k:: 's m~~hods. Equatbu 0fC"<I!liJHlity !!1: C:tmcsian. cylindrical -anr1 sph~ricd! polurcotlr-din:nes. R-ot:.'1dary :;~:d1v~~', Str~nai·htcs-< rath-linD; and :<;!rc.a.m Iln0J, \'t'i·"K:ir~'"J'0!e~lfi;d irr0;cHi0::~aJ :nr::-icn

l)uii $:

Euk~r'~ l;ydro~yn:1ro:li.-: cgn:nio""- Bc;r!ou:Ji's th':.D:·ern. Helmi-Hlil?.: eql!::nin:l"'- C:md:.'/;: ink-g.ruL Motlq, due ~v i . .,lpuisive :r-~r.:-es. i,1n~ion in twn-dimt"J~inm:. S~.r;_:.:Jm fimctb:: t',_,:·npi!".·; norc.::nni. ~-"U>('C:.:·· 5Cirrt:~'- D:;ubk-~5. ~" \''io ,;;;>:l:e:!

• MAT 401: Functional Analysis II and Advanced Calculus

Unit- l

Adjoint of an operator on a Hilbert space. Self-adjoint, Positive, Normal and Unitary operators and

their. propertics.Projection on a Hilbert space. Invariance. Reducibility. Orthogonal projections.

Unit-2

Derivatives of a continuous map from an .open subset of Banach space to a Banach space. Rules of

derivation. Derivative of a composite, Directional derivative. Mean value theorem and its

applications.

Unit- 3

Partial derivatives and Jacobian Matrix. Continuously differentiable maps. Higher ~erivatives.

Taylor's formula.

Unit- 4

fnverse function theorem. Implicit function theorem. Step function, Regulated function, primitives

and integrals. Differentiation under the integral sign. Riemann integral of function of real variable

with values In norrned linear space.

PAPE~-2-

!7~ 74? fm;G-;J

23

Unit -I

Viscosity , Analysis of stress and rate of strain, Stoke's law of friction, Thermal conductivity and

generalized law of heat conduction, Equations of state and continuity , Navier- Stokes equations of

motion.

Vnit-2

Vorticity and circulation, Dynamical similarity, Inspection and dimensional analysis, Buckingham

theorem and its application, Non-dimensional parameters and their physical importance : Reynolds

number, Froude number, Mach number, Prandtl number, Eckart number, Grashoff number,

Brinkmann number, Non- dimensional coefficients : Lift and drag coefficients, Skin friction , Nusselt

number, Recovery factor.

Vnit-3

Exact solutions of Navier - Stokes equations, Velocity distribution for plane couette flow, Plane

Poiseuille flow, Generalized plane Couette flow, Hagen- Poiseuille flow, Flow in rubes of uniform

cross-sections.

Unit- 4

Flow betv.reen tv.ro concentric rotating cylinders. Stagnation point flows : Hiemenz flow, Homann

flow. Flow due to a rotating disc.

fM£1{,.- 3 MAT COl: Mathematical Programming -I

Unit -1

Separating and supporting hyperplane theorems. Revised simplex method to solve Unear

Programming problems, Bounded variable problems.

Unit -2

Integer programming: Gomory's algorithm for all and mixed integer programming problems, Branch

and Bound algorithm; Goal programming: Graphical goal arrainment method, Simplex method for

GPP.

Unit- 3

Separable programming: Piece-wise Linear approximations to non-linear functions, Reduction to

separable programming problem to l.p.p., separable programming algorithm, fractional programming:

computational procedure.

Unit- 4

Dynamic programming: Introduction, Bellman principle of optimality, solution of problems with

finite number stages, solution ofl.p.p. by dynamic programming.

~ - • 'T' rn-

MAT EOl: Integral Transforms

Unit -1

Fourier transform - Defiition and properties of Fourier sine, cosine and complex transforms.

Convolution theorem. Inversion theorems. Fourier transform of derivatives.

Unit- 2

Mellin transform- Definition and elementary properties. Mellin transforms of derivatives and

integrals. Inversion theorem. Convolution theorem.

Unit- 3

Laplace transform- Definition and its properties. Rules of manipulation. Laplace transform of

derivatives and integrals. Properties of inverse Laplace transform. Convolution theorem.

Unit- 4

Complex inversion formula. Infinite Hankel transform- Definition and elementary properties. Hankel

transform of derivatives. Inversion theorem. Parse val Theorem.

MAT E02: Integral Equations

Unit -1

Linear integral equations- Definition and classification. Conversion of initiaJ and boundary value

problems to an integral equation. Eigen values and Eigen functions. Solution of homogeneous and

genera! Fredholm integral equations of second kind with separable kernels.

Unit- 2

Solution of F dh 1 d re om an Volterra integral equations of second kind by m th ~- f .

SUb ftu( d e 0~ 0 SUCCeSSIVe s I wns an successive approximations. Resolvent kernel and its results.

Conditions of unifonn convergence and uniqueness of series solution.

Unit- 3

Integral equations with s t · k 1 ymme nc ern~ s- Orthogonal system of funct" · F d . f . . 10ns. un amental properties

o eJgen_values and eJgen functions for symmetric kernels. Expansion in eigenfunctions and bilinear

f~nn. Hilbert-Schmidt theorem. Solution of Fredholm integral equations of s~cond kind b . Htlbert~Schmidt theorem. Y us1ng

Unit- 4

Solution of V It · o erra mtegral equations of second kind with convolution

transform. Solution of singular integral equations by Fourier transfoml. type kernels by Laplace

Classical Fredholm theory- Fredholm theorems.

kind by using Fredholm first theorem. Solution of Fredholm integral equation of second

34

MAT Jill: Numerical Analysis- I

Unit- I

Iterative methods- Theory of iteration method, Acceleration of the convergence, Chebyshev method,

Muler's method, Methods for multiple and complex roots.

Unit- 2

Newton-Raphson method for simultaneous equations, Convergence of iteration process in the case of

several unknowns. Solution of polynomial equations- Polynomial equation, Real and complex roots,

Synthetic division, the Birge-Vi eta, Bairstow and Graeffe's root squaring method.

Unit- 3

System of simultaneous Equations (Linear)- Direct method, Method of determinant, Gauss-Jordan,

LU-Factorizations-Doolitte's, Crout's and Cholesky's. Partition method. Relaxation methods.

Unit- 4

Eigenvalue problems- Basic properties of eigenvalues and eigen vector, Power methods, Method for

finding all eigenvalues of a matrix. Jacobi, Givens' and Rutishauser method. Complex eigenvalues.

Singhania University

M.Phil (Mathematics)

Svllabus & Examination Rule

Paper Code

1 Max. Mark · Min.llfarks

i Times j

I Course

' -\ MPH ' 801 '

3hrs. Research Methodology 100 40

MPH 3hrs. i I

Jhrs. I I '

I 3hrs.

Generalized Hypergeometic IO~t' 40 ~- 802 Function & Fractional C.alculus

MPH Relativistic Cosmology&--JoO - 40 803 Differential Forms. L ____ ___ --:-=----+-=:---1

I ' - i ; f--MP~~H;-+----~Dissertation 1 00 I 40

'

~~ Opernti on Research I' I 00 : 40

805 I I ···--'

Note:-

L A student is required-to score 50 per cent marks in aggregate in order to pass the themy examination. Pass mars in the 1ndividual course is 40 per cent as explained above.

2. Thus, there will be 400 marks for theory examination of which a candidate is required to score minimum of 200 marks in order to pass the theory examination.

3. Candidate has to opt any three paper.

4. In addition to the three paper, each candidate has to submit a dissertation (based upon the papers ·opted by the candidates in M. Sc./ M.Phil. Course equal to a paper earring !00 marks)

5. There will be eight question in each theory paper. Two question will be set from each unit candidates are required to attempt five question in all taking one question from each unit. All question carry equal marie

, ,

/ Paper-! RESEARCH MATHODOLOGY

Maximum Marks:IOO Time Allowed: 3Hrs.

Unit-1

Introduction: Concept.of research and its appliC3t.ion. Survey of literature Process of

research: Steps involved in research process, various methods of research design.

Unit-11

Data collection through experimental techniques and theoretical calculations. Types of data

and various methods of data collection and compilation.

Unit-Ill

Analysis and interpretation of data obtained: coding, editing and tabulation of data various

kinds of charts and diagnims use in data analysis. Application of statistical techniques for

analy;cing the data. Application of analysis -of variance (ANOVA). Uses of data analysis

tools like SPSS and Excel.

Unit-JV

]'reparation of Dissertation: Types and layout of research, precautions in preparing the

research Dissertations. Bibliography and annexure discussion of results, Drawing conclusion. Giving suggestions and Recommendations to the concemed persons.

Maximum Marks:l 00 Time Allowed: 31-lrs.

Unit-.1

Generali:a:d hypergeometric function- Definition, Convergence of the series for pFq,

Differential equation and its solution. Contiguous function relations. Saalschutz's theorem. Whipple's theorem. Dixon's TI1corcm. Contour integral representation forpfq,. Eulerian type involving pfq,. Integrdi representation for pFq,.

Unit-U

Meijer's G-function-Definition, Elementary properties. Multiplication formulas. Derivatives Recurrence relations. Mellin and Laplace transforms oftl>e G-function.

Unit-HI

H-function of one variable-Definition. Identities. Special cases. Differentiation funnulas.

Recurrence and contiguous function relations. Finite and infinite series. Fourier sedcs for the H-.ftmction. Simple finite and infinite integrals involving the H-function.

Unit-IV

Fractional Calculus -Definition and elementary prope1ties of Riemann- Liouville fractional integrals and derivatives. Derivatives of the fractional integral and the fractional

integral of derivatives. Leibniz's formula for fractional integral and fractional derivatives. Law of exponents. Images of elementary and generalized hypergometric function under

fractional integrals and derivatives.

/ Paper-III Relativistic Cosmology and Differential forms

Maximum Marks:! 00 Time Allowed: 3 Hrs.

Unit-!

Lie derivative of a Tensor field~ Scalar function, Contravariant and covariant vectors,

Covariant tensor of rd!lk two, Symmetry and killing equations, Integrability of killing equation, Geodesic deviatio~ ConfonnaJ cun,ature tensor, its properties, Algebraic classification ,;f conformal curvature tensor.

Unit-II

Basic equations of isotropic cosmo1ogy~ singularity and Singularities in isotropic models, Red shift in non- static fonn of de-sitter universe, Einstein-space, Cosmological principal, Godel universe and it properties.

Unit-III

Non-static cosmological models, Robertson- Walker model and its derivation and Geometrical properties, Frcdmrum- Robert.<OJl- Walker model and its scale factor, Tbrcc different forms of scale fnctor, Doppler effect in Robertson- walker model, Horizons (Event

and Particle), Big Bang Theory, Steady steady state theory.

Unit- IV

Brans- Dicke theory as an alternative theory of gravitation, Derivation of its field equation and solution based on Brans- Dicke Theory. Differential forms: Exterior differentiation, Connection 1-from. Ricci Rotation coefficients, Cartan's equation of structure, Calculation of Riemann Cmvature Tensor using Differential forms, Curvature 2 from for Vaidya metric.

----- -- -- ---------

Papcr-IV: Operation Research

Maximum Marks:JOO Time Allowed :3 Hrs.

Unit-I

Transportation Models- Mathematical fonnulation, Initial basic feasible solution, Initial basic feasible solution, Optimality test, Transportation algorithm for minimization problem, Degeneracy in transportation problems, Unbalanced transportation problem.

Integer Linear Programming:- Definition, Gomory's cutting plane mcthed, Branch and Bound method, Application ofintegt-r progrdJJlming

Unit-II

Theory of Games- Basic defmitions, Saddle point' Optimal stmtcgies and the value of game. Fundamental theorem of game theory. 2x2 games without saddle point. Graphical mcbod for 2xn and mx2 games. Dynamic Programming models -Definition, Bellman's principle of optimaliry, Minimum path problem, Single additive constrain~

MuHiplicatively and additively separable return, sin_glc muWplicative constraint,

Additively separable return, System involving more than one constraint. Application in production, inventory control, Linear programming and reliability.

Unit-ill

Inventory Models- Definition, elemen~1ry inventory models e.g. EOQ model without and with shortages and EOQ with constraints.

Replacement and Reliability Models- Replacement of items that deteriorate,

Replacement of items that fail completely and other replacement problems.

Unit-IV

Queuing Theory- Definition, Queuing system. Arrival. Distribution theorem,

Dislribution of departures, P-robabilistic queuing- models 1 to IX; Mixed queuing models­Model X; Deterministic queuing model- Xl.

......... 1

ENCINf.ERING CHE!VJ!STRY-J ['106]

Clas.s s:·~fech. 151 Semester Evaluation . Schedule per week

Lectures Tutorial

-------Examination Time - Three (3) Hour~;

2 / Maxrrnum 1,1a·ks = 100 _l ___________ i_[Mrd-rerrn (!0'• -& End-ler m (80)]

' ------------------------·----tfrli!s Ic-ontents of the s~~----1j Water

Corr1mC!n I mpuriti~~s of wai:er

li_ H.ardness c-f water: Determinaiion of hardness b_y Clark's test and cmnple:·;

metric (EDTA) method, Degree of hardness Numerical b.ised on hardness and EDTA m~thod

I Municipal \Vater Supply: Requisites of drinking vvater, Steps involved 111

. purification •)f warer, Sedimentation. coagulation, Filtration and Sterilization, ! Break _point <:hlorination 1 ·water Tre:.ttmeut

• ~:ofteniDg of water: Limt-Soda Method, Pemrutit (Zeolite) Method and Deionization or Demineralization i\1ethod -I II . ,_

[ __ j 8 Boiler troubles their causes, disadvantages and prevention: :Formation o~:·sr.::lid:;

(Scale and Sludge;, Carry O'ler (Priming :md Foaming), Corrosion and Causti: Fmbriltleme'lt

• 1--'umerical problerr.s based on Lime-Soda and Zeolite softening method>

I ; =-~----

! Polyme·r~iff.~rent mer:hods )f classifi-cation and constituents c.f polymers

IV

'

i

.. PlasTic:;: Themosets and Thennopla;;;ts • Preparation. Properties and uses ofpolyehylene, Bakelite, T-~!J-Iene <rnd N\ ·QI

El'"'torr.ers -- c'iatural rubber, \'Uicanizariou, Synthetic Rubber:; ; iz. J:;una-:<­Buna-\J~ Butyl and neoprer11.:: rubbers

I Cement -------1 i i

; ! Glass I

r I

I

Definition, Cor_1position_ ba~.ic constituents and their Manu!'acturing of ?orrland eement by Ro'ary Kiln Technology

.. Chemistry of setting and hard·:ming of cement and role- of gypsum

·Definition, Properties, Manut:1cturing of glass ·Types of silicate glasses and the:ir commeccial uses • Irnpl)rtance ofannt·aling in glass: making

significar. :::,

Refractorilcs " Detlnition. classification, pnJperries, .~equi:>ites of goc·d refractor) and

manufilduring o:f re fracto~/ • Det~ikd study of silica and fire clay retractcry and thc,ir u>es • Seg,,r':' {Pyrometri.;) Cone Tesr and RUL Test

V Lubricants ~ Introd~lction, classifi~:atioJI ond uses c.f lubri(:.ants. • Types of lubrication.

( •· Viscosity & vi~;eo:;ity index. flash and tire poiJTJ, cloud and pour poim, :;·-:earn

-~--l _____ er:m~~-~:cat~·n nwr~~r, pre:~~':ltiOJ:-~::ber cu~~~~ neu~rali7~~on number·----~-- J

ENGINEERING CHEMISTRY LAB-I [1 08]

Class B. Tech. 15 Semester 1 Evaluation Schedule per week

Practical 2 I Maximum Marks- 50 [Sessional (30) & Practical (20)]

----· I S.No. I List of Ex~eriments

(Any 7 experiments are to be performed)

1. To determine the hardness of water by HCL method. -

2. To determine the hardness of water by EDTA method.

' Determination of C02 in a water sample. ~-

4. To determine free chlorine in a gtven water sample.

5. I To determine the •;iscosity of a given lubricating oil by Redwood VISCOmeter. --

6. Measurement of residual chlorine in water.

7. To determine the tlash and fire point of a given lubricating oil.

8. / Measurement of dissolves oxygen in water. J '

L 9. To determine cloud and pour point of a given oil.

j I 10 .. Measuremeno of nitrate in water

.

-

• ENGINEERING CHIEMISTRY-11 [206]

Semes.ter I Evaluation · ::J ~~ Examination i ime. = Three (3) HourS

I Class B. Tech. 2""

L eperweek Lectures Tutorial

2 1

Maximum Macks~ 100 I [Mid-term (20) & End-term (80)]

~~-,.~~~~~~~---------------------------------. Units I Contents of the Sub'ect

Fuels (General Aspects) .. Organic ?uels: Origin, classification and general aspec1:s of organic fuels

Solid fuels: CoaL carbonization of coal: manufacturing of coke. by Beehive oven and Ely p:-oduct 0\·en method.

I Liquid fuels: Advantages and refining of pen·oleum. Cracking. refining. reforming,

I polymerization and isomeriza.1ion of refinery products Synrhe1ic perrol( Coal to Liquid. CTL. Tee/moJo&~'): Berguis and Fischer Tmpsch

.. j process

L·/-. · .. Knocki:lg, octane number and anti-knocking agents •· Gaseous fuels: Advantages, manufacturing, (;omposition and calorific value

I eas and oil gas.

I I' Ftlels (Analyses)

:Jf coa~,

~Ultimate and proximate analysis of coal. • De1e:_-mmaDOJi o: sol,d and g_a~'f.'(IU; fuels by bomb and Junker"s Calonme:-er

1 II I re<pectlVel)'

-

Ill

v

• Calculatnns of calorific value based on Dulong s fom!Ll)a • Combustion and requirement of oxygen/ air in combusrio. n process. •· Flue f!a~~ anaLvsis bv Orsar's apparatus and its si~'Ilificance.

se Rule

• •· STatement. Definition and mecmlng ofthe rem1s involved • Application to one component ~.ysltm: V./ater and Sulphur :.ystems

• Reduced ?hase Rule and study (lf!'..vo components Ag-Pb, Bi-Cd systems also i~s-

indus-.:ria. application. ·

f New Engineer-ing Materials J i FuJJere-nes: Introduction, properties. preparation and uses. i Superconductors: ln:roduction, prcperties, preparation and uses .

1

_. Organic Electronic Materials (ir:cluding cc·nducting polymers- poly(r•-pheJJyJene::, polythiophent-:s .. Polyphenylen~·. vinylenes, polypyroles, poJyanili:1e). ,__,H .. , ... _,, j

/ Optica: fires: .[ntrociuction, :roperjes, preparation, optieal fiber grade glass an~

I Corrosion j l Definition and its si!!nificance

corrasio:r

l

j Protection from conosion: Protcct1ve coanngs_ cath·JdJc protectJOn. sacJJficJa) anode and rnc1dificaxion in designs etc

II •· Mechc..nisms of corrosion Ch(~mJcal(DryJ corros1on and ElectroclJemJc:tl(\~'elj

__ l ·----·--

• ENGINEERING CHEMISTRY LAB-II [208]

Class B. Tech. 2" Semester l Evaruation Schedule per week

Practical 2 I, Maximum Maiks- 50

[Sessional (30) & Practical (20)L

S.No. List of Experiments

(Any 7 experiments are to be pel"formed)

I. Proximate analysis ofscdid fuel.

2. I Experiments based on Bomb Calorimeter.

3. Measuremen' of pH of & given sample by pH-merer.

4. Measurement of conductivity of a given sample by conductivity meter.

5. Measurement of fluoride in water.

6. To determine the strength ofCuS04 solution with the help of hypo solution.

7. ··- To determine the strength of ferrous Ammonium sulphate solution with the help of K2Cr20, solutio;!.

8. Determination ofNa/K/Ca by flame photometer in a given sample.

9. To determine the strength ofNaOH and Na2C03 in a given alkali mixture.

I 0. Detem1ination of barium as barium .sulphate ,gravimerricaJJy. I

-

·:$~);·

··--·~~:

ENGINEERING CHE'111STRY-I --co\s:\.o1i~H .Ist "8"'

r . 1• .Sem,.ster eaule per week

[1 06]

1 Evaluotior.

Lectur€i\: ,_ 2 Tulonal ~---

i Exar:-!inatic:'~ ---=-.~~T- :! = Three (3) Hours ) !·~axitnU:!l F.'la:kE:..: JOO

.. _____ .LlMid-l,.rm (10'· & E~o:.o--"te'-'r"-m'-'(-"8"-0u_'-------..1 c-~- -

W!I!its.'-· _.,..~---:':C:':o"'n"te=cnccts=..oocfc..toohccec..S=uccbJc. e"c"t __ j ! Water

Cor:,mon Jrnpuriti\~S of water 1-!arom:ss of w<eler: Determina:JOn o;' ha.·dness bv Clark's rest and complex lll".''"ic (EDTA) nc<thod, Degree ofharcwso ··;;rneri~al based -:n hardness and F.DTA method fv1ur~ici,;al \Vater Supply: Re·~uis~,:es o-_~ drinking water~ Steps involved in

i puriric-atii)l: .Jf wa;:er, Sedirnentation., c.r:'.i_guJation, Filtration and Sterilization _ _____ L__ bre;~roinr chlori;Jation

~>V::::ter T•·eatnH.~nt

• ~:m'lening of w2.1er: Lim<;-So:Jc, Merhod, Pennutil (Zeolite) Method and fleion i;:ation 01 Deminen-:1 izc.1ion Method

•· E::iie:r :roubles rhe·,r causes, disc.dvcmtage.:; and prevention: Formation o·.:·soiids (S-:·:·lL ::md Sludge;, Carry over ~~Priming and Foaming), Co:·~~osion and Ca.usti:: E.rnLrit1\eme:.1t

L.-~~

•· Numeri"al problen'5 based e-n Lime-Soda and Zeolite softening methods

I I

Poi;,'mers ·Different methods )fclas,iiication and constituents of polymers •· Piasjco: Themosers and Thennoplasts

i

L

.. Preparation. Prc-perries and uses ofpolyet'Jylene, Bakelite, Terylene and Nvlon Elastorr,ers -- 'la1Ural rubbn \'ulcanization, Synthetic Rubbers viz. E:una-S, buna-~~' Butyl ancl neoprene: rubbers

I I

1 Cement Definition, C.)Jtlposition, ba~ic constituents 2.nd their s1gnificanc:,

]\.1anuf3cturing of~:>c~rtland cement by Ro·~ary Kiln Technology •· Chemi~:lTJ-' of sening and hard~ning 01~ (:ement and r·)k of gyps urn

1 IV : Glass · •· Deflnir.ion, Properties, Manttfacturing of gla.ss

L "Types u·f siiicate glasses and their commecial uses . ··Jmportance ofanm:aling i~1 glas~ making

---' -----:---·-'''{'' ! Refractories

. -~ ·· De:lnition, dassd~~-ation~ pnJpen:i.t~S: ·~equisltes nf good refracwry a.nd

I i I

r:-JanuLi·~turing a·:·: ehactor_:·· •· Detc..iled s.rudy ofs lic:a and fire day refraGtcry and"/]"";.-~:~:· uses .. Se.ge.i:C~ :Pyrome1ri,~) Com~ Test and RUL Test

V Lu ~;ric~mts " Ir:troduction, clc,.£.sifr.::a1io~·: <::nd uses c.f lubri1::ants:. •· Types 0 f lubricalion . .. Viscostt:,: &.viscosity indc·x .. flash .:.nd fire p;)int, c.ioud and pour point, .:;·:eam

emu!sificaticn number, precipiratior! number and neutrali.z.a~1or ;lumber : L ...... ______ , ____________ -----· ____ .... _________ _ .. _______________ , __ . I

I'

ENGINEERING CHEMISTRY LAB-I . • 111 T.'SI St:IV'

Class 8. Tea h. 1 s Semeste1· ' Evaluation

I Schedule per week Practical 2

Maximum Marks = 50 Sessional (30 & Practical (20)

--~-·

S.No. List of Experiments

(Any 7 experiments are to be performed)

1. To determine the hardness of water by HCL method.

2. To determine the hardness of water by EDTA method.

- Determination of C02 in a water sample. .0.

4. To determine free chlorine in a gi·ven water sample.

5. To determine the viscosity of a given lubricating oil by Redwood viscometer.

6. Measurement of residual chlorine in water.

7. To detennine the tlash and fire point of a given lubricating oiL

8. Measuremenr of dissolves ox:.rgen in \Vater.

I~ 9. j To determine cloud and pour point of a given oiL

I 10. - I Measure~en• of nitrate in water

-

-

[1 08]

_j

Schedule per week Lectures 2 Tutorial 1

[206]

-1 Evaluation ::J Examination Time = Three (3) Hours Maximum Marks= 100 Mid-term (20'> & End-term (80))

~U~n~it~s~~c~·o~n~t~e~n~~~o~f~t~h~e~S~u~b~i·~,e~ct~---------------------------------------------------

I~

II

Fuels (General Aspects) •· Organic ~els: Origin, classification and general aspeciS of organic fuels

Solid fuels: Coal, carbonization of coal, manufacturing of coke by Beehive oven and By p:-oduct O\'en method.

•· Liquid fuels: Advantages and refining of pen·oleum. Cracking, refining, ref.:mning., p-olymerization and isomerization of refinery producEs Synthedc petrol( Coal to Liquid, CTL, TechnJlog}'): Berguis .md Fisc.her Tropsci1

j process ---· ~ Knocking, octane number and anti-knocking agents j ~ Gaseous fuels: Advantages, mamdacturing. o::omposition and calorific value / !BS and oil 2as

i Fuels (Analyses) ·"----. ----

/ .. Ultimat~ and proximate analysis of coaL / •· Dere:-mination of solid and e.asf.c•u:; fuels b1· bomb and Junker's Calorimeter I

~ ~

respectively. .. Calculat.i~ns of calorific value based on Dulong's formula.

, •· Combustion and requirement of o.xygen/ air in combustion process. f.-------..J..i _____ •. _ F._,lu:ce~gas"'·'-"ane.a,_,~sis by Orsat's apparatus and its si!!Dific.ance. --

Phase Rule •· Si.atement, Definition and m~aninf; oftht ten11s involved

ill • Applice;.tion to one component :::.ystem: \l/arer and Sulphur systems • Rt:duced .?hase Rule and study of two cornpont:JES Ag-Pb, B1-Cd !-:ysterns aJso 11s

,i~~~~~i~n~d~u~srn"-·~·a~.~a~p~p:cl~ic~a~ti"o~n~.-----------------------------------

1-·, -·----

!.· New Engineering Materials

I I,. Fullerenes: Introduction, properties, preparatiou and uses.

Superc.onductors: ln:roduction, properties, preparation and uses • IV ' ' Organic Electronic Materials <)r:cluding cc-nducting polymers- pnly(p-rheJtyJene.~., r· polythiophenes. Po!yphen:ylen~: vinylenes, poJypyroles, poJyaniline).

I Optica·. fires: lmroriuction., proper-;ies, preparation, optical fiber grade glass and uses.

/ Corrosion

v

I Definition and its si!!nificance I · Mech~nisms of C(~rrosion: Chemicai(Dry) corrosion and Elecrro_chernic:~I(Wet)

corrosion ~ Prowction from conosion: Protective coarings, cath·:dic protection, sC~crificiaJ anode and modification in je-signs el"c.

·----- ----------------· .

ENGINEERING CH!j:l\11STRY LAB-II - \12i.vm/\..'l..l'Gj Class l!t:&Gh. znd Semester

[208]

Schedule per week Practical 2

S.No. List of Exoeriments

(Any 7 experiments are to be performed)

I. Proximate analysis of solid fuel.

0 Experiments based on Bomb Calorimeler.

I 3. Measuremen' of pH of" given sample by pH-merer.

4. Measuremem of conductivity of a given sample by conductivity merer.

5. Measurement of fluoride in water.

I L6 To determine the strengi:h of C uS04 solutiOJJ with the help of hypo solution.

- 7. .. - I To delennine the strengt.h of Ferrous Ammonium sulphate solution with the help ofK2Cr20 7 solution.

8. Determination ofNa!K!Ca by flame photometer in a given sample. I 9. To determine the strength ofNaOH and Na2C03 in a given alkali mixtme. I 10. Determination of barium as barium sulphate gravimetrically. I

-

-

:1

0 ~

B.Sc. Part-1, Syllabus I 1

B. Sc. PART-I UNIFIED SYLLABUS

CHEMISTRY Paper I: Inorganic Chemistry M.M.:SO,

Unit -I : (I) Atomic Struture : Idea ofde-Broglie matter waves, Heiseliberg uncertainty principle, atomic orbitals, Schrodinger wave equation; significance of ljl and 1j12, quantum numbers, radial and aqgular wave functions and

, probability distribution curves, shapes of s, p, d, orbitals, Aufbau and Pauli exclusion, principles, Hund's multiplicity rule, Electronic configurations of die elements effective nuclear charge. ·

(II) Periodic Properties : Atomic and ionic radii, ionization energy, electron affinity and electronegativity-definition, methods of determination or evaluation · !rands in periodic table and applications in predicting and explaining the chemical behaviour.

Unit-II: (III) Chemical Bonding: (A) Covalent Bond-Valence bond. theory and its limitations directional characteristics of covalent bond, various types of hybridization and shapes of simple inorganic molecules ·and ions, valence shall electron pair repulsion (VSEPR) theory to NH,, H,o+, SF., CiF ,, ICI,- and H,O, MO theory, homonuclear and heteronuclear (Co and· NO) diatomic molecules, multicenter bonding in electron deficient molecules, bond strength and bond energy percentage ionic character from dipole moment and electro-negativity difference.

{B)Ionic Solids-Ionic structures radius ratio effect and coordination number, limitation of radius ratio rule, lattice defects semiconductorS, lattice energy and Bron-haber cycle, salvation energy and solubility of ionic solids polarizing power and polarisability of ions Fajan's rule, Metallic bondCfree electron valence bond and band theories.

(C) Weak Interactions--Hydrogen bonding, Vander Waals forces. Unit-III.: (IV) s-Biock·Elements : Comparative study, diagonal

relationship, salient features ofhydrides, solvation and complexation tendencies including their function in biosystems, an intJ:oduction to alkyls and aryls.

(V) Chemistry of Noble Gasses: Chemical properties of the noble gases, chemistry of xenon, structure and bonding in. "@.On 'compounds.

Unit-N: (VI) p-Biock Elements : Companuiv'estudy (including diagonal relationship) of groups 13-17 elements, compounds like hydrides, oxides, oryacids and halides ofgroup 13-16, hydrides ofboron"diborane and higher boranes, borazine, borohydrides, fullerenc.es, .carbides, fluorocarbons, silicates (structural principle), tetrasulphur tetra nitride basic properties of halgoens, interhalogens and polyhalides.

I I

I I

I '

I

l l.

i l

2 B.Sc. Part-1, Syllabus

Paper II: Organic Chemistry M. M.: so Unit-I: (I) Structure and Bonding : Hybridization, bond lengths and

bond angles, energy, localized and de localized chemical bonding, van der Waals interactions, inclusion compounds, clatherates, charge transfer. complexes, resonances, hyperconjugation, aroillaticity, inductive and field effects, hydrogen bonding.

(II) Mechanism of Organic Reactions: Curved arrow notation, drawing electron movements with· allows half-headed and double-headed arrows, homolytic and heterolytic bond fission. Types of reagents- electrophiles ans nucleophiles. Types of organic reactions, Energy considerations.

Reactive int~mediates- Carbocations, carbanions; free iadicals, carbenes, arynes and nitrenes (with exarnples).Assigning formal charges on intermediates and other ionic species.

Methods of delermination of reaction mechanism (product analysis intermediates, isotope effects, kinetic and stereochemical studies).

(III) Alkanes and Cycloalkanes : IUPAC nomenclatute ofbranched and unbranched alkanes, the alkyl group, classification of carbon atom in alkanes, Isomerism in alkanes, soutces methods of formation (with special reference to Wurtz reaction, Kolbe reaction, Corey-House reaction and decarboxylation of carboxylic acids), physical properties and chemical reactions of alkanes, Mechanism of free radical halogenation of alkanes : orientation, reactivity and selectivity.

Cycl&alkanes- Nomenclatute, methods of formation, chemical reaction, Baeyer 's strain theory and its limitations. Ring strain in small rings (eye lopropane and cyclobutane ), theory of stain less rings. The case of cyclopropane ring, banana bonds.

Unit-II: (IV) Stereochemistry of Organic Compounds : Concept of isomerism. Types of isomerism;

OPtical isomerism - elements of symmetry, molecular chirality, enantiomers, stereogenic center, optical activity, properties of enant_iomers, chiral and achiral molecules ":ith two stereogenic centers,disasteromers, thteo and erythro diastereomers meso compounds, resolution of enantionmer, inversion, retention and recemization.

Relative and absolute configutation, sequence rules, D & Land R &.S systemS of nomenclatute.

Geometric isomerism - dete_rmination of configuration of geometric isomers, E & Z system of noniencJature, geometric isomerism iri oximes and alicyclic compounds.

Conformational isomerism- conformational analysis of ethane and n­butane; Conformations of cyclohexane, axial and equatorial bonds,. conformation of mono substituted cyclohexane derivaiives, Newman projection and Sawhorse

. I ,. j

B.Sc. Part-1, SyJiabus J 3

fonnulae, Fischer and flving wedge formulae, Difference between configuration ' .

and conformation.

\\ Unit-III: (V)Alkenes, Cycloalkenes, Dienes andAikynes: Nomenclature

of alkenes, methods off ormation, mechanisms of dehydration of alcohols and

dehydrohalogenation of alkyl, halids, regioselectivity in alcohol dehydration.

The saytzeff rule, Hofinann elimination, physical properties aii'd rbtative .

stabilities of alkenes.

Chemical reactions of alkenes- mechanism involved in hydrogenation,

electrophilic and free radical additions\, MArkownikoffs rule,.hydroboration­

oxidation, oxymercuration-reduction. Epoxidation, ozoi10lysis, hydration,

hydroxylation and oxidation with KMno4 Po!ymerization of alkenes, Subsitution

at the allylic and vinylic posi(ions of alkenes, Industrial applications of ethyle!le

and propene.

Methods of formation, conformation and clemical reactions of

cycloalkenes;

Nomeclature and classification of dienes : isolated, :conjugated and

cumulated dienes, Structure of allenes and butadiene, methods of formation,

polymerization, chemical reaction- I ,2 and I, 4, additions, Diels-Aiderreactibn.

Nomenclature, structure and bonding in alkynes, Methods. of forniation,

Chemical reactions of alkynes, acidity of alkynes, Mechanism o(electrophilic

and nucleophilic additimi reaction, hydroboration-oxidatlon, metal-ammonia

reductions, oxidation and polymerization.

Unit-IV : (VI) Arenes and Aromaticity : Nomenclature of benzene

derivatives. The aryl group, Aromatic nucleus and side chain structure. of

benzene; molecular formula and kekule structure, Stability.and:carbon,carbon . ·-·

bond langths of benzene, resonance structure, Mo picture.

Aromaticity :The Huckle rule, aromatic ions.

Aromatic electrophilc substitution- general pattemofthe mechanism; ..

role or cr and 1t complexes, Mechanism of nitration, halogenation; .sulphonatioit,, .

mercuration ~'d Friedel -Crafts reaction.·Energy profile diagrams·. Activating·

and deactivating substituents, orientation and ortho/para ratio; Side chain

reaction of benzene derivatives, Birch reduction; Methods of formation and chemical reactions of alkylbenzenes,

alkynylbenzenes and anthracene;

(VII) Alkyl and Aryl Halides: Nomenclature and·classes of alkyl halides,

methods of formation, chemical reactions Mechanisms ofnucleophilic substitution

reactions of alkyl halides, SN' and SN' reactions withene;gyprofile diagr~;

4 1 B.Sc. Part-.!, Syllabus

Polyhalogen compounds: Chloroform, carbon telrachloride;

Methods of formation ofaryl halides, nuclear and side chain reactions;

The additio11-elirnination and the elimination-addition m€:chanisms of nue-leophic aromatic substitution reactions;

Relative reactivities a alkyl halides vs allyl, vingl and aryl halides,

Synthesis and uses of DDT and BHC.

* ~'3tl<itrit~ i6J<ff.lq; ~

Paper-III :Physical Chemistry M.M.i50

Unit-!: (I) Mathematical concepts and Computers: (A) Mathematical concepts : Logarithmic relations, curve, sketching

linear graphs and calculation of slopes, differentation of functions like Kx, e', X', Sin X, log X; maxima and minima, partial differentitation and reciprocity relations, Integration of some usefuVrelevant functions; permutations and conbinations, Factorials, rrobability.

(B) Computers : General introduction to computers, different components of a computer, hardware and software, input-output devices, binary numbers and arithmetic's introduction to computer languages, programming, operating systems.

Unit-II : (II) Gaseous States : Postulates of kinetic theory of gases, deviation from ideal behavior, Vander Waals equation of state;

Critical Phenomena: PV isotherms of real gases, continuity of states, the isotherms of Vander Waals equation, relationship between critical constants and vander Waals constants, the law of corressponding states, reduced equation of state.

Molecular velocities : Root mean square, average and most probable velocities, Qualitative discussion of the Maxwell's distribution of molecular velocities, collision number, mean free path and collision diameter, liquification of gases (based on Joule- Thomson effect).

(III) Liquid State: Intermolecular forces, structure ofliquids (a qualitative description). . .

Structural differences between solids, Liquids· and gases; Liquid crystals : Difference between liquid crystal, solid and liquid,

classification, structure of nematic and cholestric phases, Thermography and seven segment cells.

Unit-III: (IV) Solid States: Defmition of space lattice, unit cell; Laws ofcrystallography-{i) Law of constancy ofinterfacial angles, (il,

Law of rationality of indices (iii) Law of symmetry, Symmetry_ elements in. crystals.

(

: I '

j

i ' ' ' i

RSc. Part-1, Syllabus I 5 ·

X-raydilfraction by crystals, Derivation of Bragg equation, Determination of crystal structure ofNacl, KCI and CsCI (Laue's method and power method).

· (V) Colloidal States : Definition of colloids; classification of colloids; Solids in liquids (sols): properties-Kinetic, optical and electrical; stability

of colloids protective action Hardy-Schulze law, gold number. Liquids in liquids (emulsions): types of emulsions preparation, Emu)sifier, Liquids in solids (gels) : classification, preparation and properties,

inhibition, general application of colloids, colloidal electrolytes. Unit-IV: (VI) Chemical Kinetics and Catalysis: Chemical kinetics and

· its scope, rate of a reaction,. factors influencing. the rate of a reaction.­coilcentration, temperature, pressure, solvent, light catalyst, -concentration dependence of rates, mathematical characteristics of simple chemical reactions -zero order, first order, second.order, pseudo order, half life and mean life, Determination of the order of reaction - differential method, method· of integration, method ofhalf life period and isolation method.

Radioactive decay as a first order phenomenon; Experimental methods of chemical kinetics; conductometic

potentiometric, optical methods, polarimetry and spectrophoto-meter. Theories of chemical kinetics :effect of temperature on rateofreaction,

Arrhenius equations, concept of activation energy. • · Simple collision theory based on hard sphere model, transition -state

theory (equilibrium hypothesis), Expression for the rate constant based on equilibrium constant and thermodynamic aspects.

Catalysis characteristics of catalysed reactions classification of catalysis . homogeneous and· heterogeneous catalysis, enzytne catalysis, miscellanceous examples.

Practical Inorganic Chemistry: Semi micro Analysis -cationanalysisseparation

and identification of ions from Groops I, II, III, IV, V and VI Anion analysis. · Organic Chemistry: Laboratory techniques: Calibration of Thermometer : 80-82° (Naphthalene),ll3:5~114°

(Acetanilide) 132.5,133° (Urea), 1000 (Distilled Water) Determination of melting point: Naphthalene 80-82°· Benzoic acid 12 1.5-122° Urea 132.5 -133°· Succinic acid 184.5-185° Cinnamic acid 132.5-133°, Sallicylicacid 157.5-158° Acetanilide 113.5-114° m-Dinitrodenzene 90° p-Dichlorobenzene 52°, Aspiriill35°

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6 I B.Sc. Part-!, Syllabus

Determination ofboiling point: Ethanol78°, Cyclohexane, 81.4°, Toluem ll 0.6°, Benzene 80°

Mixed melting point determination : Urea-Cinnamic acid mixture o· various compositions (I :4, L l, 4: l)

Distillation : Simple distillation of ethanol-water mixture using wateJ condenser, Distillation of nitrobenzene and aniline using air condenser.

Crystallization: Concept of induction of crystallization, Phthalic acid from hot water (using fluted filter paper and stemless funnel) Acetanilide from boiling water Naphth•lene from ethanol Benzoic acid from water Decolorisation and crystallization using charcoal : Decolorsation of

brown sugar (sucrose) with animal charcoal using gravity filtration. Crystallization and decolorisation ofimpure naphthalene l OOg of napthalene

mixes with 0.3 g of Congo Red using I g decolorizing carbon) from ethanol. Sublimation (Siple and Vacuum): Camphor, Naphta-Jene,Phthalic acid

and succinic acid. Qualitative Analysis: Detection of extra elements (N, Sand halogc:IS)

and functions groups (phenolic, carboxylic, carbonyl, esters, carbohydrates, amines, amides. nitro and anilide) in simPle. organic compounds.

Physical Chemistry Chemical Kinetics:

I. To determine the specific reaction rate of the hydrolysis of methylacetate/ ethy acetate catalyzed by hydrogen ions at rooms temperature.

2 To study the effect of acid strenght on the hydrolysis of an ester. 3. To compare the strengths ofHCI and H2S04 by studying the kinetice of

hydrolsis of ethyl acetate. 4. To study kinetically the reaction rate of decomposition of iodide by

H,O,. Distribution Law:

l. To study the distribution of iodine between water and CCI4•

2 To study the distribution of benzoic acid between benzene and water. Colloids:

I. To prepare arsenious sulphide sol and compare the precipitating power of mono-bi and crivalent anions. Viscosity, surface Tension:

I. To determine the percentage composition of a given mixture (non interacting systems) by viscosity method.

2 To determine the viscosity of amyl alcohol in water at different concentratiOn, and calculate the excess viscosity of these sol uti<.

3. To determine the percentage composition of a given binary mixture by surface tension method (acetone & ethyl methyl ketone). ·

/

Bsc Parf-JZ

-----/ !CHEMISTRY I PAPER I : INORGANIC CHE;MISTRY

UNIT-1-(i) Chemistry .of Elements of First Transition Series : Characteristic properties of d-block-elements. Binary compounds (hydrides, carbides and oxides) ofthe elements ofthe first transition series and complexes

· with respect to relative stability oftheir oxidation states, coordination number and geometry. ,

(ii) Chemistry .of -Eiemen.ts of Second. ani! Third n·ansi!ion Series : Oener91 characteristics, coqtparative treatment of Zr/Hf, Nb/Ta, Mo/W in

4 I ll. Sc. l'art-II (Syllabus)

respect of ionic radii, oxidation states, magnetic behavior, spectral properties and stereochemistry. UNIT-II- (iii) Coordination Compounds: Werner's coordination theory and its experimental verification, effective atomic number concept, chelates, nomenclature of coordinatiori compounds, isomerism in coordination compounds, valence bond theory of 'transition metal complexes. UNIT-111-(iv) Chemistry of Lanthanide Elements: Electronic structure, oxidation states and ionic radii and lanthanide contraction, cornple·x fomwtion, occurrence and isolation, eerie ammonium sulphate and its analytical uses. (v) Chemistry of Actinides: Electronic confi(;uration, oxidation states and magnetic properties, chemistJy of separation of Np, Pu and Am from U. UNIT-JV---.-(vi) Oxidutloit and Reduction : Electrode potential, electrochemical series and its applications, Principles involvefi in the extraction of the elements. (vii) Acids and Bases :Arrhenius, Bronsted-Lowry, the Lux-flood! solvent

i system and Lewis concept of acids and bases. I (viii) Non-aqueous Solvents : Physical properties of a ~olvent, types of l solvents and their general characteristics, Reactions in non-aqueous solvents I witlt reference to liquid NH_, and Liquid so2. I PAPER II : ORGANIC CHEMISTRY

I I

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UNIT -1-(i) Electromagnetic Spectrum Absorption Spectra :Ultraviolet (UV) absorption spectroscopy- absorption laws (Beer-Lambert law); molar absroptivity, presentation and analysis of UV ·spectra, types of electronic transitions, effect of conjugation. Concept ofchromophore and auxochrome, Bathochromic, hypsochromic, hyperchromic and hypochromic shifts. U. V. spectra of conjugated enes and en ones. Infrared (l.R.) absorption spectroscopy -molecular vibratiOns, Hook~·s·law, .selection rules, intensity and position ofl..R. bands, measurement ofi.R. spectrum, fingerprint region, characteristic absorptions of various functional groups and interpretation of I.R. spectra of simple organic compounds.

. UNIT -II-(ii) Alcohols : Classification and nomenclature, Monohydric alcohols- nomenclature, methods of fonnation by reduction of Aldehydes, Ketones, Carbqxylic a~;ids and Ester~, Hydrogen bonding;. Acidic nature, Reactions of alcohols. Dihydric alcohols-nomenclature, methods ofl'onnation, ch.emical reactions of vicinal glycols, oxidative cleavage [Pb(0Ac)4 and Hl04] and pinacol- pinacolone rearrangement. Trihydric alcohols­nomenclat.ure, niethods of formation, chemical reactions of glyceroL (iii) Phenols : Nomenclature, structure and bonding, preparation of phenols, physical properties and acidic character, Comparative acidic strengths..oJ alcohols ,1·· ·

1 phenols, .resonance stabilization of phenoxide ion. Reactions

!l. Sc. l'art-11 (Syllabus) I 5

of phenols-electrophilic aromatic substitution, acylation and carboxylation. Mechanisms of Fries rearrangement, C!aisen rearrangement, Gattem1an' syntheis, Hauben-Hoesch reaction, Lederer-M.anasse reaction and Reimer­Tiemann reaction.

UNIT -111-{iv) Ethers and Epoxides: Nomenclature of ethers and methods of their fonnation, physical prope.t1ies, Chemical reactions-cleavage and· autoxidation, Ziesel 's method. Synthesis of epoxides, Acid and base-catalyzed' ring opening of epoxides, orientation of epoxide ring opening, reactions of Grignard and organolithium reagents with epoxides.

(v) Aldehydes and Ketones : Nomenclature and structure of the carbonyl groups, synthesis of aldehydes and ketones with particular reference to the: synthesis of aldehydes from acid chlorides, synthesis of aldehydes and. ketones tJses I, 3-dithianes, synthesis of ketones from nitrites and from: carboxylic acids, Physical properties. Mechanism ofnucleophillic additions: to carbonyl group with particular emphasis on benzoin, aldol, Perkin and i Knoevenagel condensations, Condensation with ammonia and its derivatives. \ \Vittig reaction, Mannich reacti.on. Us(> .)f aceta Is as protecting group, ; Oxidation of aldehydes, Baeyer-Villiger oxidation of Ketones, Cannizzaro : reaction, MPV, Clemmenscn, Wolff~Kishner, LiAIH

4 and NaBI-1

4 reductions.:

Halogenation of enolit.able ketones An introduction to ±, 2 unsaturated ; aldehydes and Ketones. i UNIT-IV-{vi) Carboxylic Acids : Nomenclature, structure and bonding, : physical prope11ies, acidity of carboxylic acids, effects of substituents on; acid strength, Preparation of carboxylic acids, Reactions of carboxylic acids,; Hell-Volhard-Zelinsky reaction, Synthesis of acid chlorides, esters and amides, ; Reduction of carboxylic acids, Mechanism of decarboxylation. Methods of: fofmation and chemical reactions of halo acids, ~-lydroxy acids : malic, ·!

trartaric and citric acids. Methods of forlllation and chemiCal reactions of·' unsaturated monocarboxylic acids. Dicarboxylic acids: methods of formation ! and effect of heat and dehydrating agents. i (vii) Carboxylic Acid Derivatives : Structure and nomenclature of. acid i

chlorides, esters, amides (urea) and acid anyhydrides. Relative stability of, acyl derivatives, Physical Properties, interconversion of acid derivatiyes by I

nucleophilic acyl substitution. Preparation of carboxylic acid derivatives, chemical reaction. Mechanisms of esterificaton and hydrolysis (acidic and ' basic)

(viii) Organic Compounds of Nitrogen : Preparation of nitroalkanes and nitroarenes, Chemical reactions of nitroalkanes. Mechanisms of nuclephi'IC substitution in nitroarenes and their reductions in acidic. neutral and alkaline media, Picric acid. Halonitroarenes: reactivity, Structure and nomenclature of amines, physical properties, Stereochemistry of amines, Separation of a mixture of primary, secondary and tertiary amines. Stmctural features effecting

6, I B. Sc. l'art-Il (Syllauus)

basicity ·Of amines. Amine salts as phase-transfer catalysts, Preparation of alkyl and aryl amines (reduction of nitro compounds, nitrities), reductive amination of aldehydic and ketonic compounds, Gabriel-phthalimide reaction, Hofmann bromamide reaction. Reactions of amines, electrophilic aromatic substituton in atyl amines, ~eactions of amines with nitrous.aci~. Synthetic transfonnations of a1yl diazonium salts, azo c.oupling.

PAPER JI1 : !'HYSICAL CHEMISTRY UN IT-I-{J"hermodynamics & ChemiCal Equilibrium) (i) Thermodynamics - I Definitions of thermodynamic terms : System, surroundings etc. Types of systems, intensive and extensive properties·, State and path functions and their diiTerentials, Thermodynamic processes, concept of heat and work. First Law of Thermodynamics : Statement, definition of internal energy and enthalpy, Heat capacity, heal capacities at constant volume and pressure and their relationship, Joule's law- Joule-Thomson coefficient and inversion temperature. Calculation of w, q, dU &. dH for the expansion of ideal gases under isotheral and adiabatic conditions for reversible process. Thermochemistry : Standard state, standard enthalpy of formation- Hess's Law of heat summation and its applications, Heat of reaction at <:onstant pressure and at constant volume, Enthalpy of neutralization, Bond dissociation energy and its calculation lfom thenno-chemical data, temperature dependence of enthalpy, Kirchhoff's equation UNIT -11-{ii) Chemical Equilibrium: Equilibrium constant and free energy, Thermodynamic derivation of law of mass action, Le Chatelier's principle Rt'action isotherm and reaction isochore -Clapeyron~clausius equation and its applications. (iii) Thcrmodynamics-11 Second Law of Thermodynamics : Need for the law, different statements of the law, Co mot's cycle and its efficiency, Camot's theorem. Thermodynamic . scale of temperature. Concept of entropy : Entropy as a state function, entropy as a function ofV & T, entropy as a function ofP & T, entropy change in physical change, clausius inequality, entropy as a criteria of spontaneity and equilibrium, Equilibrium change in ideal gases and mixing of gases. Gibbs and Helmholtz functions: Gibbs function (G) and Helmhotz function (A) as thermodynamic quantities, A & G ~s criteria for thermodynamic equilibrium and spontaneity, their advantage over entropy change, Variation of·G imd."A with P, V and T. Third Law of Thermodynamics : Nemst heal theorem, statement and concept of residual entropy. Nernst distribution law-thermodynamic derivation, applications.

B. Sc. Part-II (Syllabus) I 7.

UNIT-UI-{Eiectrochemistry - I & Solutions) (iv) Electrochemistry-! : Electrical transport : Conduction in metals and in electrolyte solutions, specific conduCtance molar and equivalent conductance, measurement of.· equivalent conductance, variation ofrno lar equivalent and specific conductance with dilution. Migration of ions and Kohlrausch's Jaw, Arrhenius theory of electrolyte dissociation and its limitations, weak and strong electrolytes,: Ostwald's dilution law its uses and limitations, Debyc-Huckei-Onsager's. equation for strong electrolytes (elementary treannent only), Transport number, definition and determination by Hittorf's method and moving boundary method. Applications of conductivity measurements: detennination of degree · of dissociation, detennination of Ka of acids, detennination of solubility product of a sparingly soluble salt, conductometric titrations. (v) Solutions : Liquid - Liquid mixtures- Ideal liquid mixtures, Raoult's and Henry's law, Nonideal system-azeotropes - HCI-1-120 and ethanol - · water systems. Partially miscible liquids- Phenol- water, trimethylamine­water, nicotine-water systems, Immiscible liquids, steam distillation. UNIT-IV-{Electrochemistry- II & Phase Equilibrium) (vi) Electrochemistry -II :Types of reversible electrodes~ gns-mctal ion, metal-ion, metal insoluble salt-anion and redox electrodes, Electrode reactions, Nemst equation, cterivation of cell E.M.F. and single clectr0~e potential, strandard hydrogen electrode-reference electrodes and their applications, standard electrode potential, sign conventions, electrochemical series and ·its significance. Electrolytic and Galvanic cells-reversible and irreversible cells, conventional representation of electrochemical cells; EMF of a cell and its measurements, Computation of cell EMF, Calculation of them10dynamic quantities of cell reactions ("G, "H and K) Concentration cell with and without transport, liquid junction potential. application of concentration cells, valency ofions, solubility product and activity coefficient, potentiometric titi-ations. Definition of pH and pKa, determination of pH using hydrogen, quinhydrone and glass electrodes, by potentiometric methods; Buffers -Mechanism ofbufferaction, Henderson-Hazel equation, application of buffer solution, Hydrolysis of salts (vii) Phase Equilibrium : Statement and meaning of the temts-phase, component and degree of freedom, derivation of Gibb's phase rule, phase equilibria of one component system-water, 'C02• and 'S' systems Phase equilibria of two component system- solid liquid equilibria simple eutectic - Bi-Cd, Pb-Ag systems, desilverisation of lead. Solid solutions- compound formation with congruent melting point (Mg-Zn) and incongruent melting point, (FeCirHPJ and (CuS04-H20) system

PRACTICALS INORGANIC CHEMISTRY

Calibration of fractional weights, pipettes and burettes, Preparation of standards solutions, Dilution·· 0.1 M to 0.001 M sc Jns.

8 I B. Sc. Part-11 (Syllabus)

Quantitative Analysis : Volumetric Analysis: (a) Detemtination of acetic acid in commercial vinegar using NaOB. (b) Determination of alkali content- antacid tablet using HCI. (c) Estimation of calcium content in chalk as caldum oxalate by pcrmanganometry. (d) Estimation of hardness of water by EDTA. (c) Estimation of ferrdus and ferric by dichromate method. (f) Estimation of

copper using thiosulphate. Gravimetric Analysis : Analysis of Cu as CuSCN and Ni as Ni

(dimethylgioxime). ORGANIC CHEMISTRY

Laboratory Techniques A. Thin Layer Chromatography Detennination ofR/ values and identification of organic compounds; (a) Separation of greenleaf pigments (spinach leaves may be used). (b} Preparation of separation of2, 4-dinitrophenylhydrazones of acetone, 2- butanonc, hexan-2, and 3-one using toluene and light petroleum (40:60) (c) Separation of a mixture of dyes using cyclohexane and ethyl

acetate (8.5:1.5). B. Paper Chromatogrophy :Ascending and Circular Determination of R/ valqes and identification of organic compounds: (a) Separation of a mixture

,,of phenylalanine and glycine, Alanine and aspartic acid, Leucine and glutamic acid. Spray reagent- ninhydrin. (b) Separation of a mixture ofD, L- alanine, glycine, and L-Leucine using nbutanol : acetic acid:water (4:! :5), Spray reagent- ninhydrin. (c) Separation of monosaccharide- a mixture of D· galactose and Dfructose using n-butanol:acetone:water ( 4:5: i ), spray reagent

- an i!ine hydrogen . phthalate.

Qualitative Analysis : ldentificat ion of an organic compound th.rough the functional group analysis, detcnninition of melting point and preparation of suitable derivatives.

PHYSICAL CHEMISTRY

Transition Temperature l. Detemtination of the transition temperature of the given substance by themtometric /dialometric method (e.g. MnC12.4l·lpiSrBr2.2H20).

Phase Equilibrium 2. To study the effect of a solute (e.g. NaCI, succinic acid) on the critical solution temperature of two partially miscible liquids (e.g. phenol-water system) and to detennine the concentration of that so\ute in the given phenol­water system. 3. To construct the phase diagram of two component (e.g. diphenylamine - benzophenone) system by cooling curve method.

Thermochemistry I. To determine the solubility of benzoic acid at different temperatures and to detcnnine "H of the dissolution process. 2. To detennine the enthalpy of neutralization of a weR :id/weflk base versus strong base/strong acid

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B.Sc. Part~fll. Syllabus. · 5.

CHEMISTRY Paper I : Inorganic Chemistry ~

Unit·I: Hard and Soft Acids and Bases (ii:SAB) : Classification of acids and· bases as hard and soft. Pearson's 'HSAB concept acid-bOse strength and· hardness and -~

, _ softness. Symbiosis, theoretical basis_ Of hai"dness and softneSs,~ei~tron~gativi~Y.-~:IQd ·i ·hardness and softness. -. .- _ _ . ·---~ .,- ·. ·. ~ "'"-\ . Metal~Jigand Bonding in 'Iran.Sitio~ Met.:il Complexes _:crJ-mitatiOOS_-Pf y~rerlCe ! , bpnd theory, and elementary idea of cry;;tal~field tJieiJry,.erystal. te(a".:sjiliiivgjp 1: octahedral, tetrahedral and square planner complexes, factors affecting the-t'rystal-j'icid. ! parameters. · ··. ·. · ·- -- · --, · - · -·:· · ·- ·- --:. ·._:: ( ' - Unit-Ii _:MagnetiC Pr<!perties of.Tra.J;~Sition Me~- ~o~ple~_;_J~-of ~~&i-le-#c. -

behaviour, methods of. determining magnetic susceptibility; spin:Only· foOJ)irla;. L..S · .. coupling, correlation Of Jts arid ftef! vaJUCs, orbiultc'ontribiitio~ la.n]agi}etic.riiiQ_iljeO·ts, .- . application of. magnetic mpment data for 3d-¢etai (:Qmpr.,res ... ,,c;' .~., '.;: ·.:: ·.:~;: ,. . .

i' !

. Electro"' Spectra ofTrans1tion Metal Compi~.S':,_lfpe,S ofele<:tioiiic ~~tions, .. ·,. selection rules for d-d transitions~ spectro~scopic- &ro.und_~mi~~s~ s~~qchem~~-~rie;:­Orgel-energy level diagram for d1 and ci9 states, disCUssion of the electroiuc .p;;;u-,;m ~f ..

I rn (rhO )6 ]3 complexion. . .• - . . ' . '' . . . ·J :. · Thermridyri.a_mic and Kinetic Aspe(;ts-bCMetal Complexes: A. brfc!f oilt_liJlC~~flb~ . · -· ..

thermodytiamic stability of metal ~omplexed and factors· affecting-.tbe>.s[abilify, "I 1 substitution reactions of square planer com pi~.· ·. ·. · . . . · · . .' · .. :··'":.~··, , . 1. • Unit-III: Organometallic Chemistry :J)efinition,nomenclature arid'ctil~c3tion

~~-rganometalfic compounds. Preparation, properties, bonding.and applications._ of Is and aryls of U, AI, Hg, ·sn and TI, a brief account of·metal..eth)'fenic complexes

J . homogeneous hydrogenation, manoclear carbonyls and the· nature of bonmnfiri •

I Jf.a~~~~">;lsBio'<lrganic· Cbe~is~.; ~ntia~ ~~. tra:~ ... ~~~~~ ln '~bib;~· r>foCesse5, metalloporphyrins with special reference'ta haemoglobin ;arid' myoglobin;" · .

. , - BiolOgical role oflilkali arid alkalinO'earil!metalions witt('specialrefe~en~to:eaz~. ' Nitrogen fooition. · . · ·. . .· -' · . · . ,- • ·• ·· ··. -. · .. _--. ·~ :•··>: .

. Unit·V·: Sllieones and Phosphazenes: Silicones arid phosphazen.Sas examplc:S'ol ·

inorg::zr:; nature of bonding in tri~hosphazeites.. • . .... ,.., '. . -~ ~r·-.,

I ;q,falR<Ji~ . . . ~~~ . P3perll:.-Org3~~:kChemistry. __ _,~3:'-__ ~--,-~----~, __ :~_-~

· Unit-! :.(a) ,Spectroscopy: U.V.. Spectroscopy. and its appliCation iil .organic· .chc!rnisiry. !.R. · Spe<;troscopy. and. its application in organic chemiStry: N:M:R.. Spectroscopy and its·application in organic chemistry. , .. . . . · ~ .. · ,, . ?rJ Synthetic Dyes: COlour and·constitution (electi:onitcconcept~. Cl3ssincatioi!Of dyes• ChemiStry andsynthesiS-()f Methyf orange; Congo re~,l.{a_lachit~green,,C!JIS!") vtolet; Phenophthalem; Hourescem,Ahzarm.and Indlg,9,:": . . · . . c:/ c.- ,. , . . : ·.: -. :

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· Unit-Il : (a) Organimetallic Compounds : Organomagn'esium compounds ::the .. Grigriard reagents-forinat.iori. structu~e-.. and ·chemical .reaC1_ions:-· Organic compciu~~ ·: ~~ ... '. ~_.:~ formation anctchemjcal reactions. Orgaoolithium compounds: formation and_~hemic31 ··> , .. reactions. _ _ --~-~--

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(b) OrganOS~Jpbur Compounds_: NOmenclatur-e, structu-ral featur~;~~eU:i~.of: ~· formation .and ch,em.ical reaction of tbiols; lhietbers, sufpfi_~nJc- acids, sulphor.!'!'!llide$-. _.· a~d sulphaguanidine .. · .. · . . . · . ·. . ' . . ·'. ·.~ _'.' · Unit'III : (a) Hatel'OC)'Iic Compound dntroductmn : Molecular orbital E'cture

and aromatic characteristics of pyrrole; furan thiophene· ana pyridine, Methods of·

·,.;

6 B.Sc. Part-Ill, Syllabus I 1

synthesis· and chemical react)ons wlth particular emph.1sis on the mechanisin of 1

•! electrophiJic substitution. Mechanism of Nucleophilic _ _substi£ution reactions in-pyridine derivatives. Comparison of basicity of pyridinf?, piperidine and pyrrole.

IntrOduction lO condensed five and six membered heterocycles. Preparation and reactions_of indole1 quinoline and iscquinoline with special reference to F~sher indole !

synthesis, Skraup syhthesis and .Bischler-Napieraiski ·synthesis. Mechanism ~of· }j cJectrophilic substitution reactions of indOle, quinoli~e nnd isoquinoline~ . _ .i

(b) Fats, Oils and Detergents: Natural fats, edible· ancj industrial oils of vegetable ·' origin, common farty acids, glycerides, hydrogenation of unsaturated ·oils. 1!

Saponification vLi.lue, iodine valu~, f.lcid value. Soap.:; syi1thetic detergents, alkyl and aryl !I sulphonates. · . . 11

Unit-IV : Carbohydrates : Classification and nomenclatUre. Monosacch-arides, !! mechanism of isazoQe fornla!ion, intcrconvcrsion of glucose and fructose, chain · 1

' Ienthening and chain shortening of aldoses. ConJiguratlbn of mrinosacch3rides: Eryihro :.l: and rhea dias'tereomers. Conversion of glucose into mannose. Formation of Glycosides, ethers and esters. Derermination_of ring size of mouosaccharidf:s. CycliC's~ructufe of :.·,'1

D( +) glucoSe. Mechanism' of mutarotation. Structure-ofiibose and deoxyribose.· An introduction to disaccharides (maltose,· sucrose· and 13ctose) and U

polysaccharides (Starch and ceJJLil9se without involving structure determination}. ;..) Unit V : Amirio Aci~ Pe(>tides, ·Protein...:;: and Nudk Acids-: Classification, i I

structure and srcreOchemistry of amino aclds. Acid·base beh~viOur, isoelectric point H and electrophorCsis. Preparation and reactions of a·amino acids. · . . · ~ i - Structure -and nomenclature of pep_tides ·and proteins. Classification of pro~7_s; . . )1" Pept.ide structure determination,_ and grou. p analysis, selective_.hydrolysis of peptf pes. . Oa'>.Sical peptide synthesis, solid-phase peptide synthesis. Structures of peptides; ~nd · proteins. Levels of protein structure. Protein.Penarurat~on/renaturation. : ' ;

N~c/ein acids : introduction. Consdtuenls of nucl~ic acids. Ribon. ucleosides--. 00. ,;

1:-.

ribonucleotides. The double helical structure of DNA :~· ;· . (b) Synthetic Polymers : Addition or cbain-groMh polymerization. Free radical \:i

vinyl pofymerization, ionic vinyl polyme~ization, Ziegle~·Narta pO!ymeiisatiCJp. an.~ Vinyl ·~, oolvmers. · . . l · · Condens~!Lon or step .growlh polymerization, POlyesters, Polyamides, phenol, ~ !

i'' formaldchyde_resins, urea formaldehyde resir.s, eposy resigns and pOlyurethanes. ,_·--'N--·a--t--u_r.cal_a_n--d~sy'-n--t_h_et_ic---..ru_b_b'-e_rs_.'--~---------------------, . ·! ;

~~=~ ~~3lirnl j H

Paper III: Physical Chemistry M.M. : 34 .. Unit-1 : Elementary Quantum 1\-fechanics :·Black-body radiation, PJanCWs l ~

radia. tion Jaw, photoelectric effect, heat capacity of-solids .. Bohr's model of bydroge. n ; \ mom (no derJYation) and its defects. Compton etiect. De Broglie hypothesis the · .1 ·1 Heisenberg's uncertainty principle, Schrodinger wave equation, Hamiltonian oper(;!tOr.. l ·l Schrodinger "'ave equation and ilS importance, physical interpretation of the wave. ''I function; postulates of quar_1tum mechanics, particle in one dimensional~ · f-.. 1

Schrodinger wave equation of H·atom. _separ~tion into three equation (\'J'ithout l i derivation), quantum numb~rs ·ai:Jd their importance, hydrogen like wave .functions, j i

. radial wave fu~ctions, angular wave functions. · · \ UnH-II: (a)MoleCular orbital thec:>ry: Basis ideas-<:riteria for forming M.O. from

AO., construction of M.O.'s by LCAO-H2 + ion, calCulation of enetgy levels from wave fuOc!ions, physical picture of bonding and ami bonding wave functions,.concept ofu,_ a•,

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s.sc. i>ari-m,. Syllabus 1 - . . ,·

-n; ;r• _orbitals and their charactefist!cS: Hybrid or~itals:SJf.sP3~ sp3,. ci!J~Iatiod bt coefficients of AO.'s used in lbese--hybi'"id orbitals. ·. ·"".·_~,-~_. ~.- · - · -~

. Introduction to;,.,Jence bond model'ofHz, cOm]iari.sori·lJfM.O. and v.·Ji. models. ·

(b) _Spectroscopy _:_ .I~frodU~'tfa:n. ~-- _EI~omagncti~-~~di~ti~n,- --~egio~ ~bL ihe_ spectrum basic feature of ·_ different- _$pectrometeisj- -statem~nt · , of -Ahi Born-Oppenheimer approximation; cieirees of freedom. ',:-· -~ · _____ : :-__ ,_ -·;' .. ·_ ·

{c). RotatioDaf Spedi-um ·: Pi3t_O~ic_ mf:J.~~Ies~···Enijgy--I~~~:a.~ri~id .rotor_'· _ ·. ('"mH:Iassical ptiriciples), selection _niles, _spectraL intensity, dlsri:ibuiion using -population distributiop (MaxzweU-Bol\ZffilmJl disttibutioil) deterininati9i1 Of bond -length, qualitative description of n_On~iigi9 rotor, ~tqpe· effe¢t.·- . ··.· ... ·. · ... · ... · .. ~ : ·: · ·

. Unit-lll: (a) Vibrntiond! Specirum_; II!f~ared spectr~t.i: EiJe~gyl.;ye~ of~impJe,_ ' - · har~onic oscillator, selection fules,:-pure;vibr~tiC;lpa_l SJ*-U:i;im,J~f~D.S.it)';_:dettrQ:iiilri.tiQn · : of force constant and quaH~tivt; relat\~.? Ciffurq: ccinstll_nf~~~:~n_e,,~es,idea of- . vtbrat1onal frequencies of dJffer::ent:~~ll..'ff:.iO~J gro_ups .. · .. : .. <::.;_t4:. ,.-.-: ·· ;: .. ·;~· ~~ -:·. :-·1 .. ' · ~;:· ·~. -·.

•• ' . . . ~, . • . ·- ·- : . .. ·; . - _.--r . . . , . Raman Spect-rum : concept ot:_pol_~bll~!y1 Q~.re ro_til~~al an':t pur~ Jli..bf:ati6hal Raman spectra· of diatb~ic wolecuJes~.~~ti?~ _r:-ul~. :_ . . · :~::~./. ···:· :/>-:._ ·:,:"'i.L~-- -~;·~- ·. _ .. .-•.. ·­

(ti)' Electronic Spectrum--: C9ncept· of potentiaLenergy~curvei 1\lt'olii:inding''and anribonding molecular oibitals~:. qUajitativ~-- d~ptjo.!:J;l-rif .·:-sCiection-.:.rm.~ .. ·aizd.-.:· < Franck-Condon.pnnciple. · • - .· · · - ··- -.·· ·"-: '• -' - ·- ·- <, :·--:·~ < · .

Qualitative description ofO', "· anc{ii, M.ci:,'th~ir ener£':1.;,;~ and th~ r~~e ·:·- - . transitions. · ~ · · ._ · ··· .,. _·:. . · .. ·-·: :.:_: -: · :· .• :- .. ;;_ ~--~-:.· 0:;~:-;,~- · ~-:- ·

Unit-IV : . Photochemistry·: ; Inteiacti6n of _radi3ti0~---~--~att~~,-~ir;f!b~.erlce · between thermal and -photochemical prQ!:esses .. LaW._ oC photocliernjsitY,: ~< ~ __ Grothus-Drapper law, Sl;!rk-fiinstOin 'Jaw_, Qualitative di!scfiption· of flucirSpeilce, -: _ .. · ·

. J'hOtsphorescence, non-radiative prcic~s (ioternal-conversfoq,.-intersystem<irn$.';_l_!lg);·;.~- . · quantum yield, photosensitized reaction5-ener.gy transfer p~ (simp)~ exath~). :'-_' _ _.-. chemiluminescence, kinetics of photochemicafcombinationp[H2-Cizanc>lf.l-~- ·'· '

Urut-V : (a) Physical Properties~iuid ,Moleculat .sfructure- :'-oj)iif.ijj~cl;'ttf.:· Polaiization ·{aausis-Mossotti, eqtiittion); orjentatiori of..df~I~ ip..~an":'-e1_c£tlic;:;ti_61d;<_· dipole ·moment, ".induced dipole. ~Onj~pt,_ .me~uremenfiif~dipote,rm~~t~:-~.Je--~ mOment and . structure of -~Oie~Ies, '-!Jla8J:let~c :-pl:opc:ttj~s~Rara~e·ti.Sni~ · diamagnetism and ferromagn~tis~J?~ -_. :_, : . .. . ·._._·-_.., : :~-~ ·_ · ·:_- ·-,_.;:·"<' .. :·~-~~;;;~~-~, ::,_.,

(b) Solutions~ Dilute Solutio~·.and ~ig3tiv~.Pro~~-~IdCat:-a;I~;n~:-~-~: ·· :u~~::~t.~ethod of expressing ~ncentrations of S()ltJ!r, •_<tivity a_n~ --~ty _ _ •. l!i

- Dihiie solution, -coU~ative.-·properti~, RaoUJ~'s-Jaw; .. :r~lativ¢ loweririg:;~r~pUr··.· -· pressure, molecular weight deterffi~atiorl. "Gsmasis;._Jaw:-m~9SmG-tic pres&~¢:""a_ifdjf.i. ~-:: . -.-_ ~ measurement, determination·of mdiei:Ular "Weight from :osmbti~· pressure.._.F.JeV'atiori·.Of"·' · II boiimg point and depression of freezing point, Thennildynamifderf"in!c?iiof'ii:t<itrdn; · , .-, . _ '[ between molecular W(:ight arid elevation iri lxiiling•poilit-~!ld· d~I;r~i~ In;'!feeti~g :_ , · , ~ ! pomLExperiniental methods of detenntmngvanous colligatll(e propert'."': .'-' -,-,,._; · .-. · _ 1 I ::.-;;: .. m-. ~ .. .., ..... ,, ~'"""""""""""' : ~ r : : . -~~. " ~mt~_--<

Practical : ,

The duiation of practical examinatjOil.Will be of six: ~ouri. '· . _. '. -. ·.•

8 B.Sc. Part-Ill, Syllabus

Unit J: Inorganic .'\nalysis and Preparation i

. (i) Paper Chromatographic Separation .of Metal ions Cu2+, Pb2+, t Co2+, Ni2+, Cd2+ ions (binai)' mixt~res only) l

(ii) EDTA titrations of ea2 +, Mg2+; Zn2+ and Cu2+. :l (iii) Determination ofha,rdnesS of water. ·1 (iv.) PreparJlion of Simple Inorganic Complexes. --l

Unit II: Organic Analys"is oi lndustriallmporta:Dce 3 (i) Separation of a simple mixture of twO organic (solid) compou~ds Sef"li

by water and dil. acids and systematic identif-qtion of the compounds. 1 (ii) Paper chromaroiraphic separatiOn of arrtino acids an_d sugarS (only -b~

mixtures) 1 Unit III: Physical Chemistry Experiments _ I

(i) Hydrolysis of methyl acetate catalysed by an acid i (ii) Hydrolysisof ethyl acetate catalysed by an acid -~' (iii) Absorption Of acetic acid on charcoal. · : (iv) Heat of a Solution of a substance (oxalic acid) by solubility method. . (v) Transition Temperature of Glauber•s S3lt by Thermometric methCJ:d. j

· (vi) Heat a( Neutralization ofNaOH and HC!. · Students shall be given three experiments each of two -hour duration (Inoi

experiment of 10 marks, orga_pic experiment of 15 marks, and physical experimeri' marks, 5 marks for viva and 5 marks for records(= Total 50 marks) in the·_.,1 practi~al examination. . ~ , ·. ~

[2] [ 3]

CHEMISTRY ' · · · h · · 1 · · · · b · f h. 1 b · ·:· .. • ' Asymmctnc synt es1s, oplica activity 1n a sen~e o. c tra .car on . . !"'· Sc.- ~Prevtous) .. · (Bipilcnyls), stereo chemist!); of corn pound containing Nitrogen. Paper 1-Inorgamc Chemistry . . . . Unit 11-Reaction mechanism : Types 6f mechanism, types·

Un~t !-Reaction Mechanism of Transition Metal Corhp·, of reaction, methods of determining mechanism structure, Stability !exes: Energy,profile·of,a reaction, reactivity of metal complexes, and reaction of Carbocation carbanions free radicals Carbene's, - · mscrt and labile complexc~:., kinetic application of valence bond Nitrenc, effect of structure on reactivity~ resonances & field effect and cryst~l field theories, kinetics of octahedral substitution, acid Steric effect. · 1 . hydrolySis,- factor affecting aCid hydrolysis, base hydrolysis, Unit III~Nz, SN 1 mecha~iSJn classical and nonclassical conjugate base med1amsm, direct and indirect evidences in favour Carbo cation, Phcnoumiom, Nucleophilic·substi!Ution at an allylic, of Conjugate Tnechanism, anation reactions, reactions without vinyllic Carbon. SF 2, SE1, Electwphilic Substitution accompanied metal ligand bond dcawage, subtitUtiO_"n reactions in Square planer hy double- bqnd shift. The arcnium on mechani-sm, orientatioh complexes,_ the trans effect, mechanism of the substitution reactivity ortho pariiratio Sn,Ar, Sn 1 Bcnzy.ne E2, E. reactions. . Unit JV-Mcchanistic arid Streco chemical aspect of addition

Unit II -Metal-Ligand Bonding : Linlitation of crystal field r, •ction, involving elcctrophilcs, nucleophiles and free radicals. theory, molecular ofbital theory, oct~hcdral, tetrahedral and square H! "'rogCnation of double bo~d _&.trip!~ bond, aromatering, Hydro planar complexes, rr-bonding and moic.cular orhital theory. . foLiation. Mechanism of theta!· hytlrides reduction of saturated

Unit Ill-Metaln-Complexes : Meta} carbonyle, 'structure, and_ unsaturated carbonyl compounds, acid, Addition of Grignard and bonding, vibr~ti?~al spectrri.of metal' carbonyls for bonqing reagent aCid to ~arbonyl c?!TIP~urids ~echaniSt!l o~ Al~ol, and struc.tural elucJ~latJOn,'mlportant reactions of metal carbonyls; Knocvcn:gel Cla1ses, Manmch Ocnz01n, Pcrk1n reactiOn: preparatiOn, bondltlg, structure and important reactions, of· HydrolySIS of est~r. . . . . _ . _ _ . . tra~sition metal nitrosyl, dinitrogen and dioxygcn complexes; Uni~ V-Type~ o_f free radicals : Fr~e radical SubstliUti~n tert1ary phosphine as ligand. . · mcchams~; mechamsm of. an. aromatic. substrate allyl_llc

Unit IV -Met 1 Cl t • · · '- halogenation (NBS), auto bx1datwn, couphng of alkynes and a us ers . Higher boranes, car_boran.es, anylation of aromatic cOmpound by diazonium salt. Sandmyer's

metalloboranes and m~tallocarborancs me.tal carbonyl and halide reaction. Molecular orbital Symmetry, trompier orbital of ethylene clusters, compounds \\flth metal-metal multiple bonds. 1.3 butadiene classification of. Peri cyclic reaction Wood ward.

Unit V -Isopoly and Heteropoly Acids and salts. Hoffmann correlation diagram Fi-10 PMO approach anlerafacial l_)aper 11-0rganic Chemistry and super facial ;;idtlition: ·

Unit !-Nature of Bondi no : Paper III-Physical Chemistry . (a) .Delocalized Chemi~al bonding-Conjugation, cross/ Unit 1-Quan.tum Cherhi<ttry_: _ . .

conjugallon resonance, Hyber-conjugation, tautomcrson. Aromatic (a) Intr~duchon. to ~xac_t Quantum Mechamcal Results • in benzenoid and non beriZenoid COmpounds a!t t d - The Schrodmger equatiOn ~nd the postulates of quan_tum , ernan an non . . . . f . f h h d. · t

. ahcrnant hydrocarbOn, huckle rule, ailnulenes. mcchan~cs, D1scussto~ o sol~tlo~s o · t esc ro t~g_er. equn~IOn a (b) Conformational analysis of cyclo alkanes dicaliries, sam~ t~odel systems vtz., particle m a box, the hamlOnJC osc!llator,

confo·rmat1·0 n of sugars Ele n nts f S , h' 1; the ng1d rotor, the hydrogen atom. . . ... . 1 e . o ymmetry, c tra~y . · . .- · 1 1·

molecules with 111Are th -h · 1 1 Tl & . · (b) Approxtmate Method : The vanat10n t1eorcm, mear , ~, en one c nra cen er, ueo cryt ro . . -. . . . · isomers metllods of resolutt' 1· t . . & d. . vanat10n pnnciple, PerturbatiOn theory (f1rst order and non on enan 10 rop1c tastercotoptc . . . . · :1toms Groups sterc<> spe·c··,r· & 1 1 . · .·1 . degenerate). ApplicatiOn of vanat10n method and perturbation . , . 1c s ereo se ect1ve synt 1es1s ·1h. 1 H 1- t

eory to 11e e Jum a om.

.,·

[ 5] [ 4]

1 of Jroplets (Kelvin Equatio:1), Gibbs ·adsorption isothems,. (c) Angular l\'lomenlum · Ord 1.,u1y Ull"ular 1 estimation of surfaCe area (BET equation), surface films on liquids

· " c nomcntum ·· . . . . . · generalized a_ngular momentum, ~~ gcn functions 'for angula1(ElectrokJ~etJc Phenornepon), ~<JtalytJC aciJvJty _at su~f aces. 1 ~omerll~m. etgcn v~l~es of an .gular 111 omem 4m, Operator usint . (b) Micelles_:_ sur:ac~ actJve agents, <:Ias_?Jficau~n of su_r~ace ~adder o~erators~ at.ldt~IOJ~ of angubr momenta spin, an_tisyrnmetrfc_tlvc agents, mtce~ltzatwn, hydrophobic Jnt~ractJOn, en tical_ unu Pauh e~cluswn pnnc1ple. micellar ConcentratiOn (CMC), factors uffecung the CMC of

Unit II-Thermodynarilics: surfactants. (a) Classical thern~o<;iyn~mics: Brief resume of concepts ol (c}'·M<l:c.lomolecules·: Polymer-definition, types of polymers,

laws ~f therm~dynanjics, free energy, chemical potential an~e~ectr.i~al1/. conductio~, f:re resistant, .liquid cryst~l po.lym.ers, entr?p1es. Parl!al molar propert_ies, Partial mol or fret! ent!rg kme_t1cs ot. polymer.JZ<illon, .mcc~~msm of· polymensatwn. P.an~a-~ molar volume and p~rtial mrill;lr ht:~t content and thel;scdmle~l\ali~n, cham_ con.hg:Hatw~ of n~acromoleculcs, stg,tu_!.Jcances, De~efl~lination of their quantities. Concept oJCalculauon of a~verage <hme?swns of vanous cha~n struc:ures .. fug~c.Jty &, detenm.natton of f.ugacily. Non ideal systems : Execs~ Unit V'-----Eiectrochenustry : Ele~trochen11~try ?f. solutwn. funclions tor non-Jde<tl sohJttons. Activity, activity coefficients.Debye-Hucklc-Qusajer treatment & Hs extensiOn, JO:t solvent ~eb~e-~ucklc ~he~ry f~r a~t~\ity coefficient of electrOiyticintera.c~h?n: Debye-Huckl.e-Jerum mode. 'Thermodynamics of

. .soluttons, detennJnallon of activlty and pctivity coefficients ionicelectnfJed mterfacc cC)uatwns. Ov_er potentw.l exchange current strength. ' density. Semiconductor interhces-Theory of double layer at . (b) Statistical thennod}'namics: Panition functions T a ,·_semiconductor electrolyte so1ution interface, Structure of double

tiona!, rotational, v~bnHional & clectr~nic partition fu ~· nsi. layer interface. Effect of light at semiconductor solution interface. Calc~lation of lhermodynamic properties in terms of pnactiOt_ns, PolarQgraphy theory, 11 kovic equaiion. half wave potcminl & its fu Ct A I. . r 1 1011 . . 1.. 1 . . · H '1

n '.on, pp ~catwns o~ paf(itjo11 functions. Heat capacit s1glll 1cance. ?troduct1o~· to cn~ros.wn, amoge.ncous/t 1eory, ?~havJour of soiJds : Chenucal equilibria and tLJL.iilibriunl co t y forms of corros10n, Corros10n momtonng & preventiOn methods.

t f ·· · .. · nsam 111 CJ_·ms/o p~rt1t.wn tunctwn, Fermi-Dirac statistics, distdbutions Paper IV -Spectroscopy cmd diffraction methods law and appl.wauon fomatal, B{;sc·-Einstcia Statistics-distribution Unit I-Vibrational Spectrosco-py: law an?_ application to Helium.', ' . (A) Infrared spectroscopy : Review ·of linear harmonic

Umt .I~I~Ch~mical. Dyfl:&mics : ~ethods of determiniilo rate oscillator, vibrational eilcrgies of diatomic molecules, zero point laws, CoJ!J.SIOn theory .o! _re~c.t~,~n _.r~tt:s, steri_c factor, acti~ated energy, force constant and bond strengths~ antiannonicity, Morse compte~ l~:or~, .. ~~r-hen~~s.:~u~tj9n_ 3nd the activated complex potential energy diagram, Vihratio_n-rctation sp.ectr~scopy: P, 9· R ~~eor~, JOllie reucuon, Km.eqc ·s~h,_effec~s. steady state kinetics, branches, lJreakdJ?wn ?f oppenheuner app~oxJmatJon, V1brauons l~etics & thenno~ynun_Hc. C:~~l.t_rql of reactiori, treatment of of poly atomic molecules selection rules, normal modes of

um~n_olccular re~ctwn~. Dy_namic chain (hydrogen-bromine vihi'ation, group frequencic:.s, overtones, hoi' bonds, factors reaction, P~rolys1s of actald~hyd.e decomposition of ethane), affecting the band position and intensities, for IR region, met.:! Phot?chemJCal (hyd~q?en·~brvnune. and · hydroge_n-chloriJlc ligand vibrations, normal coordinatt; analysis. reactwn)~ Homog~~eoUs·:·cataly~is, kinetics \if-·· enzyme reaction (B) Uaman Spectroscop:{: Classical anJ quantum theories of general~ fe~turcs ot fast reac;:tioJl.;. I-Jach Photolysis and the nuclea; Raman effect Pure rotational vibrational and vibrational-r,)tational magnell.c res_onance method. · . , Raman £pt:clra, sele.uion rule.s., mutual exclusion princ'tple,

Umt IV =-Surface Chemistry: · . Resonance Raman speclroscopy, Coherent anti stokes Raman (a) Adsorp~ion -:_ S~~_facc- tensiou, capill:iry i;i.Ction, pressure -Ji sp~ctroscopy (CARS). . .. ;~ .-:

h_erence across curved surf<fe (Laplace cquatio':) vapour press•·

·-·---·-··· . --~ ·-·-- --··

[ 6] 171

Unit II-Eiectrunic Spectroscopy : [ \ M. Sc. (Previous) Chemistry

(A) Ator:nic Spectroscopy: Energies of atomic orbitals, vecto~ Practical represe_ntation qf momenta and vectOr cat,Jpling, spectra of: Iilorganic Chemistry: ·. . hydrogef1 atom anQ alka~i i:}toms. · · . :A Qualitative and Quantiladvc Analy-sis:

(B) Molecular Spectroscopy.: Energy levels, molccuia/1 (a) Less common ,,,etal ions-TI.IJ.1o, W, Ti, Zr, Th, Y, U orbitals, vibronic· transitiOns,_ vibrational progressions and; (two metal ions in CaUoi:HCia~IOnJC fonn~)- · _ geometry of the e~citeP stateS ·Fra·nk-Coridory prin_ciple;_ electr~mic\ {b) Separation rind dctennination of two m_etal io,ns ~u-N_l, spectrz of poly atomic ~olecules, E~ission spectra, radiative and~ Ni-Zn, Cu-Fe, etc:, involving volumetnc & gravnnctnc non-radiatiVe decay, intCrn~l conversi?n spectra of transition r:netal1

1 methods. · complexes, charge, transfer spectra. ! B. Chramatography :

Unit Ill-Magnetic Resonance Spcctro.scopy: \ Separation of Cations and· Anions by Paper

, (A) Nucl~ar MDgnetic resonance sp"ectroscopy : Nuclear: . chromatography. spin, nuclc~r re.Sbi1aJ~~e. S_lil~_r_ation; S_hielding of magnetic nuclei~ C. Preparations . : . chemical shifl and .its meas':lre.ments, factor· influencing chemical: Preparation of Selected· inorganic Compounds hke : shift, deshielding, spin-spin !inte'ra<;tions, factors influencing; 1. K [Fe(C,04 )6 j 2. [Ni(NH3),]CJ, coupling cons~ant 'J' classification (ABX, AMX, ABC, A2 B2_. etc.)! 3_ N: (dmg), 4. [Cu(NH 1 )4]S04.H 20

Spm dccouphng, baSic 1.dcas about mstrument, NMR studtcs of' 5 [C (NH ) I [CO(NO ) 1 6. ·rr~ssian Blue nuclei other than proton 13 c. 19F .and 31 p, Fl' NMR advantages of · .

0 •

3 6 2 6 ,

FT NMR use of MNR in h1Cdical diaonostics ' Orgamc Chemistry : · fi-. • •. · .

0 · • . • A. Qualitative Analysis : · · · · ' · . ·

(B) Electron ·'PI" Resonance spectroscopy : Baste . P 'fi · · · d ·d t'fication of compounds of . . r· I . I 0 'd K 0 d f Sl'paratJOn UTI !CaliOn an I en I . pnnc1plcs, zero 1e d sp ettmg f!.rL ramer s egeneracy, actors b" . ' · (T s· 1-d )

ff · · • .~ · 1 '"· · · d : · mary mixture wo o 1 s a ecttng the g va ue. Isotropic an · anisotropic hyper fine . . . coupling constan!s<Sp_in Hainlltonian spin "densitieS and Me B. Orgamc .syntheSIS: . r r ··d "th a ctyl Caunell relationship me.·~suremcnt icchnique, .. application. 1 Acct~latiO~ : A~etylauon ~f. Sa ICY~ 1 ~ act '. wit .· cf p

• . 1

. ·. · . . • . • . • • • : chlonde, Aromat1c Electrophthc substJtutton-Synt 1es1s o -Umt IV -X-ray D!ffractJ~:m.: Bragg condttlon, Mtllermd1ccs, '. nitro~ni"line and P-bromoaniline from aniline.

Lane method, Bragg method, Dehye-Scherrer method of X-ray, Aldol Condensation : Dibcnzal acetone from benzaldehyde. str~ctural analysiS of cry~t~l,s tn~c~ _refl~ctl0.11, Ide~tdicaoun of: sandmeyer. reaction : P-chlorotolucne from. P-~?ludtne. unll cells frm_n systematic· absences ·tn d1ffractwn. pattern.. Cannizzaro reaction : Benzyl alcohol &_.Denzotc acJd, from Structl:Jre of simple lattices and x~r~y i"ntensitics structure factor Benzaldehyde. . . . . and its relation ·w)ntensity and elec~ron.deitsity, phaSe probl~m. Friedel Crafts recation : p -Benzoyl propionic acid from Description of the procedure for an,· X~ray strucllire analysis, succinic anhydride and benzene. ··'; · absotUte configuration of molecule~·! Ramchti~dran diagram.. "Qrign3rd reaction : Synthesis of triphenyl methanol from

Unit Y_.-Eiect.ron Diffractioil :· · Sc~ttering intensity vs. 1 ben.z9i~ acid. . . . Scauering angie •. Wi¢rl .euati"on · mcas'Ufemerft techniqUes,.\ .c. Quantitative Anall:'sis: . elucidati.on of" strutturc of simple gas· Phase 1'nol·e·cules, Low 1' (a) Detennination of ~he percentage or numb~r of hy~roxyl

· · · · · · l ps ·,n art organic compound by acetylatiOn method . .-\'crgy elect rOil ~~~fractiOn and stJ~UCht_re of surface~. gro 1 .

.~r·

[ 8]

(b) Estimation of aminestrlh:.a£'.ts using b'romate bromide solution/or ·acetylation method.

· Physical Chemistry :

Each experiment will be of 3-4 hours duration.

I. To Study surface 'cnsion-~once.ntration re_lationship for solution (Gibbs equation)

2. Determination of the effect of (a) change of temperature (b) ' change of concentration·of reactant & c'atalyst on the velocity constant of hydrol'ysis of an .ester/ionic reaction.

· 3. DetCrrry.ination of the velocity constant of hydrol)'sis. of an ester/iOnic reaction in micellar media.

4. Dct!!rmination of molecular weight of non-variable and. non­electrolyte/electrolyte by. cryscopic method ~ to d~tennine the activity coefficients of an electrolyte.

5. Determinati011 of Solubility & Solubility product of sparing soluble sails (~.g. PbS04 , BaS0 4) conductometrically.

6. Detennination of the strength of strong and weak .acids in a 1

given mixture conductometdcully. 7.. Determination of the strength of stroQg. and weak aciJ In a

given mixture using a potentiometer/pH meter. 8. Determiuation of rate constant 'for hydrolysis/inversion of

sugar using a polarimeter. 9. Acid· base Titration in a non· aqueous media using a pH meter.

CHEMISTRY M. Sc. (Final)

Paper I-Inorganic General

Unit I-Vibrational Spectroscopy: Symmetry_·and shapes of AB 2, AB 3 , AB4 , AB 5 and AB6 mode of bonding of ambidentate

.. ligands, ethylenediamine and diketonato complexes, application of resonance Raman Spc~.:troscopy partricularly for the study of active sit~s of metalloproteinf!.

Unit II-Nuclear l\1~gnetic. Resonance of Paramegnctic. Sub.Stanccs in Solution .: The contact and pseudo contact shifts. factors ~ffecting nuclear rclnxation, some applicatiom including hichcrnical systems, an overview of NMR of metal nudides with emphasis on Pt19.'i and Sn l.'i9 NMR.

[91

, Unit IU-(i) Metal ions in Riologica) Systems Essential and trice m'etals ·

(ii) N~+/K"'" Pump Role of metal ions in biological process. (iii). Transport and Storage of Dioxygen. Heme Proteins and

oxygen. uptake, structure and. fur.Ction of i-Iaemoglohin, myoglobins, _Hemocyanins and hemeryihrin, model synthetic complexes of irons Coball Copper.

Unit- (i) Bioenergetics and ATP cycle : DNA Polymerisation, Glucose storage, metal compleXes in transmission of energy chlorophylls. Photosystem I and Photosystem II in cle<ivage of water. Model system.

' (ii) Electron transfer in Biology : Structure and function in metalloproteins in electron transport procr;::sscs-cytochromes and ion-sulphur proteins, synthetic models.

(iii) Nitrogenase : Biological nitrogen fixation, molybdenum infrogenase, spectroscopic and other evidence, other nitrogenases model systems.

Unit V -(i} Soils : Composition, mjcro and macro nutrients P,1\lution-Fertilizcrs, pesticides, plastics and metals. Waste Treatment.

(ii) Hydrosphere : Chemical composition of water hodies.­Jakes, streams, rivers and wet land etc. Hydrological cycle Aquatic pollution-inorganic, orgnnic Pesticide, agricultural, industrial and sewage detergents, oil spills and oil pollutants. Water quality parameters-dissolved oxygen, biochemical Oxygen demand, solids, metals, content of chloride, sulphate, Phosphate, intrate and micro organisms, water quality standards. Purification anll treatment of water. P~per 11-0rganic General

Unif 1---,0pticnl Rotatory Dispersion (ORD) and circular Dichroism (CD) Definition, dcducation of abso_lutc configuration octal rule for "ketOne. Mass Spectr('rnetry-lntroduction­Fragmentation, Molecular ion peak, metastnble peak, Nitrogen rule. High resolution mass Spectral fragmentation of organic compound with respect to their structure determination.

Unit II-N.rvt.R. : Introduction, definition; Chemical Shift, Spin-Spin Interaction. Shielding Mechanism. Mechanism _of

[ 10 l

measurement Chemical Shift .value and .correlation 'for proton bonded to Carbon (Aiphntic, Aromatic) and other nuclear (Alcohol PhCnol), Carbolic acid, amine, effect of deuferation complex spin~ spin interaction between two three nuclei. Carbon 13 NMR Spectroscopy'lntroduction, cosy, Nocsy-Technique chemical s·hift

. aliphatic, obfinic, alkyne, Aromatic, Carbonyl Carbon. Unit Ill-Photo Chemistry :· Type of excitation, fate of

excited mole, types of Photo Chemical reaction Photo dission gas Photolysis, Intramolecular reactions of ·OJifinic bond intra molecular •Nction of Carbonyl Compounds-Saturated Cyclic, .a~ Unsaturat compounds. intra mOlecular cyclo addition reaction­dinerisahan Isomerisation addition and Substitution.

Unit IV-::::::-- Enzyene : Introduction : Noinenclaluse & Classification. Fischer lock and key; Kosi and and Induced hypothesis; Trari.sitio,n State theOry, acid bllse catalysis, covalent catalysis,- Nucleo-philic displacement on Phosphorus atom, n~ultiplc di_splacernent reaction and the coupling of ATP, cleave to endergonic Proc.csses, Addition and Elimination reaction Enzyme Catalyzed Carboxylation & Decarboxylation.

Unit V-Coenzymes, Apoenzyne, Structure & BiologiCal Function o.f coenzymes, production, Purification of e.nzyme, method of Immobilization of enzyme effect of immobilizatiml' on enzyme activity. Application of Immobilized Engyrne, Clinical use of Enzyme, Disposal of Wastes ·and their management, .. Biodegradability, Chemical Solution to environmental Problem. Paper III-Physical General

Unit 1-Solid Slate Reaclions: General Principles, cxperi­.rnental procedures. co-precipitatio1,1 as a precu.Ssor to solid state reactions, kinetics of solid state reactions. Crystal defects an_d Non­Stoichiometry. Perfect and imperfect crystals, Intrinsic and extrinsic defects-point defects, line and plante ·defects, vac3ncics~ Schollky defects and Frenked defects, Thermodynamics of Schottky & Frenkel defect formation, colour centres, non stoichiometry and defects. Biological Cell and its constituents : Biological cells structure and functions of proteins; enz.ymes, DNA and RNA in living systems, Helix·coil Transitions.

Unit II -Electronic Properties and Band Theory : Metals, insulators and semicon..Juctors, electronic structure of solids, band

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structure of metals, bat'11· theory, intrinsic ~nd extrinsic semicOnductors, doping. semiconductor, p-n junction, super conct~'etors Optical properties. Optical rcflectftnce. Photocon.duction-photoelcctric· effects,· Magnetic Properties­Classification of materials, Qu~ntum thc.ory of ·Paramagnetics­Coopcrative;Phcnomena. MagnetiC domains: hyst~risins.

Unit III-,- Thermodynamics of ·Biopolymer Solutions : . Thermodynamics of. biopolymer solutions, osmotic pressure, membrane equilibrium·, muscular contraction and energy generation in meciianochernical system.

Biopolymer's and their Molecular Weights : Evaluation of size, shape, molecular wilght. and extent of hydration of biopolymer.s by various experimental techniques, sedimentation equilibrium, hydrodyryamic methods; diffusiOn, sedimentation velocity, Viscosity, electrophoresis and rotational motions.

Diffraction Methods Light Scattering, low angle X-ray scattering, X-ray deffraction and photo corclation spectrosCopy, ORD ..

Unit IV-Bioenergetics : Standard tree energy change in biochemical reactions, cxcrgonic endergonic, Hydrolysis·of ATP; Synthesis of ATP from ADP. Statistical Mechanics in Biopolymers : Chain configunt\ion of macromofecules, statistical distribution end ·to . end dimension, calodation of average dimension for various chain structures, Polypeptide and protein structureS, introduction to protein folding problein.

Cell Membrane and Transport of Ions : Structure and functions of cell mernbrrine, ion transport ·through cell membrane, irreversible thermOdynamic treatment of lnembrane .transport,

Nerve conduction. Unit V ~Organic Solids : Electrically conducting solids,

. organic charge ··transfer complex, organic metals, new super

coductors.· Biopolymer Interactions : Forces involved in biopolymer

interactions, electrostatic charges and molecular expqnsion, h)'drOphobiC forces, Jispeision force interaction. Multiple ~·-1uilibrias and .va.rious types of building processes in biologic;:ll

.yste\ms·, Hydrogen ion titfnrion cur\'CS.

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Paper IV (i)-Inorganic Chemistry (Special) Unit l-(i) Transiti(m metul n:-compJexes: Transition rn~1al

n-complexes with unsata,JrateJ·organic molecules, alkenes, illkynes, allyl, dienc, dienyl, arene and trienyl complexes, preparations, properti~s. nature of bonding and structural features. Important reactions relaring to nucleoPhilic and cle'ctrophilic attack on ligands and to organic synthesis. ·

(i_i) Transitipn me1al compounds with Bqnt.ls to Hydrogen. Uqit Jl-(i) ·Metal storage Transport anJ lliomincralis:.•rion

Ferritin, Transferrin and siderophores.

(ii) Calcium in Biology : Ca!.:ium in living celis, Tr:-msport . itnd regula'tion! molecu.Jar aspects of intramolcculbr processes, extJ:acellular binding prOieins.

llnit 111-MetaJioenzJme,s : ZinC enzymes-Carboxypq?ti~­dase and carbonic Lillhyllruse, Iron enzyme.s--c'at<~lase, .pcn)xiJasc" and cytochrome P-450. Copper cnzymes-superoxide JiSJilutasc molybdenum oxatransferase enzymes-xanthine oxidase. Coenzyme vitar~1in B 12. ,

Unit IV-(i) Meal Nucleic Acid liit~ractions ; Mctn/ 1ons and metal ~omplex interaction metal complexes-nucleic acids.

(ii) lVIetal in L\1edicine : Metal deficiency and diseas~. ~oxic effects of metals, metals used for diagnosis and chemotherapy with panicular reference to anticancer drug~.

Unit V -Excited states of Metal Complexes : Excited sr;:Hes of metal cOmplexes : comparisori with organjc compounds, electronically excited states of nwtal complexes, dmrge-trar,sfer spectra, change transt(:r exci!_ations, methods for obtaining charge­tra·nsfer spectra.

Unit IV (H)-Organic Chemistry (Special) : Terpcnuid & Carotenoid :

Unit 1-Chis·sificat-ion, nomenclature occurance., IsohHio!l, Isoprene rule structure ,dtffen_nination of citra!, a-tepeneol, ?.ingi berene,. P-carotene, Biosynthesis of terpene.

Unit II-Alkaloid : Definition, nomerwlaiu.:~e- nnd physio­logical action-;· ocCurrence· Isolation; clas;-;ification b~1s~d 011

Nitrogen hetrotyclic ring stn,lcture of Nicotine, Atropine, Quinine and Morphine. Biosynthesis of Albdoid.

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Unit .III-St<,•oids : Occurence, nomonclature, diels hydrocarbon siructlm .. determination of cholesterol, Androsterone. Testosterone, Progest )ne,'Biosymhesis of steroid.

UnJt IV:P1ant :.<~igment: Occurence nomenclature. Isolation strucwre determin-ttion of· querc_etin, Cyanidil'!. Hirsutidin, Auceusin, Dio synthesis of flavonoid. Structure of Hflemoglobin and ('ltiorophyll.

tl!,it' V-AntiLiotics ~ P-lactamring, st~ucture & syrithesis of Peni~iliin' G. Penicillin V, Ampicillin, amoxycillin Chloram­pher.i(:IJid, Tetracyclin and Streptomycin. Paper IV (iii}--Physical Chemistry (Special)

Unit 1-Thin Films and Langmuir-Blodgett Films : · Preparatibn tech1_1iques, e_vaporation/sputtering, chemical·· processes, MOCVD, Sol-gel, etc. Langmuir-Biodgell (LB) films, growth techniques, Photolithography, properties and application of· thin .1:· LB films.

Liquid CrystaJs ·: Mesmorphic behaviour, thermotropic liquid crysrals, positional order, bond orientational order, nematic and smetic me.sophates, smetic-nematic, transition and clearing temJ)t;rature, homeotropic, planar and schlieren tex.iufes, twiste'd nematics·, c:hiral nematics, molt:cular arrangement in smctic A and SI;Jletk C phases, Optical properties of li(Juid ci-ystals, Dielectric susceptibility and dielectric constants. Lyotropic Phases and their description of orderit:t£ in liquid crystiils. ·

Unit 11-Pol)'meric Materials·: Molecular shupe, structure anl~ configuration, crystalinity, stress-strain behaviour~ thermal behaviour, polymer types and their application, conducting and feno-clcctric polymers. . Ionic Conductors : Types of ionic conductors, mechanism of

ionic, .conduction, iriterstitial jumps (Frel)kel); Vacancy,. mechanism, diffusion superionic·conductf,lr, phase tr<:insitions and mechan

1ism of conduclion in super ionic conductors, examples and

applkation of Ionic -conductors. · . Uitit Iil-llleor~tical arid computational treatrrlen.t of atoms

and molecules, Hartree-Fock theory. Review of the principles of quantum mechanics., Born-oppen-heimer approximation, Staler. Condon rules. Hartree Fock equation, Koopmans and Brilloning theorie:;, Roothan equatiO!l, Gaussian bu,sis sets.

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Unit IV -General Properties of Liquids : (a) Liquids as dense gases, liquids as disordered solids, some

thermodynamic relation, internal pressures ami its significance in liquids. Equation of state, critical constants. Different types of intermolecular forces in liqUids, different potential function for liquids, additivity of pair potential approximation.

(b) A classical paftitiqn function for liquids, correspondence principle, configi1rati9n integral, Configuration properties.

Unit V --.Polymer l,rocessing: Plastic, elastomers and fibres, compounding. Processing techniques. Calendering dil! casting, rotational caSting, filri1 casting, inj!!ction moulding, Blow moulding, ex·trusion moulding, thermoforming, foaming, reinforci~g and fibre spinning.

M.Sc. (Final) Inorganic Chemistry Practic.al I. Flame Photometric Determinations.

(a) Sodium and Potassium when present together. (b) Li/Ca!Ba/Sr (c) Cd and Mg in tap water.

2. Spectrophotometric Dctenninations. (a) Fluoride/Nitrite/Phosphate

. (b) Copper-Ethylenediamine complex; slope ration rnethod. 3. Chroma~ographic Separations. ·

. (a) Cd and Zn (b) Zn and Mg (c) Thin-layer chromatography

Separation of Ni, Mn, Co & Zn Determination of Rf values.

M.Sc. (Final) Organic Cluimistry PRACTICAL

1. Separation and indentification of Components of mixture of three organic compounds.

~- Multi step Synthesis of organic compounds. · (i) Benzene-Buzophenone-Benzopheri one o.xi·mc Benzilide.

(ii) Benzaldehyde-·Benzoin-Benzil-Bcnzili~ Acid.· (iii) Skramp Sy.nthcsis-Bepar~tion of quinoline from anilenc. (iv) Fischer-Indole Synthesis-Preparation of 2 Phenylindolc

! f~nrn Phenylhydrozine.

i. r 1sJ ·,

(v) Reduction of Ethyl ACetoacetate using Baker yeast to Yield enantiomeri~ cxcen of e~hyl-3 hydroxy butanoate.

3. Extraction.·of organic ~ompounds, from natural sources:

(i) Isolation of caffeine fror.n tea·leaves. (ii) Isolation of casein from milk. (iii) Isolation of Lactose from milk. (iv) Isolation of Nicotinc-Di-Picrate from Tobacco. (v) Isolation of Lycopene fromotomatoes. (vi) Isolation of Bcarotene from carrot.

4. Paper Chromatography : Separation and identification of· sugars Present in mixture of glucose, Fructose, Sucrose by Paper chromatography and determination of RF values.

5. Spectra PhOto!Tietric estimation : (i) Amino acid (ii) Carbohydrale (iii) Ascorbic Acid (iv) Aspirin (v) Caffeine.

M.>!ic. (Final) Physical Chemistry PRACTICAL

Number of hours for each exper)ment 3-4 hours. A list of experiment under different heildings nrc given below.

Typcinl experiments are to be selected from ench type . Thermodynamics

(i) Determination of partial molar volume of solute {t.c·• KCI) and solvent inn binary mixture.

(ii) Determination of the tempcr<!.ture dependence of the solubility of a compound m two solvents having similar intermclecular interaction (henzoic acid in water & in· DMSO water mixture) and calculate the partial molar heat of solution.

Spectroscopy : (i) Detemiination of vka vf an indicah .. r (e.g. Methyl red)' in

(a) aqueous and(b) micellar media. I

(ii) Determination of stoichiometr'y anci Stability_ constant.of inorganic (e.g. ferric-salicylin acid) and organic ceg. amine i_odine) complexes.

{iii) Characterisation of the complexes· by electronic and IR Spectral Da~a. · !

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Polarography.: . · . . ... · (i) Estimation o(Pb2+-~nd .C~f2+iZn 2+ and-Ni~+ ions in a

mixture· of P.b 2+ a!Jd Cd2+fZn 2+ and Ni2+ bY Polarography.· (ii) Detennination o(dissolved oxygen in aqueous sqlutiori of

organic solvents:-_;,-:· Eh!ct.-Onics : · ·

(i) Measurements of resistance with muJtimetcr. (ii) To measure the resistance of the given ammeter.. . . . . (iii) Use of a wheatstone bridge for accuraiemeasuremcnt of· ·

resistance. (iv) Capacito~ as a ~harge storage device. · (v) Verification of Kirchoff's Laws. (vi) Measuremen-t of c.in.f. with thermocouples. (vii) To plot the characteristic curve of a· diode. (viii) Sctti1~g up Of a th~rmostat : c·onStaPt'terTip-erature both. ·

Op~"'tional Amplifiers : · . . .. · Ideal · characteristicS, inverter, ·sLimmer, integrator·,

differentiator Volu~ge follo'wreS' illust~~lliVc Usc of operational . amplifiets. 'Introduction to' fourier tr_ansfoim in instrumentatimL

Active C_omponents· : . . . . . · Introduction to ordinary diodes & Zener .. diodes _with some·

empha~is on p-n junction as a solid state.property_, use . .of diodes as rectifiers, clipping and clamping circuits, power s·uPPties Transistors. An extension of p~n junction .. to p-n-p and n-p-n Transistors. Charcteri_sti~s ·of tr_ansistors, hybfid par~mcter, transistor ·circuits as amplifiers, J:tigh impedance (pre amplifier) circuits, Darlinction pairs, differential amplifiers. . Basic Electronics :

Notation used in an electric circ~it, study of electronic cOmponents & co\o!Jr coqes, conversion of chemical quantities into electrical q·uantities, .Transdu¢cr, illustration with ·eleCtrodes, them10Couples & thennistors. · ·

Passive components,· Resistors·, Capacitors & inductors yvith some emphaSis on solid s~ate prOpertieS-of materials. Net works of resistors. The venin's theorem, ·sup7rposit!on theoreJD, IO<;JP anlaysis, R.C. circuits, L.R. circuits, UCR circllits .. IIIustration of the use· -of the c-ircuits, in NQR :..spectr9s·~opy, Mosbauer spectroscopy, cyclic Voltametry and in power sup·plies·.as filter circuits.

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SYLLABUS

B.TECH.- FIRST SEMESTER

physics(common to all branches}

UNIT-1

Energy bands in solids, Semiconductors- insulators and conductors on the basis of energy bands,

types of semiconductors, Doping, P type and N type semiconductors, P-N junction, Characteristics of

a P-N junction diodes.

UNIT-2

-7 Heat transfer- conduction, convection and radiation, Pressure, viscosity, surface tension.

-7Eiements of communication system, Band width, different type of propagation of e.m. waves.

UNIT-3

Electric current, Flow of electric charge in metallic conductor, OHM'S law,Eiectrical resistance, V-1

Characteristics, Resistors,lnductors, Capacitor, Conductor-semiconductor and insulator, Electric

potential and e.m.f., capacitance of a parallel plate capacitor,energy stored in a capacitor, carbon

resistors with colour code,series and parallel combinations of resistors and capacitors, power.

UNIT-4

Need of measurement, Fundamental and derived units,System of units, S.l. Units, Abbreviations in

powers of ten, Errors in measurement, Significant figures, Dimensions of physical quantities.

UNIT-S

Newton's first law of motion(inertia), Newton's second law of motion and momentum, Friction,

Circular motion, Motion of vehicle on levelled circular road and banked road, centripetal and

centrifugal forces.

SYLLABUS

DIPLOMA- FIRST SEMESTER

physics( common to all branches)

UNIT-1

Need of measurement, Fundamental and derived units,System of units, 5.1. Units, Abbreviations in powers of

ten, Errors in measurement, Significant figures, Dimensions of physical quantities.

UNIT-2

Electric current, Flow of electric charge in metallic conductor, OHM'S law, Electrical resistance, V-1

Characteristics, Resistors, Inductors, Capacitor, Conductor-semiconductor and insulator, Electric potential and

e.m.f., capacitance of a parallel plate capacitor, energy stored in a capacitor, carbon resistors with colour

code,series and parallel combinations of resistors and capacitors, power.

UNIT-3

Newton's first law of motion( inertia), Newton's second law of motion and momentum, Frictiori, Circular

motion, Motion of vehicle on levelled circular road and banked road, centripetal and centrifugal forces.

UNIT-4

Energy bands in solids, Semiconductors- insulators and conductors on the basis of energy bands, types of

semiconductors, Doping, P type and N type semiconductors, P-N junction, Characteristics of a P-N junction

diodes.

UNIT-S

-7 Heat transfer- conduction, convection and radiation. Pressure, viscosity, surface tension.

-?Elements of communication system, Band width, different type of propagation of e.m. waves.

,.

S. No. Chflpters

1.01 Introduction

1.02 Particle Confined in One-Dimensional Box

1.03 Particle Confined in Three-Dimensional Box

1.04 Energy Eigen Values

1.05 Quantum Mechanical Tunneling

Pages

1.0]

1:02

1.03

1.06

1.08

1.06 a-Decay: Confirmation of Quantum Mechanical Tunneling "I .13

i .07 Sommerfield's Free Electron Gas Model 1.14

1.08 Fermi Energy of a Metal

1.09 Band Theory of Solids

1.10 Kronig-Penney Model

1.11 Band Theory Predictions of Conductor,

Insulators and Semiconductor

1.12 Effective Mass

• Solved Examples

• Questions and Numerical Problems

2.01 Emission of Light

2.02 . Spontaneous and Stimulated Emission

2.03 Theory of Laser : Einstein's Coefficients

2.04 Essential Components of a Laser

1.17

1.19

1.20

1.23

1.24

1.26

1.35

2.01

2.02

2.03

2.07

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2.05 Properties of Laser

2.06 Threshold Conditim\ for Laser Action

2.07 Helium-Neon Laser

2.08 Semi-Conductor Laser

2.09 Q-Switching

2.10 Mode-Locking

2.11 Application of Laser

2.12 Difference between Photography and Holography

2.13 Theory of Holography:

2.14 Holographic Laboratory

2.15 Applications of Holography

o Solved Examples

o Questions and Numerical Problems

3.0 I Introduction

. 3.02 Coherence

3.03 Interference as a Measure of Coherence

3.04 Temporal Coi;crence as a Spectral Purity

3.05 Spatial Coherence and Size of the Source

3.06 Optical Fibre

3.07 fypes of Optical Fibre

3.08 Numerical Aperture and Maximum Angle of Acceptance

3.09 Applications of Optical Fibres

o Solved Examples

4.01

4.02

• Questions and Numerical Problems

Nuclear Radiation

Gas Filled Detectors: General Consideration

2.08

208 "' 2.10

2.LI I

2.12

2.13

2.14

2.15

2.15

2.18

2.18

2.19

2.20

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2.14

2.15

2. I 5

2.18

H

4.03

4.04

4.05

4.06

4.07

(iii)

Construction, Working and Properties oflonization Chamber 4.05

Construction, Working and Properties of Proportional Counter 4.06

Construction, Working and P~opertics ofG.M .. Counter 4.07

Construction, Working and Properties of Scintillation Counter 4.09

Dielectrics Versus Conductors

4.08 Dielectric Polarization and Breakdown

4.12

4.13

4.16

4.19

4.19

4.27

4.09 Measurement of Dielectric Constant

4. I 0 Application ofDielectrics

• Solved Examples

• Questions and Numerical Problems

5.01 Scalar and Vector Fields

5.02 Gradient of Scalar Field

5.03 Divergence of Vector Field

5.04 Curl of Vector Field

. 5.05 Gauss's and Stoke's Theorems ofVectorc

5.06 Maxwell's Equations

5.07 Gauss's Law in Electricity

5.08 Gauss's Law in Magnetism

5.09 Faraday-Lenz's Laws of Electromagnetism

5.10 Ampere's Law and Maxwell's Moditication

5.11 Wave Equations andTheir Solutions

5.12 Plane Electromagnetic Waves

5.13 Poynting Vector and Energy Flow

5.14 The Boundary Conditions

• Solved Examples

5.01

5.02

5.03

5.03

5.04

5.04

5.04

5.05

5.05

5.06

5.08

5.10

5.12

5.14

5.15

• Questions and Numerical Problems 5.23

(• Experiments [- 10 ............................................................ 1-68

··:- Glossary............................................................................. i- vi

•!• Appendix........................ ........................ ......................... i- v

SYLLABUS f4PEI(-J_

(PHYSICS) B.SC.-1

UNIT-1

Mechanics of single and systems of particles, conservation laws of

linearmomentum, angular momentum and mechanical energy, centre of mass

and equation of motion, degree of freedom.

UNIT-2

Generalised coordinates, displacement, velocity, acceleration, momentum,

force and potential. Hamilton's variation principle, Lagrange's equation of

motion from Hamilton principle,Linear harmonic oscillator, simple pendulum,

atwood's machine.

UNIT-3

Rotation of rigid body. Moment of inertia, torque, angular momentum, kinetic

energy of rotation, theorems of moment of inertia( qualitative idea),moment

of inertia of- solid sphere,hollow sphere, spherical shell, solid cylinder, hollow

cylinder, and solid bar of rectangular cross section. Acceleration of a body

rollingdown on an inclined plane.

UNIT -4 Motion and rest,

Frame of reference( inertial and non inertiai),Galilion transformations and

invariations of newtons laws,centripetal and centrifugal forces,

transformations of displacement, velocity and acceleration bet. Different frame

of refrences.

UNIT-S

Zeroth law of thermodynamics,First law of thermodynamics, work done by and

on the system,carnot cycle and its efficiency,carnot theorem and second law of

thermodynamics, practical cycles used in interna combustion engines, third

law of thermodynamics.

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PAPER II (THEORY)

UNITJ .·

Electrostatic Fieid. Vector Caieulus-gradient, divergence and Curl of a Vector (Cartesian co-ordinates) and their physical significance, Gauss's Theorem, Stoke's Theorem, derivation of field Jrom potential as gradient,

I .

derivation of Laplace and Poisson equations. EH:ctric flux density, Gauss's law and its application to a sphericaJ shell, unifonnly charged infinite plane and unfonnly straight wire, mechanicalforce of charged surface, Energy per unit Volume.

UNIT II

Electric Field in Dielectrics ...., ....,

Three Electric Vector, Polarisation Vector P, Displacement Vector D and __,

Electric intensity Vector E, and their srelation, . -7 -; ~

D = e0E + P. Electric susceptibility and relaiton K = 1 +X· Gauss's Law for dielectric,

energy stored in dre!ectrics. Steady Current. Electric current and current density, equation of

. __, .

continuity Div. J + dp!dt = 0, Resistivity and electrical conductivity, Micro-1 . . . __,

scopic form of Ohm Law J = Ecr, magnetic induction, magnetic flux, solenoidal nature of Vector field of induction. Properties of B,

__, __, ...... (i) lJ. .B :: p (i i) Ll X B = 11/·

UNIT ill

Magnetic Properties of Matter. Behaviour of various substances in magnetic field. Magnetic permeability (11) Susceptibility (X), Intensity of magnetisation (I) andtheir relations. Magnetic shell; its strength, potential of a magnetic shell (infinite planes spherical) at a point. Electronic theory of dia and para magnetisation curve, Hysteresis loss, Magnetic circuits, comparison of magnetic and electrical circuits.

UNIT IV

Electromagnetic Ind!Jction. Calculation of self-inductance of a long· solenoid. Calculation of mutual inductance of two solenoids, Energy stored in

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Unit! : Fowier Series and FourierTransfonns: Fourier analysis of com­plex wave and its application for the ~olution of triangular, and rectangular waves, half and full wave rectifier outputs, Fourier transforms, Fourier u-ansforms of

2 (i)f(x) =e-x /2 (ii)j(x) 1,1 xI< a

0,/xl>a Unit II : Matrix MethOds in l'aQxial optics :. Effect of translation and

refraction. Derivation of tltin lens and rttick lens fminulae. uiut plane, nodal planes, system of tltin lenses. Aberrations: Cluomatic, sphe1ica I, coma, astigmatism and distonion and their removal

Unit Ill : lnte1ference by Division of Wavefront : Fresnel bipristn and its applications to detrmination ·of 1.. of sodium light and thickness of a mica sheet. Lloyd rrlirror, phase dunge on retlectiotJ. Interference by Division of Amplitude : Colour of tltin films, wedge shaped fihn, Newton· s rings. lntelfcrrometers: Michelson's interferometer and its applications · to (i) standardisation of a meter Iii) detcnnination of 14.

Unit IV: Flesnel Diffraction : Fresnel's half period zones, zone plate, diffraction at a straight edge, rectangular slit and circular apc1ature. Friwnhofferdiffraction: Singleslitdifti-Jction, Two slit diffraction, N-slit diffraction, plane transmission grating spectrum, Dispersive power of grating. Limit of resolution, Rayleigh 'scriterion, Resolv­ing power of teleSj:Ope and a grating.

Unit V: Polarisation and Double Refraction : Polari?.lltion by reflection, pola!ization·by scanering, Malus, Law, Phenomenon of.doublc ref! action (nom1al and oblique:incidencc), Analysis of polarized light, Nicol pristn, Quarter wave plate and halfwave plate, Produc­tion and detection of (i) plane pola!·ized light (ii) circularly polarized light and elliptically pola!izcd light, optical activity, Flesnel's themy of rotation, specific rotation, pola!imeters (Half shade and Biquartz).

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SYLLABUS FOR B.Sc. PART II (Theory)

Electronics and Nuclear Physics

Unit I :

Unit I:

PAPER SECOND

Elementary ideas of Semi-conductors : Zener diode char­acteristics, Zener diode as voltage regulators, Mech.:nism of LED, Half and full wave rectifier-efficiency and ripple fac­tor, filter circtrits (L, C, lt), low pass and high pass RC filter analysis - amplitooe and phase response, PNP and NPN muisistor amplifier characteristics in common base; com­mon emitter and.aimmon collector configurJtions (exclud-ing h parJmeter analysis) ·

Classification of Amplifiers, concept of feed back and ad­vatage of negative feed back, circwt diagram and woricing princple ofRC-coupled amp lifer-concept of band width (No derivation), feed back in oscillaoor, tuned tranSistor oscillator & Hartley oscillatDr (basic principle only), Amplitude & Frequency modulatin, characteristics and applications.

Unit III: Strucutre of Nuclear : Structure of nuclei, properties of · nucleiandtl1eir detemnination,chargeby Moseley's law, size by a-particle scattering, mass by Bein Bridge mass spectrometer, magnetic moment by atomic beam resonance

·experiment, electric quadrupole roomcnt by Coulomb ex-citation.

Forms of nuclear· potential (sbapes and relation between nuclear potential depth and nuclear range).

·Unit IV: Interaction and Detection of Nuclear Radiations: Inter-. action of charged particles with maner, energy loss (No

derivation) and range concept, Interaction of gamma-rays with matter (qualitative description ofphotD.electric, Com­pton scattering and pair production), absorption cpefficient · of ganuna-rays and its applications. Detection of nuclear radiations using gas filled counters : Ionization, proportional and GM counlers.

Unit V: Radioactivity & Accelerators: Laws of radioactive decay, half-life and meanlife, successive decay, radioactive equi­librium conditions, age of earth using radioactive dating, basic principle of nuclear ~ccelerators :Tandem accclcratDr, Linear accelerator & cyclotron. Radiation hazard.

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Pages

181 184 186

-327

216 217

220 234

15 :l49 252 '54 .l55

256

257 261 265 266 275

280 281 2R4

288 291 294

297 298

-358

328 335 343 352 363

•Viii)

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Unit-1 :

SYLLABUS B.Sc. ParHll

Paper-1 (Theory)

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. Basic Idea of Statistical Physics : Scope if statistical Physics, Basic ideas of probability, distribution of four distinguishable panicles in two compartments of. equal size, Coneept of mac­rostates, microstates, thermodyn;unic probability, effect of con- . straints on the system, deviation fr¢m the state of maximum probability, equilibrium staie of dynamic system, distribution:of indistinguishable particles in two compartments bfinon-equal

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Classical Statistics : Phase space and its division intO elementary cells, three kinds of statistics, the basic approach to three statistics, M-B statistics and its application to an' ideal gas in equilibrium.

Unit-IT : Quantum Statistics : Need for quantum statistics, B"E statistics & derivation of Planck's law of radiation, F-D statistics, Fermi

. energy, comparison of M-B, B-E and F-D statistic~,

Stati~tical interpretation of Entropy : Statistical .definition ~f entropy, change of entropy of a system, additive' nature of entropy, law of increase of entropy, reversible and irreversible processes, examples of reversible processes, work done in a reversible process, eXl!ffiple of increase of entropy in natural processes, entropy and disorder.

Unit-ill : Classical mechanics : Mechanics of a particle, mechanics •of system of panicles, generalised co-ordinatates, ··Constraints, Hamilton's principle, Derivation br Lagran~e's equations from Hamilton's principle. Applications of Lagrange's'e(juation (a) Simple Pendulum (b) qnear Harmonic Oscillator (c) ~twood's Machine (d) Double penduiUip.

Unit-IV : Wave Mechanics : Inadequacy of old quantum iheory, wave panicle dualism, Davisson and Germer experiment, Compton scattering, wave packets,(Development of Schrodinger equation, Significance of uncertainty principle, uncertainty of position' and · momentum, Energy-time uncertainty, Illustration df lind:rtliinty principle (Diffraction of electrons and Gamma ·• Ray Micro.· scope)) · . . • .· ...

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Unit-V : Applicatibnsof Quantum Mechanics: Applications ofSchrodin­ger equation! to one dimensionaL problems -

(l) Particle in a box

(il) Potential step

(iii) Potential barrier

(iv) Simple Harmonic oscillator with special emphasis to the concept of ground s~te energy, oscillator eigen functions.

(v) Rectangular potential well.

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SYLLABUS ?aper • II (Theory)

Un•t-I : Vec!or M:xlel aud Spectra of Alkali Metals : Ve::r.or &tom modei (concept of the spiuning .electr:>n and spatial Quami:u.­tion, Quantum numbe;-s associated with the ;-e.ctor 2tr>rn mode'). peoetratir.g and non-penetratin:; orbits (QualitNive descciption) spectral lines in different series of alkali spectra, spin orbit ime:acti<>n md doublet terre separation, :..s or Russel-saunder coupli~g. coupling, Is coupling, jj coupling (Expressions foe interact;on eucrgies (r Factors) for Is and jj coupling required).

Unit-JJ _ A!cm ;_nan Extemal Force Fielc:l.·: Z~emen effe~t (Normal an<! Anomalous and Paschen Back ~ffecc of one valence electron system tosing vector etom model, S:an -effect of hyamgcn ato!ll (Mat:1ematical treatment not required), Hyperfine structure of spectra a:Jd its origiil (simpie Qualitative ideas only).

Uni~-Ill : SoEd Sta:e Physics : Crystallir.e state, Bravais 1at:ices in two and :hre<. dimer.sions, Miller indice,;, X-ray diffraction (Bragg's law) Reciprocal Lattice, and its physical s;gnificance, Recipro. cal Latti~e vectors, (Anclysi~ of diffraction onditions in terms of Recip;ocallattic.e vectors not reqmred), Recipwc;;J lattice ro a simple cubic iat!ice spec:fic heat of soEds, Einstein's thtory of specific heat, Debye model of specific neat of solids.

Unit."tV : EJemer.ts of Laser : Main features of P Laser, direct'onlility, high in<ensity, monochromaticity, high det:ree oc ~oherenc~. SpatiJ.I and temporal coherence, Einst~in coefficients and pos· sibJ~ity or amplification, Momeutum tnmsfer. lJfe lime of a level, Ki~etics of opticJ.! absorption.

B'ISic P r;nciples of Lasers : Threshold :conditkn and f1urr.ping, He-Ne and r.UBY Laser {Plinciple, CO%lrU("tion and working), Somicor.ductor La>ers : Main teaturos a;rd C<'nG.itions of laser action.

i.Jnii-V : Nuclear Phy.,icc : Energetics of alpha decay, e).)l"rimental informations on alpha de-;ay- Node;~r stabili:)', Decay mecha­msm and fine strucutre. Type oi beta energetics, neutri~o

hypothesis, :2nergetics of gamo::. decey and recc il effects.

Nuclero.· reactions, conservation Jaws, Q-value and reaction threshold, Nuclear fission and fusion reactor" (Basic ;>rincipie, construction, working a.'ld uses}.

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PAPER-I: CLASSICAL MECHANICS

Max. Marks: 30 Duration 3 Hrs.

Note: In all jive questions are to be sel. Four quesrions will be our oft he four unir taking one queslionfrom eve!Ji unir with 100% imerna/ choice. One queslion will be of short answer type covering en/ire course wilh no choice. The candid ales will be required to a!/empt alii he five questions.

l. Holonomic and non-holonomic constraints: D- Alembert's Principle, Generalized coordinates, lagrangian, lagrange's equation and its applications, velocity dependent potential in lagrangian formulation. Generalized momentum, legendre tr andformation, Hamiltonian, Hamiltonian's canonical Equation.

2. Calculus of variational principal, derivation of lagrange's and Hamilton,. Canonical equation from Hamilton's variational principal. Extension of Hamilton's Principle for nonconservative and nonholonomic systems, Method of lagrange's multipliers, conservation principle and Noether's theorem. Conservation of energy, linear momentum and angular momentum as a consequence ofhomogencity of time and scope and isotropy of space respectively.

3. Canonical transformation, integral invariant of poincare: Lagrange's and Poisson brackets as canonical invariants, equation of motion in Poisson bracket formulation. Infinitesimal contact transformation and generators of symmetry, Louvilee's theorem, Hamilton-Jacobi equation and its application.

4. Action angle variable adiabatic invariance of action variable: The Kepler problem in action angle variables, theory of small oscillation in Lagrangian formulation, normal coordinates and its applications. Orthogonal transformation, Euler's theorem, Eigenvalues of the ine11ia tensor, Euler equations, force free motion of a rigid body.

Reference Books:

I. Goldstein- Classical Mechanics 2. Landau and Lifshitz- Classical Mechanics 3. A. Raychoudhary- Classical Mechanics

PAPER-II: MATHEMATICAL PHYSICS

Max. Marks: 3 Duration 3 Hrs .

Note: In all five questions are to be set. Four question will be our of the four unit taking one ques!ionfrom every unit with 100% internal choice. One question will be of short answer type covering em ire course with no choice. The candidates will be required to a/lempt all the five questions.

l. Coordinates Transformation inN - dimensional space: Contravariant and covariant tensor, Jacobian. Relative tensor, pseudo tensors (Example: charge density, angular momentum) Algebra of tensors, Metric tensor, Associated tensors, Riemann space (Example: Euclidean space and 4D Mankowski space), Christoffel S)~nbols, transformation of Christoffel symbols, covariant differentiation, Ricci's theorem, divergence, Curl and Laplacian tensor form, Stress and strain tensors, Hook's law in tensor form. lorentz covariance of Maxwell equation, Klein Gordon and Dirac Equation, Test of covariance of schroodinger equation.

2. Group of Transformation: (Example: S:mmetry transfonnation of square) Generators of a finite group, Normal subgroup, Direct product of groups, Isomorphism and Homomorphism. Representation theorem of finite groups, Invariants subspace and reducible representations, irreducible representation, crystallo-graphic point groups·, Irreducible representati-on ofC,v. Translation group and the reciprocal lattice.

3. Fourier Transforms: Development of the Fourier integral from the Fourier Series, Fourier and inverse Fourier transform: Simple Applications: Finite wave train, Wave train with gaussian amplitude, Fourier transfonn of derivatives, solution of wave equation as an application. Convolution theorem. Intensity in terms of spectral density for quasi monochromic EM Waves, Momentum representation, Application of Fourier transform to diffraction theory: diffraction pattern of one and rwo slits.

4. Laplace transforms and their properties, Laplace transform of derivatives and integrals, derivatives and integral of Laplace transfonn. Convolution theorem. Impulsive function, Application of Laplace transform in solving linear, differential equations with constant coefficient with variable coefficient and linear partial differential equation.

Reference books:

1. Mathematical Methods for Physicists: George Arfken (Academic Press) 2. Applied Mathematics for Engineers and Physicists: L.A. Pipe (McGraw Hill) 3. Mathematical Methods- Potter and Goldberg (Prentice Hall of India) 4. Elements of Group Theory for Physicists: A.W. Joshi (Wiley Eastern Ltd.) 5. Vector Analysis (Schaum Series) (McGraw Hill)

PAPER III: QUANTUM MECHANICS

Max. Marks: 30 Duration 3 Hrs.

Note: In all jive questions are 10 be set. Four question will be out of the four unit taking one question from eve1:v unit wi1h 100% imernal choice. One question will be of short answer type covering entire course with no choice. The candidates wi/1 be required to a/lempt all the jive questions.

l. (a) States, Amplitude and Operators: States of a quantum mechanical system, representation of quantum-mechanical states, properties of quantum mechanical amplitude, operators and change of a state, a complete set of basis states, products of linear operators, language of quantum mechanics, postulates, essential definitions and commutation relations. (b J Observables and Description of Quantum system: Process of measurement , expectation values, time dependence of quantum mechanical amplitude, observable with no classical analogue, spin dependence of quantum mechanical amplitude on position, the wave function, super position of amplitudes, identical particles.

2. Hamiltonian matrix and the time evolution of Quantum mechanical States: Permittivity of the Hamiltonian matrix, time independent perturbation of an arbitrary system, simple matrix examples of time independent perturbation, energy given states of a two state system, diagonalizing of energy matrix, time independent perturbation of two state system the perturbative solution: Weak field and Strong field cases, general description of two state system,Pauli matrices, Ammonia molecule as an example of two state system.

3. Transition between stationary States: Transitions in a two state system, time dependent perturbations - The Golden Rule, Phase space, emission and absorption of radiation, induced dipole transition and spontaneous emission of radiation energy width of a quasi stationary state. The co-ordinate Representation: Compatible observables, quantum conditions and uncertainty relation, Coord in ate representation of operators, position, momentum and angular momentum, time dependence of expectation values, The Ehernfest Theorem, the time evolution of wave function, the schroedinger equation, energy quantization, periodic potential as an example.

4. Symmetries and Angular Momentum: a. Compatible observables and constants of motion, symmetry transformation and

conservation laws, in variance under spaceand time translations and space rotation and conservation of momentum, energy and angular momentum.

b. Angular momentum operators and their Eigenvalues, matrix representations of the angular momentum operators and their eigenstates, coordinate representations of the orbital angular momentum operators and their eigen state (Spherical Harmonics), composition of angular momenta, Clebsch-Gordon Coefficients tensor operators and Wigner Expait theorem, c commutation relations, of J ,. J y,J, with reduced tensor operator, matrix elements of vector operators, time reversal invariance and vanishing of static electric dipole moment of stationary state.

Reference Books:

I. Ashok Das and A. C. Mel issions: Quantum Mechanics -A modern approach (Gordon and Breach Science Publishers).

2. P.A.M. Dirac, Quantum Mechanics. 3. E. Merzbecher: Quantum Mechanics, Second Edition (John Wiley and sons) 4. L.P. Landau and E.M. Lifshitz, Quantum Mechanics- Relativistic theory (Pergamon

Press) 5. A. Ghatak and S. Lokanathan: Quantum Mechanics- Theory and Applications, Third

Edition (Mac. Millan, India Ltd.

PAPERIV:ELECTRONICS Max. Marks: 30 Duration 3 Hrs.

Note: In all five ques!ions are to be set. Four question will be au/ oft he four uniltaking one question ji-om evety unil with 100% internal choice. One question will be of short answer type covering en/ire course with no choice. The candidates will be required to a/tempt all the five questions.

1. Operational Amplifiers: Differential amplifier- circuit configurations- dual input, balanced output differential amplifier, DC analysis- AC analysis,inverting and non inverting inputs, CMRR­constant current bias level translator. Block diagram of typical OP-Amp analysis. Open loop configuration, inverting and noninverting amplifiers, Op-Amp with .negative feedback, voltage series feedback, effect of feed back on closed loop gain, input resistance, band with and output offset voltage­voltage follower. Practical Op-Amp input offset voltage~input bias current-input offset current, total output offset voltage, CMRR frequency response. DC and AC amplifier. integrator and different iator.

2. Oscillators and wave shaping Circuits: Oscillator Principle- Oscillator types, Frequency stability response, the phase shift oscillator, We in bridge oscillator. LC tunable oscillators, Multivibrators-Monostable and

Astable, Comparators, Square wave and triangle wave generation, clamping and clipping. Voltage regulators- fixed regulators, adjustable voltage regulators, switching regulators.

3. Digital Electronics: Combinational logic: The transistor as a switching, circuit realisation of OR, AND, OR, NOR, NAND gates, Exclusive OR gate, Boolean algebra- De-morgan Theorenis, Adder, subtracter, comparator, decoder/Demultiplexer Data selector/multiplexer, encoder. Sequential Logic: Flip-Flops: one- bit memory, the RS flip-flop, J flip flop, JK master slave flip-flops, T flip-flop, D flipflop, shift resisters- synchronous and asynchronous counters, cascade counters, Binary counter, Decade counter. Basic concepts about fabrication and characteristics of integrated circuits.

4. Microprocessors: . Introduction to microcomputers: memory- input/output- interfacing device 8085, CPU­Architecture- BUS timings- Demultiplexing the address bus generating control signals­Instruction set- addressing modes- Illustrative programmes- writing Assembly language programmes looping, counting and indexing - counters and timing delays - stack and subroutine.

Text and Reference Books:

I. "Electronic Devices and Circuit Theory" by Robert Boylested and Louis Nashdsky, PHI, New Delhi -110001,1991.

2. "OP-AMP and Linear Integrated Circuits" by Ramakanth, A. Gayakwad, PHI, Second Edition I 991.

3. "Digital Principle and Applications" by A.P. Malvino and Donald P. Leach, Tata McGraw Hill Company, New Delhi, 1993.

4. "Microprocesso'rs Architecture, Programming and Applications with 8085/8086" by Ramesh S Gaonkar, Wiley- Eastern Ltd., 1987.

PAPER V: CLASSICAL ELECTRODYNAMICS

Max. Marks: 30 Duration 3 Hrs.

Note: in all five queslions are 10 be set. Four question will be out of the four unil taking one questionji-om eve1y unit with 100% internal choice. One question will be of short answer type covering em ire course with no choice. The candidates will be required to allempl a lithe five queslions.

I. Electrostatics: Electric field, Gauss Law, Differential form of Gaussian Jaw. Another equation of electrostatics and the scalar potential, surface distribution of charges and dipoles and discontinuities in the electric field and potential, Poisson and Laplace equations, Green's Theorem, Uniqueness of the solution with the Dirchlet or Neumann boundary Conditions, Fonnal Solutions of electrostatic Boundary value problem wit Green's function, Electrostatic potential energy and energy density, capacitance.

Boundary Value Problems in Electrostatics: Methods of Images, Point charge in the presence of a grounded comducting sphere, point charge in the presence of a charged insu Ia ted conducting sphere, point charge near a conducting sphere at a fixed potential, conducting sphere in a uniform electric field by method of images, Green function for the sphere, General solution for the potential, conducting sphere wit hemispheres at a different potentials, orthogonal functions and expansion.

2. Multipoles, electrostatics of Macroscopic Media Dielectric:Multipole expansion, multipole expansion of the energy of a charge distribution in an external field, Elementary treatment of electrostatics with permeable media. Boundary value problems with dielectrics. Molar polarizability and electric susceptibility. Models for molecular polarizability, electrostatic energy in dielectric media.

3. Magnetostatics: Introduction and defi11ition, Biot and Savart Law, the differential equations ofmagnetostatics and Ampere's Jaw, Vector potential and magnetic induction for a current loop, Magnetic fields of a localized current distribution, Magnetic moment, Force and torque on and energy of a localized current distribution in an external induction, Macroscopic equations, Boundary conditions on Band H Methods of solving Boundary value Problems in magnetostatics, Uniformly magnetized sphere, magnetized sphere in an external fields, permanent magnets, magnetic sheilding, spherical shell of permeable material in an uniform field.

• Time varying fields, Maxwell's equations conservation Jaws:Energy in a magnetic field, vector and scalar potentials, Gauge transformations, Lorentz gauge, coloumb gauge, Green function for the wave equation, Derivation of the equations of Macroscopic Electromagnetism,Poynting's Theorem and conservation of energy and mom~ntum for a system of charged particles and-EM fields. Conservation Jaws for macroscopic media. Electromagnetic field tensor, transformation of four potentials and four currents, tensor dissipation of Maxwell's equations.

Reference Books:

l. J.D. Jackson: Classical Electrodynamics 2. Panofsky & Phillip: Classical electrodynamics and magnetism 3. Griffith: Introduction to Electrodynamics 4. Landau & Lifshitz: Classical Theory of Electrodynamics 5. Landau & Lifshitz: Electrodynamics of continuous media 6.

Msc Physics Final

PAPER. VI: NUMERICAL METHOD AND COMPUTER PROGRAMMING

Max.Marks : l 00 Duration : 3hrs.

Five question are to be set taking one from each unit (each question will have an·internal choice). Student will attempt all the five question. 40% weightage will be given to problem and numericals.

UNIT- I

l. Operational Amplifiers: .Differential amplifier- circuit configurations-dual inpu~ balanced output differential amplifier. DC analysis- AC analysis, inverting and nonninverting inputs, CMRR- constant current bias level translator. Block diagram of a typical Op-Amp-analysis.Open loop configuration,inverting and non­inverting amplifiers.Op-amp with negative feedback- voltage series feed back -effect of feed back on closed loop gain, input rersistence, output resistance, bandwidth and output offset voltage- voltage follower. Practical op-arnp-input offset voltage -input bias current -input offset current, total output offset voltage, CMRR frequetency response. DC and AC amplifier, summing, scaling and averaging amplifiers, instrumentation amplifier, integrator and differentiator.

Ul'I'IT- ll Oscillators and Wave Shaping Circuits: Oscillator Principle- Oscillator types, Frequency stability, response, The Phase shifi oscillator, Wein bridge OScillator,LC tunable oscillators, Multivibrators-Monostable and Astable, Comparators, Square wave and Triangle wave generation, Clamping and Clipping.

Voltage regulators- fixed regulators, Adjustable voltage regulators, Switching regulators. UNIT- III

Digital Electronics: Combinational Logic :The transistor as a.switch;circuit Realisation of OR,AND,NOT, NOR and NAND gates, Exclusive OR gate, Boolean algebra- Demorgan's theorems Adder, Subtractor, Comperator. Decoder I Demultiplexer ,Data selector/ multiplexer­Encoder. Sequential Logic: Flip -Flops: one-bit memory; The RS Flipflop, JK Flip- Flop, JK master slave Flip -Flops, T Flip -Flop, D Flip- Flop, Shifi resisters- syncronous and asynchronous counters-

cascade counters)Binary counter, Decade counter. Basic concepts about fabrication and characteristics of integrated circuits.Fortran 77: Variable, Expression, jumping. Bracching an looping statement ,Input I Output statement Statement for handling Input I Output Files, Subroutine, External, Function ,Special statements ,COMMON,ENTR Y FORMA T,PA USE,Equvalence . Programming of simple problems involving use of interpolation differentiation, Integration, matrix inversion and least square analysis.

UNIT-IV

Errors in numerical analysis: Source of error, Round off error, Computer Arithmetic, Error Analysis, Condition and stability,Approximation, Functional and Error analysis, the method of, Undetermined Coefficients. Use of interpolation formula, Iterated interpolation. Inverse interpolation,Hannite interpolation and Spline interpolation, Solution of Linear equations, Direct and Iterative methods, Calculation of eigenvalue and eigenvectors for sysmmetric matrices. Solution ofNonliner equation: Bisection method, Newton's method,.modified Newton's method, method of Iteration, Newton's method and method of iteration for a system of cosuation Newton's method for the case of complex roots.

UNIT-·V Integration of a function: Trapezoidal and Simpson's rules. Gaussian quadrature formula, Singular integrals, Double integration. Integration of Ordinary differential equation: Predictor- corrector methods, Runga-Kutta method, Simultaneous and Higher order equations Numerical Integration and Differentiation of Data, Least-Squares Approximations, Fast FourierTransfonn .. Some elementary information about Computer: CPU, Memory, Input/ Output devices, Super, Mini and Micro systems, MS-DOS operating system, High Level Languages, Interpreter and Compiler. Programming: Algorithm and Flowchart.

Reference Book I. Ryder-Electronic Fundamentals and applications. 2. Millman and Thub-Pulse, Digital and Switching waveforms. 3. Millman and Helkias-lntegrated Electronics. 4. Ryder-network Lines and Fields. 5 Bapat-Eiectronics Devices and Circuitrs. 6. A Ralston and P. Rabinowitz, A First Course in Numberical analysis Me Graw Hill (1985) 7. S.S. Sastry, Introductory Methods ofNumerical Analysis. Prentice hall of India (1979). 8. Ram Kumar, Programming with Fortran 77, McGraw-Hill (1986). 9. "Eiectronic'Devicesand circuit theory by Robert Boylested and Louis Nashdsky PHI, New Delhi. 1100001,1991. JO."OPAmps& Linear integratedcircuits, by Ramakanth A. Gayakwad PHI, Second Edition, 1991. II. Digital principles and Applications by A.P. Malvino and Donald P.Leach, Tata Megraw­Hill company, New Delhi, 1993.

12. Microprocessor Architecture, Programming and applications with 8085/8086 by Ramesh S. Gaonkar, Wiley- Eastern Ltd., I 987.

PAPER -VII: ATOMIC AND MOLECULAR PHYSICS

Max.Marks :I 00 Duration : 31m.

Note: Five qustion are to be set taking one from each unit (each question will have an internal choice).Student will attempt all the five question 40% weightage will be given to problems and numericals.

UNIT-I

States, Amplitudes and Operators: States of a quantum mechanical system, representation of quantum,- mechanical states, properties. of quantum mechanical amplitude;operators and change of state, a complete set of basis states,.products of linear operators, language of quantummechanics, postulates, essential definitions and commulation relations.

Obsen·able and description of system: Process of measurement,expectation values,time . dependence of quantum mechanical amplitude, observables with no classical anal.ogue, spin. dependence of quantum-mechanical amplitude on position. the v>•ave fimction, super-position of amplitudes, identical particles. The Co-ordinate Representation: Compatible observables, quantum conditions and uncertainty relation, Co-ordinate representation,of operator&; position,momentum and angularmomentum,. time dependence[ of expectation values, the Ehrenfest's theorem: the time evolution of wave. function, the Schrodinger equation, energy quantization, ,periodic potential as an example.

UNIT -II

Symmetries and-Angular momentum: (a) Compatible observables and constants of motion, symmetry' transfonnation and conservation laws, invariance,under space and time translations and space rotation and conservations of momentum, energy and angular momentum.

Angular momentum operators and, their eigen values, matrix representations of the angular momentum operators and their eigenstates, co-ordinate representations of the orbital angular momentum operators and their eigenstate (spherical harmonics), composition of angular momentum, Clebsch- Gordon coefficients tensor operators anq Winger Ex part theorem, commutation relations, of Jx, Jy, Jz with reduced spherical tensor operator, matrix elements of vector operators, time reversal invariance and vanishing of static electric dipole moment of a stationary state.

UNIT- III

Hamiltonian matrix and the time evolution of Quantum mechanical States: Hemriticity of the Hamilionian matrix, Time independent perturbation of an arbitrary system, simple matrix examples of time-, independent perturbation, energy given states of a two state system, diagonalizing of energy matrix, time independent perturbation of two state system the perturbative solution: Weak field and strong field cases, general description of two state system.

Pauli matrices. Ammonia molecule as an example of two state system. Interaction with External Fields: Non degenerate first order stationary perturbation method, atom in a weak uniform external electric field and first and second order Stark effect, calculation of the polarizabi lity of the ground state of H-atom and of an isotropic harmonic osciJiator, Degenerate stationary perturbation theory. Linear Stark effect for H-atom levels, inclusion of spin-orbit and weak magnetic, field, Zeeman effect, strong magnetic field and calculation of interaction energy.

UNIT-IV Transition Between Stationary States: Transitions in a two state system, Time independent perturbations-The Golden rule, phase space, emission and absorption ofradiation,induced dipole transition and Spontaneous emission. of radiation. energy width of a quasi stationary state. Systems with Identical Particles: lndistinguish ability and, exchange symmetry, many particle wave functions and Pauli's exclusion principle, spectroscopic terms for atoms. The Helimn atom, Variational method and its use in the calculation of ground state and excited state energy, Helimn atom. The Hydrogen molecule, Heitler-London method for molecule, WKB method for one

. dimensional problem, application to bound states (Bohr-Sommerfield quantization) and the barrier penetration (alpha decay, problems.

UNIT- V Hyd rogenAtom : Gross structure energy spectnuil, probability distribution of radial and angular (I=J ,2) wave .functions (no derivation), effect of spin, relativistic correction to energy levels and fine structure,magnetic dipole interaction and hyperfine structure, the Lamb shift (only an qualitative description) Spectroscopy(qualitative) : General features of the spectra of one and two electron system­sin.gletdoublet and triplet characters of emission spectra,general features of Alkali spectra, rotation and vibration band spectrum of a molecule, PQ and R branches, Raman spectra for rotational and vibrational transitions,comparison with infra red spectra. general features of electronic spectra. Frank and Condon's principle.

ReferenceBooks:

I. Ashok Das and A. C. Melissionos. Quantum Mechanics-A modern Approach (Gordon and Breach Science Publishers). 2. P.A.M.Dirac, Quantum Mechanics. 3. E. Merzbaker. Quantum Mechanics, Second Edition (John Wiiley and Sons). 4. L.P.Landau aridH.I\1. Lifshitz, Quantum Mechanics-Non relativistic theory (pergamon Press) 5. A .. Ghatak and S. Lobnathan.- Quantum Mechanics: Theory and, Applications, Third Edition(Mac Millan India Ltd.), 6. G. K. Woodgate,EiementaryAtomic Structure, Second Edition Clarendon Press, Oxford. 7. T.A. Littlefield- Atomic and Molecular Physics. 8. Eistanberg and Rasmik-QuantumPhysicsof Atoms. Mo.lecules, Solids and Nuclear Particles. 9. White- Atomic Spectra. I 0 .Herzberg- Molecular Spectra.

..

PAPER-VIII: STATISTICAL AND SOLID STATE PHYSICS Max.Marks.: 100 Duration : 3hrs. Note: Five question are to be set taking one from each unit( each question will have an internal choice).Student will attempt all the five questions. 40% weightage will be given to problems and numericals.

UNIT-I

Basic Principles, Canonical and Grand Canonical ensembles: Concept of statistical distribution, phase space, density of states, Liouville's theorem, systems and ensemble, entropy in statistical mechanics Connection between thermodyanic and statistical quantities micro canonical ensemble, equation of state, specific heat and entropy of a perfect gas, using micro canonical ensemble.

Canonical ensemble, thermodynamic functions for the canonical ensemble, calculation of mean values, energy fluctuation in a gas, grand Canonical ensemble, thermodynamic functions for the grand canonical ensemble, density fluctuations.

UNIT- II

Partition functions and Statistics: Partition functions and Properties, partition function for an ideal gas and calculation of thermodynamic quantities, Gibbs Paradox, validity of classical approximation, determination of translational, rotational and vibrational contributions to the partition fimction of an ideal diatomic gas. Specific beat of a diatomic gas, ortho and para hydrogen.

Identical particles and symmetry .requirement, difficulties with Maxwell-Boltzmann statistics,quamum distribution functions, Bose-Einstein and Fermi-Dirac statistics, Boson statistics and Planck's fonnula, Bose Einstein condensation, liquid He as a Boson system, quantization ofhannonic oscillator and creation and annihilation of Phonon operators, quantizarion of fermion operators.

Ul'HT-lll

Band Theory: Block theorem, Kronig Penny model, effective mass of electrons, Wigner-Seitz approximation, NFE model, tight binding method and calculation of density for a band in simple cubic Janice, pseudo potential method.

Semiconductors: Jaw of mass action, calculation of impurity conductivity,ellipsoidaJ energy surfaces in Si and Ge, HaJJ effect, recombination mechanism, optical transitions and Schockely­Read theory excitons, photoconductivity, photo-Luminescence.Points line, planar and bulk defects, colour centres, F-centre and aggregate centresin alkali halides.

UNIT- IV

Theory of Metals: Fermi- Dirac distribution function, density of states, temperature dependence of Fermi energy, specific heat, use of Fermi.

Dirac statistics in the calculation ofthennal conductivity and electrical conductivity, Widemann -Franz ratio, susceptibility, width of conduction band, Orude theory of light, absorption in metals.

Lattice Vibratuibs and Thermal Properties: Interrelations between elastic constants Cl 1, Cl2 and C44 wave propagation and exparimental determination of elastic constant of cubic crystal, vibrations of linearmono and diatomic lattices, Detennipation of phonon dispersion by inelastic scattering of neutrons.

UNIT- V

Magnetism: Larmor diamagnetism.Paramagnetism,Curie Langevin and Quantum theories. Susceptibility of rare earth and transition metals. Ferromagnetism: Domain theory, Veiss molecular field and exchange,spin waves: dispersion relation and its experimental determination by inelastic neutrons scattering, heat capacity. Nuclear Magnetic resonance: Conditions of resonance, Black equations. NMR-experiment and characteristics of an absorption line. Superconductivity: (a) Experimental results: Meissner effect, heat capacity, microwave and infrared properties, isotope effect, flux quantization, ultrasonic attenuation, density of states, nuclear spin relaxation, Giver and AC and DC Josephson tunnelings. (b) Cooper pairs and derivation ofBCS Hamiltonian, results ofBCS theory (no derivation).

Reference Books: l.Huag : Statistical Mechanics 2. Reif: Fundamentals of Statistical and Thermodynamical Physics 3. Rice: Statistical mechanics and Thermal Physics 4. Kittle: Elementary statistical Mechanics 5. Kittle: Introduction to Solid State Physics 6. Patterson:'Solid State Physics 7. Levy: Solid State Physics 8. Mckelvy: Solid State and Semi-conductor Physics.

Max. Marks : J 00

Note: Five question are to be set taki choice).Student will attempt all the fiv numericals.

Duration : 3hrs.

one from each unit( each question will have an internal questions. 40% weightage will be given to problems and

UNIT-I

I. Introduction to microwaves and its fr quency spectrum, Application of microwaves. Wave guides: (a) Rectangular wave gui es: Wave Equation & its solutions,TE&TM modes.Dominan tmode and choice ofw ve guide Dimensions Methods of excitation of wave guide. (b) Circular ,;,ave guide-wave equation its solutions, TE, TM & TEM modes. (c) Attenuation - Cause of attenuation in 1 .ave guides. wall current & derivation of attenuation.

I - . constant, Q of the wave guide. 1 2. Resonators: Resonant Modes of rectangular and cylindrical cavity resonators, Q of the cavity resonators, Excitation techniques, Introduction to Microstrip and Dielectric resonators, Frequency meter.

UNIT- II

3. Farrites: Microwave propagation inferrites, Far~~. rotation, Devices employing Faraday rotation (isolator. Gyrator, Circulator). Introduction to ~ngle crystal ferromagnetic resonators, YIG tuned solid state resonators. , · 4. Microwave Measurement: \ (a) Microwave Detectors: Power, Frequency, Attenuatio$, Impedance Using smith chart, VSWR. Reflectometer. Directivity, coupling using direction coupler. . (b) Complex pennittivity of material & its measurement:idefinition of complex of Solids, liquids and powders using shift of minima method. ·

UNIT- III 3. Microwave tubes: Spacecharge spreadingofan electronbeam, Beam focussings. Klystrons: Velocity Modulation, Two Cavity Klystron, Reflex Klystron Efficiency of Klystrons. Magnetrons: types & description, Theoretical relations •between Electric & Magnetic field of oscillations. Modes of oscillation & operating characteristics. Gyrotrons: Constructions of different ,Gyrotrons, Field. -Particle Interaction in Gyrotron.

UNIT- IV i

6. (a) Avalanche Transit Time Device:Read Diode, N ~ative resistance of an avalanching p-n Junction diode JMPA TT and TRAP A TT Oscillator. (b) Transferred Electron Device: Gunn effect, two vel ey, model, High field Dotrutins, Different Modes for Microwave generation. (c) Passive Devices: Termination (Short circuit and tched tenninations) Attenuator, phase changers, E&H plane Tees, Hybrid Junctions. Directi nal coupler. ?.Parametric Amplifier: Varactor, Equation of Cap citance in Linearly graded & abrupt p­njun.ction, Man ely Rowe relations, parametric upcoll/"ertor and Negative resistance parametric amplifier,-use of circulator, Noise in parametric amplifiers.

· UNIT-"\!' 8. Microwave Antennas: Introduction to antenna pa~ameters, Magnetic Currents, Electric and magne* current sheet, Field ofHuygen's source, Radiation from a slot antenna, open end of a wave f!Uide and Electromaf'Jletic Horns. PraboJic refl~ctors. Lens antennas. . Radiation fields of Microstrip wave guide, Microstri* wave gUJde, M1crostnp antenna calculations, Microstrip design formulas. I 9. Microwave Communication: (a) LOS microwave systems, Derivation of LOS communication range, OTH microwave systems, DeriVation of field strength of tropospheric ~aves,. Transmission interference and signal damping, Ductpropagation. / (b) SateJJite Communication: Satellite frequencies aliocation, Synchronous satellites,Satellite orbits, Satellite location with respect to earth and look angle, earth coverage and slant range, Eclipse effect, Link calculation, Noise consideration, Factors affecting satellite communication. Reference Books: I. Electromagnetic waves & Radiating Systems: Jorden & Balmain. 2. Theory and application of microwaves by A.B. Brownwell & RE. Beam (McGraw Hill). 3. Introduction to microwave theory by Atwater (McGraw Hill). 4. Principles of microwave circuit by G.C. Montgomery (Me Graw HiJJ) 5. Microwave Circuits & Passive Devices by M.L. Sisodia and G.S. Raghuvanshi (New Age lnteniational, New Delhi) · 6. Foundations of microwave engineering by RE. Collin. (McGraw Hill). 7. Microwave Semiconductor Devices and their Circuit applications by H.A. Watson

I 8. Microwave by M.L. Sisodia and Vija~ Laxmi Gupta. New Age, New Delhi. 9. Antenna Theory, Part-) by RE. Collin\& EJ. Zucker (McGraw Hill, New York) I O.Microstrip Antennas by Bah I & Bharliya (Artech House, Messachausetts) I I. Antenna Theory Analysis by C. A. B~Ianis Harper & Row. Pub. & Jnc. New York. 12. Antenna Theory Analysis by E.A. vJo1 '"'(J. Willey & Sons)

' 13. Antenna Theory & Desie:n by RS Elliott (LPHJ Ltd. New Delhi) I 4. Microwave electronics b)• RE Sooh,bo (Addisen Westey pubblic company,). I 5.Microwave Active Devices, VacuoJms by M.L Sisodia new Age lntemational New Delhi. I 6. Semiconductors & Electronics dev(ce by A. Barle vs (PHI, India). I 7. Solid State physical electronics by t>..Vanderziel, (PHI, India). I 8. Hand book of microwave measurefent Vol-ll by M. Sucher & J.Fox (pol}1echnic Press,

New York). f 19. Microwave devices& circuits by .Y.Liao(PHI, India). 20. Microwave Principles by H.J. Rei h (CBS). 21. Simple microwave technique for feasuring the dielectric parameters of solids & their powder by J.M. Gandhi, J.S. Yadav, r of pure & applied physics Vol. 30, pp-427431, 1992.

PAPER -IX: CLASSICAL ELECTRODYNAMICS Max.Marks :I 00 Duration : 3hrs.

Note: Five question are to be set taking one from each unit (each question will have an internal choice). Student will attempt all the five question. 40% weightage will be given to problem and numericals.

Unit- I

1. Electrostatics: Electric field; Gauss Jaw, Differential form of Gauss Jaw. Another equation of electrostatics and the scalar potential, surface distribution of charges and dipoles and discontinuties in the electric field and potential, Poisson and-Laplace equations, Green's Theorem, Uniqueness of the solution with Dirichlet or Neumann Boundary conditions, Fomal solution of Electrostatic Boundary value problem with Green's Function. Electrostatic potential energy and energy density, capacitance. Boundary- Value'Problems in Electrostatics: Methods of Images, Point charge in the presence of a grounded conducting sphere point charge in the preseqce of a charge insulated conducting sphere, Point charge near a conducting sphere at fixed potential, conducting sphere in a unifonn electric field by method of images, Green function for the sphere, General solution for the potential, Conducting sphere with Hemispheres at different potential, orthogonal functions and expanswn.

Unit- II

2. Magnetostatics: Introduction and defmition, Biot, and Savart law, the differential equation of magnetostatics and Ampere's law, Vector potential and Magnetic induction for a circular current loop, Magnetic fields of a localized current distribution, Magnetic moment, Force and torque on and energy of a localized current distribution in an external magnetic induction, Macroscopic equations. Boundary conditions_ on Band H. Methods of solving Boundary-value problems in magnetostatics, Unifonnly magnetized sphere, Magnetized sphere in an external field, Permanent magnets, Magnetic shielding, spherical shell of permeable material in an unifonn field.

Unit- III

3. Multipoles, Electrostatics of Macroscopic Media Dielectrics: Multiple expansion, multipole expansion of the energy of a charge distribution in an external field, Elementary treatment of electrostatics with permeable media, Boundary value problems with dielectrics. Molar polarizability, and electric susceptibility. Models for molecular polarizability, Electro-static energy in dielectric media .. 4. Time varying fields, Maxwell's eqllations Conservation Laws:Energy in a magnetic field, Vector and Scalar potentials. Gauge transformations, Lorentz gauge, Coulomb gauge, Green functions for the wave equation, Derivation of the equations of Macroscopic Electromagnetism, Poyntings theorem and conservations of energy and momentum for asystem of charged particles. and EM fields. Conservation Jaws for macroscopic media. Electromagnetic field tensor. Transformation of .four ,potentials.and four currents. Tensor description of Maxwell's equation.

Unit- IV

5. Plane Electromagnetic Waves and Wa\'e Equation :Plane wave in a nonconducting medium. Frequency dispersion characteristics ofdielecttics, conductors and plasmas, waves in a conducting or dissipative medium, superposition of waves in one dimension,group velocity,casualty connection between D and E. Kramers-Kroning relation .. 7. Covariant Form of Electrodynamic Equations :Mathematical properties of the space-time special relativity,Jnvariance of electric charge covariance of electrodynamics, Transformation of electromagnetic fields.

Radiation by moving.charges: Lienard-wiechert Potentials for a point charge, Total power radiated by an accelerated charge ,Larmour's formula and its relativistic generalization, Angular distribution of radiation emitted by an accelerated charge, Radiation emitted by a charge in arbitrary extremely relativistic motion. Distribution in frequency and angle-of energy radiated by accelerated charges, Thomson scattering and radiation, Scattering by quasi free charges, coherent and incoherent scattering, Cherenkov radiation. 7. Magnetohydrodynamics and Plasma Physics: Introduction and definitions, MHD equations Magnetic diffusion viscosity and pressure; Pinch effect instabilities in a pinched plasma column. Magnetohydrodynamic waves; Plasma oscillations, short wave length limit of plasma oscillations and De bye shielding distance. 8. Radiation damping, self fields. of a particle, scattering and absorption of radiation by a bound system: Introductory considerations, Radiative reaction force from conservation of energy, Abraham Lorentz evaluation of the self force, difficulties with abraham Lorentz model;lntegro-differential equation of motion including radiation damping,. Line Breadth and level shift of an oscillator, Scattering and absorption of radiation. by an oscillator, Energy transfer to a harmonically bound charge.

Reference Books :

1. J.D. Jackson-.-Classica/ Electrodynamics 2. Panofsky andPhiiips Classical Electricity and Magnetism' 3. introduction to Electrodynamics-Gritfrths 4. Landau and Lifshitz--C/assica/ Theory of Field 5. Landau and Lifshitz.:.Electrodynamics of Continuous Media

PAPER-X: MICROWAVE ELECTRONICS Max.Marks :100 Duration : 3hrs.

Note: Five question are to be set taking one from each unit( each question will have an internal choice).Student will attempt all the five questions. 40% weightage will be given to problems and numericals.

UNIT- I

1 .Introduction to microwaves and its frequency spectrum, Application of microwaves. Wave guides: (a) Rectangular wave guides: Wave Equation & its solutions, TE&TM modes.Dominan tmode and choice of wave guide Dimensions Methods of excitation of wave guide. (b) Circular wave guide-wave equation & its solutions, TE, TM & TEM modes. (c) Atlenuation- Cause of attenuation in wave guides, wall current & derivation of atlenuation constant. Q of the wave guide. 2. Resonators: Resonant Modes of rectangular and cylindrical cavity resonators, Q of the cavity resonators, Excitation techniques, introduction to Microstrip and Dielectric resonators, Frequency meter.

UNIT- II 3. Far rites: Microwave propagation in ferrites, Faraday rotation, Devices employing Faraday rotation (isolator, Gyrator, Circulator). Introduction to single crystal ferromagnetic resonators, YIG tuned solid state resonators. 4. Microwave Measurement: (a) Microwave Detectors: Power, Frequency, Anenuation, Impedance Using smith chart, VSWR, Retlectomerer. Directivity, coupling using direction coupler. (b) Complex permittivity of material & its measurement: definition of complex of Solids, liquids and powders using shift of minima method.

UNJT- III 3. Microwave tubes: Spacecharge spreadingof an electron beam, Beam focussings. Klystrons: Velocity Modulation, Two Cavity Klystron, Reflex Klystron Efficiency of Klystrons. Magnetrons: types & description, Theoretical relations between Electric & Magretic field of oscillations. Modes of oscillation & operating characteristics. Gyrotrons: Constructions of different ,Gyrotrons, Field. -Particle Interaction in Gyrotron.

UNIT- IV

6. (a) Avalanche Transit Time Device:Read Diode, Negative resistance of an avalanching p-n

Junction diode IMPA TT and TRAPATT Oscillator. (b) Transferred Electron Device: Gunn effect, two velley, model, High field Dotrutins, Different Modes for Microwave generation. (c) Passive Devices: Termination (Short circuit and matched terminations) Attenuator, phase changers, E&H plane Tees, Hybrid Junctions. Directional coupler. 7.Parametric Amplifier: Varactor, Equation of Capacitance in Linearly graded & abrupt p­njun.ction, Man ely Rowe relations, parametric upconvertor and Negative resistance parametric amplifier,-use of circulator, Noise in parametric amplifiers.

UNIT- V 7. Microwave Antennas: Introduction to antenna paranieters, Magnetic Currents, Electric

and magne* current sheet, Field of Huygen's source, Radiation from a slot antenna, open end of a wave guide and Electromagnetic Horns. Prabolic reflectors, Lens antennas. Radiation fields ofMicrostrip wave guide, Microstrip wave guide, Microstrip antenna calculations, Microstrip design formulas. 9. Microwave Communication: (a) LOS microwave systems, Derivation of LOS communication range, OTH microwave systems, Derivation of field strength of tropospheric waves,. Transmission interference and signal damping, Ductpropagation. (b) Satellite Communication: SateJJite frequencies aJJocation, Synchronous sateJJites,SateJJ ite orbits, SateJJite location with respect to earth and look angle, earth coverage and slant range, Eclipse effect, Link calculation, Noise consideration, Factors affecting sateJJite communication.

Reference Books: J. Electromagnetic waves & Radiating Systems: Jorden & Balmain. 2. Theory and application of microwaves by A.B. BrownweJJ & RE. Beam (McGraw HiJJ). 3. Introduction to microwave theory by Atwater (McGraw Hill). 4. Principles of microwave circuit by G.C. Montgomery (Me Graw Hill) 5. Microwave Circuits & Passive Devices by M.L. Sisodia and G.S. Raghuvanshi (New Age International, New DeltJi) 6. Foundations of microwave engineering by RE. Collin. (McGraw Hill). 7. Microwave Semiconductor Devices and their Circuit applications by H.A. Watson 8. Microwave by M.L. Sisodia and Vijay Laxmi Gupta. New Age, New Delhi. 9. Antenna Theory, Part-! by RE. CoJJin & EJ. Zucker (McGraw Hill, New York) I O.Microstrip Antennas by Bah I & Bhartiya (Artech House, Messachausetts) J J. Antenna Theory Analysis by C. A. Balan is Harper & Row. Pub. & Inc. New York. 12. Antenna Theory Analysis by E.A. WOJ ""(J. Willey & Sons) 13. Antenna Theory & Design by RS EJJiott (LPHI Ltd. New Delhi) 14. Microwave electronics by RE Soohoo (Addisen Wesley pubblic company,). IS.Microwave Active Devices, Vacuoums by M.L. Sisodia new Age International New Delhi. 16. Semiconductors & Electronics device by A. Barle vs (PHI, India). 17. Solid State physical electronics by A.Vanderziel, (PH1, India). 18. Hand book of microwave measurement Vol-II by M. Sucher & J.Fox (polytechnic Press, New York). 19. Microwave devices & circuits by S. Y.Liao(PHI, India).

20. Microwave Principles by H.J. Reich (CBS). 21. Simple microwave technique for measuring the dielectric parameters of solids & their powder by J.M. Gandhi, J.S. Yadav, .1. of pure & applied physics Vol. 30, pp-427431, 1992.