information brochure for correspondence postal material

7/31/2019 Information Brochure for Correspondence Postal Material

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Order Online: Mathematics Postal / Correspondence Study Material

Dear students,

In reference to the enquiries posting by students from various states and cities, we are providing online

ordering facility to our Postal Guidance/Correspondence Material.

Here with this, we will also assist you with your dilemmas associated with the Civil Services (Main)

Examination. Since you have decided to choose Mathematics as an optional for your CSE Main examination,

we, the faculty and staff at IMS, give you warm wishes and offer you a glimpse into the world of IMS and its

functioning.

Our years of expertise in dealing with Mathematics has enabled us to come up with such comprehensive

course material which would be absolutely sufficient for you to escape the use of all other reference books.

At the same time, it has been designed in the most user friendly manner to facilitate the learning process even

for the students with the elementary level knowledge of Mathematics. Such complete study material is the

result of meticulousness and efficiency obtained due to 12 laborious years of involvement with the subject. Asper your requirements, you would be provided with the correspondence or postal material. This material

largely consists of the class notes.

The greatest proof of the efficacy of our study material lies in the fact that maximum questions asked in the

CSE Main examination are from the topics and questions incorporated in the notes. Let us assure you, thismaterial is absolutely sufficient for your exam preparation.

The exclusive features of the IMS study material are as follows:

1. An absolutely comprehensive study material.

2. Detailed explanation including Basics.

3. Includes the relevant topics as per examination point of view.

4. Previous year questions with their detailed solutions.

5. Personalised attention through 'telephonic doubt clearance facility' during exams preparation period.

(P.T.O.)


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FEE STRUCTURE & PAYMENT OPTIONS

Price of the Study Material: Rs.11000/- (Including Postal Charges)This amount either you have to send through DD (Demand draft) in favour of : IMS (Institute of

Mathematical Sciences) payable at New Delhi -110009 or you can transfer your fee directly through an

institute bank accounts or you can also transfer through online: A/C.NO.: 60028778685 (Bank of Maharashtra) A/C NO.: 06091000010710 (HDFC) [IFSC CODE: 0000609] Beneficiary Name: K.VENKATAIAH After the confirmation of the payment we shall get back to you within 24 hours and your study

material will be dispatched via courier at your shipping address. We will also send you a study material dispatch confirmation email along with your consignment

tracking number.

HOW TO ORDER ?

ONLINE:

To order this study material you need to fill order form given below with your correct shippingand contact details.

OFFLINE

You can also collect Study Material from the Institute Address. Head Office: 105-106, Top Floor Mukherjee Tower, Mukherjee Nagar, New Delhi 110009

NOTE : Study material will be delivered to you in approximately 5 to 7 working days.For any further clarifications feel free to contact us on following telephone numbers: 011-45629987,09999329111, 09999197625


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Preparation Strategy with Mathematics Optionalin IAS / IFoS Examination

The Civil Service Examination, the crme de la crme of all examinations, is known as the toughest andthe longest examination of the India,. Therefore it becomes very important to share my own view points

for the bright future of the aspiring candidates.

One can sail through this hurdle race in flying colours only by proper planning, sincere hard work and

patience.

To get the good rank in this examination proper planning is right selection of the optional. According to

my opinion should be chosen on the basis of ones interest in that subject, scoring pattern of that subject in

previous few years, availability of study material and expert guidance.

First optional should be chosen, the subject during graduation/post graduation but my advice to the civil

services aspirants is that choosing parent subject as first optional proves beneficial until and unless there

are some genuine points against that subject. And second optional should be chosen by applying the above

mentioned four points: Criteria of interest, scoring pattern, availability of study material and expert

guidance.

On the basis of above criterion of choosing optional Mathematics is one of the safest and scoring in civil

services examination. This is the only subject which can give easily 400+ marks. In every 20 is always

replete with candidates having mathematics as their one of the two optionals. Before the year of 2000,

mathematics has produced maximum number of toppers in the civil services examination, after the change

pattern in civil services examination has given bit difficulty in mathematics optional for aspirants because

of lack of guidance availability and false propaganda against the subject.

But from the last few years, popularity of subject is increasing due to availability according to the need of

examination.

Downloaded From: www.ims4maths.com



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Role of coaching

One can score 400 plus in mathematics with the help of professionally well equipped and qualitatively

upgraded and updated teaching inputs based on most meticulously and scientifically designedcomprehensive guidance programme, conceptual clarifications of all topics. Moreover coaching institute

may regular rigorous written tests feedback mechanism, which is needed to conceptual, analytical as per

requirement of latest emerging trends of the civil services examination.

An academy with its experienced and professionally trained expertise can prove to be a catalytic force to

ensure topmost proficiency and perfectionism on the subject.




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IAS Main Syllabus (Mathematics)

Exam Paper-I

Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension;

Linear transformations, rank and nullity, matrix of a linear transformation.Algebra of Matrices; Row and column reduction, Echelon form, congruences and similarity; Rank of a matrix;

Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristicpolynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and

unitary matrices and their eigenvalues.

Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem,Taylor's theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions

of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange's method ofmultipliers, Jacobian.

Riemann's definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple

integrals (evaluation techniques only); Areas, surface and volumes.

Analytic Geometry: Cartesian and polar coordinates in three dimensions, second degree equations in threevariables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere,

cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

Ordinary Differential Equations: Formulation of differential equations; Equations of first order and first degree,integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut's equation,

singular solution. Second and higher order linear equations with constant coefficients, complementary function,particular integral and general solution.

Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete

solution when one solution is known using method of variation of parameters.Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions.Application to initial value problems for 2nd order linear equations with constant coefficients.

Dynamics & Statics: Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained

motion; Work and energy, conservation of energy; Kepler's laws, orbits under central forces.

Equilibrium of a system of particles; Work and potential energy, friction; common catenary; Principle of virtualwork; Stability of equilibrium, equilibrium of forces in three dimensions.

Vector Analysis: Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence

and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations.

Application to geometry: Curves in space, Curvature and torsion; Serret-Frenets formulae. Gauss and Stokestheorems, Greens identities.

Exam Paper-II

(1) Algebra: Groups, subgroups, cyclic groups, cosets, Lagranges Theorem, normal subgroups, quotient groups,

homomorphism of groups, basic isomorphism theorems, permutation groups, Cayleys theorem.Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains

and unique factorization domains; Fields, quotient fields.

Real Analysis: Real number system as an ordered field with least upper bound property; Sequences, limit of a

sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditionalconvergence of series of real and complex terms, rearrangement of series.




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Continuity and uniform continuity of functions, properties of continuous functions on compact sets.Riemann integral, improper integrals; Fundamental theorems of integral calculus.

Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partialderivatives of functions of several (two or three) variables, maxima and minima.

Complex Analysis: Analytic functions, Cauchy-Riemann equations, Cauchy's theorem, Cauchy's integral formula,

power series representation of an analytic function, Taylors series; Singularities; Laurent's series; Cauchy's residuetheorem; Contour integration.

Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution;Graphical method and simplex method of solutions; Duality.

Transportation and assignment problems.

Partial differential equations: Family of surfaces in three dimensions and formulation of partial differential

equations; Solution of quasilinear partial differential equations of the first order, Cauchy's method ofcharacteristics; Linear partial differential equations of the second order with constant coefficients, canonical form;

Equation of a vibrating string, heat equation, Laplace equation and their solutions.

Numerical Analysis and Computer programming: Numerical methods: Solution of algebraic and transcendental

equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods; solution of system of linear

equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods. Newton's (forward

and backward) interpolation, Lagrange's interpolation.Numerical integration: Trapezoidal rule, Simpson's rules, Gaussian quadrature formula.

Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods.

Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimalsystems; Conversion to and from decimal systems; Algebra of binary numbers.

Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normalforms.

Representation of unsigned integers, signed integers and reals, double precision reals and long integers.Algorithms and flow charts for solving numerical analysis problems.

Mechanics and Fluid Dynamics: Generalized coordinates; D' Alembert's principle and Lagrange's equations;

Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions.Equation of continuity; Euler's equation of motion for inviscid flow; Stream-lines, path of a particle; Potential flow;

Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for aviscous fluid.




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IFoS Main Syllabus (Mathematics)

Paper I

Section-A

Linear Algebra: Vector, space, linear dependance and independance, subspaces, bases, dimensions. Finite

dimensional vector spaces. Matrices, Cayley-Hamiliton theorem, eigenvalues and eigenvectors, matrix of linear

transformation, row and column reduction, Echelon form, eqivalence, congruences and similarity, reduction to

cannonical form, rank, orthogonal, symmetrical, skew symmetrical, unitary, hermitian, skew-hermitian

formstheir eigenvalues. Orthogonal and unitary reduction of quadratic and hermitian forms, positive definite

quardratic forms.

Calculus: Real numbers, limits, continuity, differerentiability, mean-value theorems, Taylor's theorem with

remainders, indeterminate forms, maximas and minima, asyptotes. Functions of several variables: continuity,

differentiability, partial derivatives, maxima and minima, Lagrange's method of multipliers, Jacobian. Riemann's

definition of definite integrals, indefinite integrals, infinite and improper intergrals, beta and gamma functions.

Double and triple integrals (evaluation techniques only). Areas, surface and volumes, centre of gravity.

Analytic Geometry: Cartesian and polar coordinates in two and three dimesnions, second degree equations in two

and three dimensions, reduction to cannonical forms, straight lines, shortest distance between two skew lines, plane,sphere, cone, cylinder., paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

Section-B

Ordinary Differential Equations : Formulation of differential equations, order and degree, equations of first orderand first degree, integrating factor, equations of first order but not of first degree, Clariaut's equation, singular

solution.

Higher order linear equations, with constant coefficients, complementary function and particular integral, general

solution, Euler-Cauchy equation.

Second order linear equations with variable coefficients, determination of complete solution when one solution isknown, method of variation of parameters.

Dynamics, Statics and Hydrostatics : Degree of freedom and constraints, rectilinerar motion, simple harmonicmotion, motion in a plane, projectiles, constrained motion, work and energy, conservation of energy, motion under

impulsive forces, Kepler's laws, orbits under central forces, motion of varying mass, motion under resistance.

Equilibrium of a system of particles, work and potential energy, friction, common catenary, principle of virtualwork, stability of equilibrium, equilibrium of forces in three dimensions. Pressure of heavy fluids, equilibrium of

fluids under given system of forces Bernoulli's equation, centre of pressure, thrust on curved surfaces, equilibriumof floating bodies, stability of equilibrium, metacentre, pressure of gases.

Vector Analysis : Scalar and vector fields, triple, products, differentiation of vector function of a scalar variable,Gradient, divergence and curl in cartesian, cylindrical and spherical coordinates and their physical interpretations.




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Higher order derivatives, vector identities and vector quations. Application to Geometry: Curves in space, curvatureand torision. Serret-Frenet's formulae, Gauss and Stokes' theorems, Green's identities.

Paper-II

Section-A

Algebra: Groups, subgroups, normal subgroups, homomorphism of groups quotient groups basic isomorophism

theorems, Sylow's group, permutation groups, Cayley theorem. Rings and ideals, principal ideal domains, unique

factorization domains and Euclidean domains. Field extensions, finite fields.

Real Analysis : Real number system, ordered sets, bounds, ordered field, real number system as an ordered field

with least upper bound property, cauchy sequence, completeness, Continuity and uniform continuity of functions,

properties of continuous functions on compact sets. Riemann integral, improper integrals, absolute and conditionalconvergence of series of real and complex terms, rearrangement of series. Uniform convergence, continuity,

differentiability and integrability for sequences and series of functions. Differentiation of fuctions of several

variables, change in the order of partial derivatives, implict function theorem, maxima and minima. Multiple

integrals. Complex Analysis : Analytic function, Cauchy-Riemann equations, Cauchy's theorem, Cauchy's integral

formula, power series, Taylor's series, Laurent's Series, Singularities, Cauchy's residue theorem, contour

integration. Conformal mapping, bilinear transformations.

Linear Programming : Linear programming problems, basic solution, basic feasible solution and optimal solution,

graphical method and Simplex method of solutions. Duality.

Transportation and assignment problems. Travelling salesman problmes.

Section-B

Partial differential equations: Curves and surfaces in three dimesnions, formulation of partial differential

equations, solutions of equations of type dx/p=dy/q=dz/r; orthogonal trajectories, pfaffian differential equations;

partial differential equations of the first order, solution by Cauchy's method of characteristics; Charpit's method of

solutions, linear partial differential equations of the second order with constant coefficients, equations of vibrating

string, heat equation, laplace equation.

Numerical Analysis and Computer programming: Numerical methods: Solution of algebraic and transcendental

equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods, solution of system of linear

equations by Gaussian elimination and Gauss-Jordan (direct) methods, Gauss-Seidel(iterative) method. Newton's

(Forward and backward) and Lagrange's method of interpolation. Numerical integration: Simpson's one-third rule,

tranpezodial rule, Gaussian quardrature formula. Numerical solution of ordinary differential equations: Euler and




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Runge Kutta-methods.

Computer Programming: Storage of numbers in Computers, bits, bytes and words, binary system. arithmetic and

logical operations on numbers. Bitwise operations. AND, OR , XOR, NOT, and shift/rotate operators. Octal and

Hexadecimal Systems. Conversion to and form decimal Systems. Representation of unsigned integers, signed

integers and reals, double precision reals and long integrers. Algorithms and flow charts for solving numerical

analysis problems. Developing simple programs in Basic for problems involving techniques covered in the

numerical analysis.

Mechanics and Fluid Dynamics : Generalised coordinates, constraints, holonomic and non-holonomic , systems.

D' Alembert's principle and Lagrange' equations, Hamilton equations, moment of intertia, motion of rigid bodies in

two dimensions. Equation of continuity, Euler's equation of motion for inviscid flow, stream-lines, path of a

particle, potential flow, two-dimensional and axisymetric motion, sources and sinks, vortex motion, flow past a

cylinder and a sphere, method of images. Navier-Stokes equation for a viscous fluid.




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Recommended Mathematics Books For IAS/IFoSExamination

(For Paper I & Paper II)

1. Linear Algebra

A.R.Vasista Schaum Series (3000 solved problems book)

2. Calculus and Real Analysis

S.C Malik and Savita Arora Shanti Narayana

3. 3-D Geometry

Shanti Narayana4. Ordinary Differential Equations

M.D. Raisinghania G.F. Simmons Ian Sneddon

5. Vector Analysis

A.R. Vasista Schuam Series

6. Algebra

Joseph A. Gallian S.K. Bhambri and Khanna

7. Complex Analysis

Schuam Series J.N. Sharma J.B. Convey

8. Linear Programming

Shanti Swarup9. Numerical Analysis

Jain and Iyenger Shasthry

10. Computer Programming

Raja Raman

11. Dynamics & Statics

A.R. Vasista S.C. Gupta

12. Mechanics and Fluid Dynamics

M.D. Raisinghania H. Goldstein




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IAS Mathematics: Exam Papers Analysis - According toNew Syllabus (from 2008)

Analysis of IAS MATHEMATICS paper 1 & 2 for IAS MATHEMATICS examination

more or less the following pattern of examination is going on: According to NewSyllabus (from 2008)

Candidates should attempt Questions 1 and 5 which are compulsory , and anythree of the remaining questions selecting at least one question from each section.

Question Paper Model Paper-I : Section-A(Topics to be covered : LA, CAL, 3-D)

Time : Three Hours

Maximum Marks : 300

a, b LA

c, d CALQ1.

e, f 3-D

125=60

a LA

b CALQ2.

c 3-D

203=60

a LA

b CALQ3.

c 3-D

203=60

a LA

b CALQ4.

c 3-D

203=60

SECTION-B:Topics to be covered : ODE , Dy & Statics , VA

a, b ODE

c, d Dy & staticsQ5.

e, f VA

125=60

Q6. a, b, c, d ODE 154=60




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ODE : Ordinary Differential Equations Dy & Statics : Dynamics & Statics VA : Vector Analysis MA : Modern Algebra RA : Real Analysis CA : Complex Analysis LPP : Linear Programming Problem PDE : Partial Differential Equations NA & CP : Numerical Analysis and Computer Programming Mech & Fluid Dy : Mechanics & Fluid Dynamics




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IFoS Mathematics: Exam Papers Analysis - (from 2011)

For IFoS Mathematics examination more or less following pattern of examination isgoing on: Question Paper Model (from 2011)

IFoS : Paper - I

Question Paper Model (from 2011) Paper -I

Candidates should attempt questions 1 and 5 which are compulsory , any three of the remaining questions

selecting atleast one question from each section.

Time-3hours

Max Marks : 200

a, b LA

c, d CALQ1.

e 3-D

104=40

Q2. a, b, c, d LA 104=40

Q3. a, b, c ,d CAL 104=40

Q4. a, b ,c ,d 3-D 104=40

SECTION - B

a, bODE

c, d Dy & Statics & HydrostaticsQ5.

e, f VA

104=40

Q6. a, b, c, d ODE 104=40

Q7. a, b, c Dynamics, Statics and Hydro Statics

14

13

13

= 40

Q8. a, b, c, d VA 10 4 = 40




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PDE

NA

12

12

Q8. a, b, c

Mech

CP

Fluid Dy

14

12

12

= 40

LEGEND

LA : Linear Algebra CAL : Calculus 3-D : 3-Dimensional Geometry ODE : Ordinary Differential Equations Dy & Statics : Dynamics & Statics VA : Vector Analysis MA : Modern Algebra RA : Real Analysis CA : Complex Analysis LPP : Linear Programming Problem PDE : Partial Differential Equations NA & CP : Numerical Analysis and Computer Programming Mech & Fluid Dy : Mechanics & Fluid Dynamics




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