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DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: Differential equations&Abstract Algebra Class: I BSc Semester: I
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jul – 26
I Week 6 Linear differential equations,differential equations reducible to
linear form,Exact differential equations
II Week 5 Integrating factor ,change of variables, total differential equations,
Method s of solving integrable total differential equations
Assignment
III Week 6 Simultaneous differential equations, methods of finding general
solution of F(x,y,p)=0
IV Week 9 Orthogonal trajectories, groups-elementary properties, binary
operations,
Class Room Seminar
Aug – 21
I Week 6 Groups. Finite groups and group tables, subgroups
II Week 4 Cosets, Lagrange’s theorem
III Week 3 Normal subgroups & factor groups Class Room discussion
IV Week 8 Homomorphisms-definition and elementary properties,
Isomorphisms, fundamental theorem of homomorphism
Assignment
Sep – 23
I Week 6 Automorphism, permutation groups,cayley’s theorem
II Week 4 Groups of permutations,cycles, Alternating group Class Room Seminar
III Week 6 Cyclic groups- definition and examples, classification of cyclic
groups
Assignment
IV Week 7 Generators and subgroups of cyclic groups Assignment
Oct – 26 I Week 6 Revision
II Week 5 Revision
III Week 6 SEMESTER END EXAMS
IV Week 9 SEMESTER END EXAMS
Nov – 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: 2A, Abstract Algebra & Real Analysis Class: II BSc Semester: III
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
June - 10
III Week 3
Binary operations ,definitions and properties ,Groups-definition
and elementary properties ,finite groups and group composition
tables.
IV Week 7
Subgroups and cyclic subgroups ,permutations ,functions and
permutations,groups of permutations ,cycles and cyclic notation.
Practical.
Assignment
Jul – 26
I Week 6
Even and odd permutations ,the alternating groups ,cyclic groups
:elementary properties ,the classification of cyclic groups.
Practical.
Class Room discussion
II Week 5
Subgroups of finite cyclic groups ,isomorphism -definition and
elementary properties, Cayley’s theorem ,groups of cosets
,applications.
Class Room Seminar
III Week 6 Normal subgroups :factor groups, criteria for the existence of a
coset group ,inner automorphism and normal subgroups.
Assignment
IV Week 9
Factor groups and simple groups , homomorphism :definition and
elementary properties ,the fundamental theorem of
homomorphism ,applications.
Practical.
Aug – 21
I Week 6 The completeness properties of IR.
Practical.
II Week 4 Applications of the supremum property.
III Week 3 Sequences and series
IV Week 8 Sequence and their limits ,limit theorems ,monotonic sequences
and the Bolazano – weierstrass theorem.
Assignment
Sep – 23
I Week 6 The cauchy’s criterion.
Practical.
II Week 4 Properly divergent sequences. Assignment
III Week 6 Introduction to series ,absolute convergence.
IV Week 7 Test for absolute convergence.
Practical.
Oct – 26
I Week 6 Test for non absolute convergence.
Practical.
Class Room Seminar
II Week 5 Revision
III Week 6 SEMESTER END EXAMS
IV Week 9 SEMESTER END EXAMS
Nov – 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: Linear Algebra, 3A Class: III BSC Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
June-10
III Week 3
Vector spaces, general properties of vector spaces , n-
dimensional vectors, addition and scalar multiplication of
vectors ,Internal and external composition .
IV Week 6
Vector subspaces, algebra of subspaces ,Linear combination
of vectors, linear span of a set
Practical..
Jul – 26
I Week 5
linear sum of two subspaces , Linear independence and
dependence of vectors .
practical.
Class Room discussion
II Week 5 Basis of vector space, Finite dimensional vector spaces,
dimension of vector space.
III Week 5
dimension of subspace ,Homomorphism of vector spaces,
Isomorphism of vector spaces, quotient space .
practical.
Assignment
IV Week 7
dimension of quotient space , Linear
transformations,properties of linear transformations,range
and null space of linear transformation.
Practical.
Aug – 21
I Week 5 Rank and nullity of linear transformations and its
applications
II Week 4 Linear transformation as vectors, product of linear
transformations, invertible linear transformations
Assignment
III Week 3 Linear functional, dual space,dual bases,Annihilators,the
adjoint of a linear transformation
IV Week 7
Sylvester’s law of nullity, Characteristic values and
characteristic vectors.
Practical.
Class Room Seminar
Sep – 23
I Week 5 Cayley-Hamilton theorem, Diagonalizable operators.
Practical.
II Week 4 Inner product spaces, Euclidean and unitary spaces, length of
a vector
III Week 5 Schwartz inequality, orthoganality, orthonormal set
IV Week 6
Complete orthonormal set, orthonormal basis, Gram-schmidt
orthogonalization process, Bessel’s inequality.
Practical.
Class Room discussion
Oct – 26
I Week 5 Bessel’s inequality, Practical
II Week 5 Revision
III Week 5 Revision
IV Week 7 SEMESTER END EXAMS
Nov – 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: 4A ,Numerical Analysis Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun - 10
III Week 3
Errors in numerical computations , Numbers and their
accuracy, Errors and their computation ,
IV Week 6
Absolute , Relative and percentage errors. A general error
formula .
Practical .
Jul – 26
I Week 5
error in a series approximation,
Solution of algebraic and transcendental equations:
Practical.
Assignment
II Week 5 Bisection ,the method of falsi position .
III Week 5 The iteration method , the Newton – Raphson method.
IV Week 7
Generalized Newton -Raphson method , Ramanujan’s method
Muller’s method .
Practical
Class Room seminar
Aug – 21
I Week 5 interpolation :forward differences ,backward differences ,
II Week 4 central differences , symbolic relations.
III Week 3
Detection of errors by use of D – tables ,differences of
polynomial .
Practical.
IV Week 7
Newton’s forward interpolation formula ,Newton’s backward
interpolation formula .
Practical.
Sep – 23
I Week 5
Gauss’s central difference formula ,stirling’s central
difference formula ,
Additional input:Bessel’s central difference formula .
Class Room seminar
II Week 4
Everett’s central difference formula , Divided differences and
their properties .
Practical.
Class Room discussion
III Week 5 Lagrange’s formula ,errors in Lagrange’s formula .
IV Week 7 Derivation of governing equations , end conditions,
Assignment
Oct – 26
I Week 5 Newton’s general interpolation, Practical
II Week 5 Revision.
III Week 5 Revision
IV Week 8 SEMESTER END EXAMS
Nov - 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: 4A ,Discrete Mathematics Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun - 10
III Week 3 Sets and operations of sets, Relations and functions.
IV Week Some methods of proof .
Practical.
Jul – 26
I Week 6 Problem Solving strategies. Class Room Seminar
II Week 5 Fundamentals of logic.
III Week 6 Logical inference.
Practical.
Assignment
IV Week 7
Methods of proof of an implication, first order logic and other
methods of proof.
Practical.
Aug – 21
I Week 5 Rules of inference for quantified propositions. Class Room discussion
II Week 4 Mathematical induction ,the principle of inclusion-exclusion.
III Week 3 Generating functions of sequences , calculating coefficients
of generating functions.
Assignment
IV Week 7 Recurrence relations ,solving recurrence relations by
substitution.
Practical.
Sep – 23
I Week 5 Generating functions , the method of characteristic roots.
Practical.
II Week 4 Solutions of inhomogeneous recurrence relations .
III Week 5
Relations and directed graphs ,special properties of binary
relations.
Practical.
Assignment
IV Week 6 Equivalence relations , ordering relations
Practical.
Class Room Seminar
Oct – 26
I Week 5 Latice and enumerations
II Week 5 Revision
III Week 5 Revision
IV Week 8 SEMESTER END EXAMS
Nov - 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: Differential equations&Real Analysis, 1B Class: I BSc Semester: II
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5
Linear differential Equations with constant coefficients,
Homogeneous linear differential equations with constant
coefficients
IV Week 8 Solution of homogeneous linear differential equations of order n
with constant coefficients
Dec – 23
I Week 6 Solution of non homogeneous linear differential equations with
constant coefficients by means of polynomial operators
Assignment
II Week 5 Linear differential equations with variable coefficients, method of
variation of parameters
Class Room discussion
III Week 6 Linear differential equations with non-constant coefficients, the
Cauchy Euler equation, method of undetermined coefficients
Class Room Seminar
IV Week 6
System of linear differential equations: system of first order
differential equations, solution of a system of linear equations
with constant coefficients,an equivalent triangular
system,degenerate case
Assignment
Jan – 19 I Week 5
The Real numbers: the set of natural numbers, integers, rational
numbers and real numbers,the set of real numbers, IR has
complete ordered pair intervals, bounds&orders-completeness of
the set of real numbers
II Week 3 Some important properties of real numbers, the dense property of
the set of real numbers, the modulus of real numbers
III Week 2 Limit point of a set, existence of limit point
IV Week 9
Sequence, bounded and unbounded sequence, limit point of a
sequence,convergent sequences,limit of a sequence,algebra of
convergent sequences,bounded non convergent
sequence,Important theorems on limits,Cauchy sequence
Assignment
Feb – 21
I Week 6
Convergency of a sequence, monotonic sequence and their
convergency,subsequences,Infinite series with positive
terms,Infinite series of its convergency and sum
Class Room Seminar
II Week 4 A necessary condition for the convergency of an infinite series,
cauchy’s general principle of convergence
III Week 6 General test for convergency of positive term series, two
important standard series,
Assignment
IV Week 5 Comparison test for the convergency of positive term series,
comparison test of the first type
Mar – 22
I Week 6 Practical comparison test of the first type and comparison test of
the second type
II Week 5 Practical comparison test of the second type, D’Alembert’s ratio
test, Cauchy’s root test
III Week 4 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: Abstract Algebra&Real Analysis, IIB Class: II BSc Semester: 4
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Definition and basic properties, fields
IV Week 8
Integral domains, divisors of zero and cancellation laws,integral
domains ,the characteristic of a ring .
Practical .
Class Room discussion
Dec – 23
I Week 6 some non-commutative rings , examples
II Week 5 matrices over a field, the real quaternions
III Week 6 Quotient rings and ideals .
Practical .
Assignment
IV Week 6 Homomorphism of rings-definition and elementary properties
Jan – 19
I Week 5 Maximal and prime ideals, prime fields .
Practical .
Class Room Seminar
II Week 3 Rings of polynomials-polynomials in an indeterminate form
III Week 2 The evaluation of homomorphism
IV Week 9
Continuous functions, combination of continuous
functions,continuous functions on intervals .
Practical .
Assignment
Feb – 21 I Week 6 Uniform continuity, the derivative, the mean value theorems
II Week 4 L’Hospital rule, Taylor’s theorem, Assignment
III Week 6 Riemann integration- Riemann integral
Practical.
Class Room Seminar
IV Week 5 Riemann integrable functions
Mar – 22
I Week 6 Fundamental theorem
Practical .
Assignment
II Week 5 Revision
III Week 4 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: Multiple integrals & Vector Calculus (3B) Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Introduction, the concept of a plane curve, Introduction to line
integrals, properties of line integrals, examples
IV Week 7
Sufficient condition for the existence of line integral, the area of a
subset .
Practical
Dec – 23
I Week 5
Introduction to double integrals, Darboux’s theorem, necessary
and sufficient condition for integrability, double integral over a
rectangle of a limit of sum.
Practical
Class Room discussion
II Week 5 Problems on double integrals, integration over non
rectangular,change of order of integration and its applications
III Week 5
Fubini’s theorem, Jordan’s theorem,change of variable in a
double integration.
Practical
Assignment
IV Week 5
Introduction to length of the curves, Rectifiability of a curve,
property of rectifiable curves, surface areas.
Practical
Jan – 19
I Week 5
Introduction to vector differentiation, derivative of a vector
function, theorems,partial differentiation.
Practical
II Week 3 Differential operator-directional derivative at a point
III Week 2
Gradient of a scalar point function and its applications,
divergence of a vector,solenoidal vector,laplacian operator, curl
of a vector
Assignment
IV Week 7 Irrotational vector, problems on divergence and curl of a vector.
Practical
Class Room discussion
Feb – 21
I Week 5
Vector identities, theorems, Introduction to vector integration,
definite integrals, line integrals and its applications.
Practical
II Week 4 Surface integrals, Volume integrals and its applications Class Room seminar
III Week 5 Gauss divergence theorem and its applications.
Practical
IV Week 5 Green’s theorem, Stoke’s theorem and its applications
Mar – 22
I Week 5 Revision
II Week 5 Revision
III Week 4 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: 4B ,Numerical Analysis Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Curve Fitting : Least squares curve fitting procedures ,fitting
a straight line ,non linear curve fitting .
IV Week 7
Curve fitting by a sumof exponentials ,numerical
differentiation , errors in numerical differentiation , maximum
and minimum values of a tabulated functions.
Practical.
Dec – 23
I Week 5
Numerical integration : Trapezoidal rule , simpson’s 1/3 rule ,
simpson’s 3/8 rule.
Practical.
Assignment
II Week 5 Boole’s rule and weddle’s rule , linear systems of equations.
III Week 5 Solution of linear systems – direct methods .
Practical
Class Room discussion
IV Week 5 matrix inversion method ,Gauss elimination method .
practical.
Jan – 19 I Week 5
method of factorisation ,ill - conditioned linear systems
iterative methods
practical.
Class Room Seminar
II Week 3 Jacobi’s method.
III Week 2 Gauss siedal method .
IV Week 7
Numerical solution of ordinary differential equations :
Introduction, Solution by Taylor’s series.
Practical.
Assignment
Feb – 21
I Week 5 picards method of successive approximations .
Practical.
II Week 4 Euler’s method ,modified Euler’s method.
III Week 5 Runge – kutta methods . Class Room Seminar
IV Week 5 Predictor-corrector methods .
Mar – 22
I Week 5
Milne’s method.
Additional input:Revised Euler’s method.
Practical.
Class Room Seminar
II Week 5 Revision.
III Week 4 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2013 – 14.
Department: Mathematics Paper: 4B ,Discrete Mathematics. Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Basic concepts , isomorphisms and sub graphs.
IV Week 7 Trees and their properties.
Practical.
Dec – 23
I Week 5 Spanning trees , directed trees.
Practical.
II Week 5 Binary trees . Class Room discussion
III Week 5 Planar graphs, Euler’s formula.
Practical.
IV Week 5 Multi graphs and Euler circuits.
Practical.
Assignment
Jan – 19
I Week 5 Hamiltonian graphs.
Practical.
II Week 3 Chromatic numbers . Class Room Seminar
III Week 2 the four color problem
IV Week 8 Introduction,Boolean algebras , Switching mechanisms. Assignment
Practical.
Feb – 21
I Week 5 Boolean functions ,Minimization of Boolean functions.
II Week 4 Additional input:
Network flows: graphs as model of flow of commodities.
III Week 5 Flows.
Practical.
Class Room Seminar
IV Week 5 Maximal flows and minimal cuts.
Practical
Mar – 22
I Week 5 Revision.
II Week 5 Revision.
III Week 4 SEMESTER-END EXAMS
IV Week 6 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15
Department: Mathematics Paper: Differential equations&Abstract Algebra Class: I BSc Semester: I
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jul – 25
I Week 6 Linear differential equations,differential equations reducible
to linear form,Exact differential equations
II Week 5
Integrating factor ,change of variables, total differential
equations, Method s of solving integrable total differential
equations
III Week 6 Simultaneous differential equations, methods of finding
general solution of F(x,y,p)=0
Assignment
IV Week 8 Orthogonal trajectories, groups-elementary properties, binary
operations,
Class Room Seminar
Aug – 21
I Week 6 Groups. Finite groups and group tables, subgroups
II Week 4 Cosets, Lagrange’s theorem
III Week 4 Normal subgroups & factor groups
IV Week 7 Homomorphisms-definition and elementary properties,
Isomorphisms, fundamental theorem of homomorphism
Assignment
Sep – 23
I Week 6 Automorphism, permutation groups,cayley’s theorem
II Week 5 Groups of permutations,cycles, Alternating group
III Week 6 Cyclic groups- definition and examples, classification of
cyclic groups
Assignment
IV Week 6 Generators and subgroups of cyclic groups Class Room discussion
Oct – 19
I Week 1 Revision
II Week 5 Revision
III Week 6 SEMESTER END EXAMS
IV Week 7 SEMESTER END EXAMS
Nov – 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15.
Department: Mathematics Paper: 2A Solid geometry&Real analysis Class: II BSc Semester: III
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 24
I Week 6 Coordinates of a point in IR
3,Distance between two
points,section formula.
II Week 5 Angle between two lines ,equation of a plane ,shortest
distance from a point to a plane and related results .
III Week 6 Angle between two planes ,plane bisecting the angles
between two planes ,joint equation of two planes .
IV Week 7 Projection on a plane ,symmetric form of equation of a line
changing the equations of a line in to symmetric form .
Jul – 25
I Week 6 Angle between a line and a plane, incidence and coplanarity
skew lines and the shortest distance between them .
Assignment
II Week 5 Length of the perpendicular from a point to a line ,equation of
sphere ,plane sections ,circle .
III Week 6 Tangent planes and tangent lines ,polar plane and intersection
of two spheres, radical plane .
IV Week 8 Coaxial systems ,algebraic operations on functions ,Bounded
and unbounded functions ,limit of a function .
Aug – 21 I Week 6 Algebra of limits ,one sided limits ,right handed and left Class Room Seminar
handed limits .
II Week 4 Limits at infinity and infinite limits ,continuous functions
discontinuity of functions .
III Week 4 Algebra of continuous functions ,criteria for continuity .
IV Week 7 some properties of continuity of functions at a point Assignment
Sep – 23
I Week 6 Properties of functions continuous in closed finite intervals,
uniform continuity
II Week 5 Derivability of a function ,A necessary condition for the
existence of a finite derivative .
Class Room discussion
III Week 6 Algebra of derivative , Geometrical meaning of the derivative
.
IV Week 6 Meaning of the sign of derivative at a point , Dorboux
theorem .
Class Room Seminar
Oct – 19
I Week 1 Revision.
II Week 5 Revision.
III Week 6 Revision
IV Week 7 SEMESTER END EXAMS
Nov - 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15.
Department: Mathematics Paper: Linear Algebra, 3A Class: III BSC Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 24
I Week 5 Vector spaces, general properties of vector spaces
II Week 5 n-dimensional vectors, addition and scalar multiplication of
vectors,Internal and external composition
III Week 5 Vector subspaces, algebra of subspaces .
Practical.
IV Week 6 Linear combination of vectors, linear span of a set,linear sum of
two subspaces
Jul – 25
I Week 5
Linear independence and dependence of vectors, Basis of vector
space.
Practical.
Assignment
II Week 5 Finite dimensional vector spaces,dimension of vector space,
dimension of subspace
III Week 5
Homomorphism of vector spaces, Isomorphism of vector spaces,
quotient space,dimension of quotient space.
Practical.
Class Room Seminar
IV Week 7
Linear transformations,properties of linear transformations,range
and null space of linear transformation.
Practical.
Assignment
Aug – 21
I Week 5 Rank and nullity of linear transformations and its applications
II Week 4 Linear transformation as vectors, product of linear
transformations, invertible linear transformations
III Week 4 Singular and non singular transformations, Matrix of a linear
transformation,the adjoint of a linear transformation,
IV Week 6
Sylvester’s law of nullity, Characteristic values and characteristic
vectors.
Practical.
Class Room discussion
Sep – 23
I Week 5 Cayley-Hamilton theorem, Diagonalizable operators.
Practical.
II Week 5 Inner product spaces, Euclidean and unitary spaces, length of a
vector
III Week 5 Schwartz inequality, orthoganality, orthonormal set.
Practical.
Assignment
IV Week 5 Complete orthonormal set, orthonormal basis, Gram-schmidt
orthogonalization process
Oct – 19
I Week 1 Bessel’s inequality
II Week 5 Revision
III Week 5 Revision
IV Week 6 SEMESTER END EXAMS
Nov - 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15.
Department: Mathematics Paper: 4A ,Numerical Analysis. Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 24
I Week 5 Errors in numerical computations.
Practical.
II Week 5 Numbers and their accuracy.
III Week 5
Errors and their computation ,Absolute , Relative and percentage
errors.
Practical.
IV Week 6 A general error formula , error in a series approximation.
Practical.
Assignment
Jul – 25
I Week 5 Solution of algebraic and transcendental equations.
II Week 5 Bisection ,the method of falsi position .
III Week 5 The iteration method , the Newton – Raphson method.
IV Week 7
Generalized Newton – Raphson method , Ramanujan’s method ,
interpolatrion , forward differences.
Practical.
Class Room Seminar
Aug – 21
I Week 5 Backward differences , central differences , symbolic relations.
Practical.
II Week 4 Detection of errors by use of D – tables ,differences of
polynomial .
III Week 4 Newton’s forward interpolation formula ,Newton’s backward
interpolation formula .
Class Room discussion
IV Week 6 Gauss’s central difference formula ,stirling’s difference formula.
Practical.
Sep – 23
I Week 5 Divided differences and their properties .
II Week 5 Lagrange’s formula ,errors in Lagrange’s formula . Assignment
III Week 5 Derivation of governing equations , end conditions.
IV Week 5 Newton’s general interpolation.
Practical.
Oct – 19
I Week 1 Revision. Class Room Seminar
II Week 5 Revision.
III Week 5 Revision
IV Week 6 SEMESTER END EXAMS
Nov - 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15.
Department: Mathematics Paper: 4A ,Discrete Mathematics. Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 24
I Week 5 Sets and operations of sets.
II Week 5 Sets and operations of sets.
III Week 5 Relations and functions.
Practical.
IV Week 7 Some methods of proof .
Practical.
Assignment
Jul – 25
I Week 5 Problem Solving strategies.
II Week 5 Fundamentals of logic.
III Week 5 Logical inference.
IV Week 7
Methods of proof of an implication, first order logic and other
methods of proof.
Practical.
Class Room discussion
Aug – 21
I Week 5 Rules of inference for quantified propositions.
II Week 4 Mathematical induction ,the principle of inclusion-exclusion.
III Week 4 Generating functions of sequences , calculating coefficients
of generating functions.
Assignment
IV Week 6
Recurrence relations ,solving recurrence relations by
substitution.
Practical.
Sep – 23
I Week 5 Generating functions , the method of characteristic roots.
Practical.
Class Room Seminar
II Week 5 Solutions of inhomogeneous recurrence relations .
III Week 5
Relations and directed graphs ,special properties of binary
relations.
Practical.
Assignment
IV Week 5
Equivalence relations , ordering relations ,lattice and
enumerations.
Practical.
Oct – 19
I Week 1 Revision
II Week 5 Revision
III Week 5 Revision
IV Week 6 SEMESTER END EXAMS
Nov - 10 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15
Department: Mathematics Paper: Differential equations&Real Analysis, 1B Class: I BSc Semester: II
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 6
Linear differential Equations with constantcoefficients,
Homogeneous linear differential equations with constant
coefficients
IV Week 7 Solution of homogeneous linear differential equations of order n
with constant coefficients
Dec – 24
I Week 6 Solution of non homogeneous linear differential equations with
constant coefficients by means of polynomial operators
Assignment
II Week 5 Linear differential equations with variable coefficients, method of
variation of parameters
III Week 6 Linear differential equations with non-constant coefficients, the
Cauchy-Euler equation, method of undetermined coefficients
Class Room discussion
IV Week 7
System of linear differential equations: system of first order
differential equations, solution of a system of linear equations
with consftant coefficients,an equivalent triangular
system,degenerate case
Assignment
Jan – 17 I Week 5
The Real numbers: the set of natural numbers, integers, rational
numbers and real numbers,the set of real numbers, IR has
complete ordered pair intervals, bounds&orders-completenes of
the set of real numbers
II Week 2 Some important properties of real numbers, the dense property of
the set of real numbers, the modulus of real numbers
III Week 3 Limit point of a set, existence of limit point
IV Week 7
Sequence, bounded and unbounded sequence, limit point of a
sequence,convergent sequences,limit of a sequence,algebra of
convergent sequences,bounded non convergent
sequence,Important theorems on limits,Cauchy sequence
Class Room Seminar
Feb – 22
I Week 6
Convergency of a sequence, monotonic sequence and their
convergency,subsequences,Infinite series with positive
terms,Infinite series of its convergency and sum
II Week 5 A necessary condition for the convergency of an infinite series,
cauchy’s general principle of convergence
Assignment
III Week 5 General test for convergency of positive term series, two
important standard series,
IV Week 6 Comparision test for the convergency of positive term series,
comparison test of the first type
Class Room Seminar
Mar – 22
I Week 5 Practical comparison test of the first type and comparison test of
the second type
II Week 5 Practical comparision test of the second type, D’Alembert’s ratio
test , Cauchy root test
III Week 5 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15.
Department: Mathematics Paper: 2B , Abstract Algebra & Real Analysis. Class: II BSc Semester: IV
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 6 Rings and elementary properties : Definition and example
Divisors of zero and cancellation laws .
IV Week 7
Integral domains and fields ,The characteristic of a ring non –
commutative rings matrices over a field ,Ideals and
homomorphism .
Assignment
Dec – 24
I Week 6 Ideals ,factor rings ,Maximal Ideal and prime Ideals .
II Week 5 Homomorphism of rings ,prime fields ,polynomial rings
Definition of polynomial ring .
III Week 6 Mean value theorem,,Role’s theorem ,Geometrical interpretation
of Rolle’s theorem .
Class Room discussion
IV Week 7 Increasing and decreasing functions ,monotonic functions
Cauchy’s mean value theorem ,Generalized mean value theorem .
Jan – 17
I Week 5 Taylor’s theorem with schlomitch and Roche , Cauchy’s
Lagranges form of remainders
Assignment
II Week 2 maclaurin’s Infinte series
III Week 3 power series expansions of some standard functions . Class Room Seminar
IV Week 7 Riemann integrability : Introduction ,partitions and Riemann
sums, some properties of Darboux sums ,Upper and Lower
Riemann integrals .
Feb – 22
I Week 6 Riemann integral, another equivalent definition of integrability
and integral , Second definition of Riemann integrability .
II Week 5 necessary and sufficient condition for integrability, particular
classes of bounded integrable functions .
III Week 5
Integrability of the modulus of a bounded integrable functions
definition of if b≤a , inequalities for an integral
functions defined by definite integrals.
Assignment
IV Week 6 fundamental theorem of integral calculus , Generalised mean
value theorem.
Class Room Seminar
Mar – 22
I Week 5 Abel’s lemma , second mean value theorem, change of variable
in integral , integration by parts.
II Week 5 Revision.
III Week 5 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15.
Department: Mathematics Paper: Multiple integrals & Vector Calculus (3B) Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 6 Introduction, the concept of a plane curve, Introduction to line
integrals, properties of line integrals, examples
IV Week 6
Sufficient condition for the existence of line integral, the area of a
subset .
Practical.
Dec – 24
I Week 5
Introduction to double integrals, Darboux’s theorem, necessary
and sufficient condition for integrability, double integral over a
rectangle of a limit of sum
Practical.
Assignment
II Week 5 Problems on double integrals, integration over non
rectangular,change of order of integration and its applications
III Week 5
Fubini’s theorem, Jordan’s theorem,change of variable in a
double integration.
Practical.
Class Room Seminar
IV Week 6
Introduction to length of the curves, Rectifiability of a curve,
property of recdtifiable curves, surface areas.
Practical.
Jan – 17
I Week 5 Introduction to vector differentiation, derivative of a vector
function, theorems,partial differentiation
II Week 2 Differential operator-directional derivative at a point
III Week 3
Gradient of a scalar point function and its applications,
divergence of a vector,solenoidal vector,laplacian operator, curl
of a vector
IV Week 6 Irrotational vector, problems on divergence and curl of a vector.
Practical.
Assignment
Feb – 22
I Week 5
Vector identities, theorems, Introduction to vector integration,
definite integrals, line integrals and its applications.
Practical.
II Week 5 Surface integrals, Volume integrals and its applications.
Practical.
Class Room
seminar
III Week 5 Gauss divergence theorem and its applications
IV Week 6 Green’s theorem, Stoke’s theorem and its applications.
Practical.
Mar – 22
I Week 5 Revision
II Week 5 Revision
III Week 5 SEMESTER-END EXAMS
IV Week 6 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15.
Department: Mathematics Paper: 4B, Numerical Analysis. Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Curve Fitting : Least squares curve fitting procedures ,fitting
a straight line ,non linear curve fitting .
IV Week 6
Curve fitting by a sum of exponentials ,numerical
differentiation , errors in numerical differentiation , maximum
and minimum values of a tabulated functions.
Practical.
Dec – 24
I Week 5
Numerical integration : Trapezoidal rule , simpson’s 1/3 rule ,
simpson’s 3/8 rule.
Practical.
Assignment
II Week 5 Boole’s rule and weddle’s rule , linear systems of equations.
III Week 5 Solution of linear systems :direct methods .
Practical.
Quiz
IV Week 6 matrix inversion method ,Gauss elimination method .
practical.
Jan – 17
I Week 5 method of factorisation ,ill – conditioned linear
systems,iterative methods .
II Week 2 Jacobi’s method.
III Week 3 Gauss siedal method ,numerical solution of ordinary
differential equations : Introduction
IV Week 6 Solution by Taylor’s series.
Practical.
Assignment
Feb – 22
I Week 5
Solution by Taylor’s series , picards method of successive
approximations .
Practical.
Class Room Seminar
II Week 5 Euler’s method ,modified Euler’s method.
Practical.
III Week 5 Runge – kutta methods . Classroom discussion
IV Week 5 Predictor-corrector methods .
Practical.
Mar – 22
I Week 5 Milne’s method.
II Week 5 Revision.
III Week 5 SEMESTER-END EXAMS
IV Week 6 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2014 – 15.
Department: Mathematics Paper: 4B ,Discrete Mathematics. Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13 III Week 5 Basic concepts , isomorphisms and subgraphs.
IV Week 6 Trees and their properties.
Dec – 24
I Week 5 Spanning trees , directed trees.
Practical.
II Week 5 Binary trees .
Practical.
Assignment
III Week 5 Planar graphs, Euler’s formula.
Practical.
Class Room discussion
IV Week 6 Multi graphs and Euler circuits.
Practical.
Jan – 17
I Week 5 Hamiltonian graphs.
Practical.
II Week 2 Chromatic numbers .
III Week 3 the four color problem Class Room Seminar
IV Week 6 Introduction,Boolean algebras ,Switching mechanisms.
Practical.
Feb – 22 I Week 5 Boolean functions ,Minimization of Boolean functions.
Practical.
II Week 5 Additional input:
Network flows: graphs as model of flow of commodities.
Assignment
III Week 5 Flows.
IV Week 5 Maximal flows and minimal cuts.
Practical.
Class Room Seminar
Mar – 22
I Week 5 Revision.
II Week 5 Revision.
III Week 5 SEMESTER-END EXAMS
IV Week 6 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16.
Department: Mathematics Paper: Differential Equations,IA Class: I BSC Semester: I
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jul – 25
I Week 6 Linear differential equations, Differential equations reducible
to linear form
II Week 5 Exact differential equations, Integrating factors, change of
variables
III Week 5 Simultaneous differential equations, orthogonal trajectories
IV Week 9 Equations solvable for p, equations solvable for y, equations
solvable for x
Assignment
Aug – 22
I Week 6 Equations that do not contain x(or y), equations of the first
degree in x and y-Clairaut’s equation
II Week 5 Solution of homogeneous linear differential equations of
order n with constant coefficients
III Week 5 Solution of the non-homogeneous linear differential equations
with constant coefficients by means of polynomial operators
Class Room Seminar
IV Week 6 Method of variation of parameters, linear differential
equations with non-constant coefficients
Sep – 23 I Week 5 The Cauchy-euler equation, system of linear differential
equations
II Week 5 Formation of partial differential equations, equations of first
order
Assignment
III Week 5 Lagrange’s linear equations, Charpit’s method
IV Week 8 Standard types of first order non linear partial differential
equations
Class Room Seminar
Oct – 19
I Week 5 Revision
II Week 5 Revision
III Week 3 Revision
IV Week 6 SEMESTER END EXAMS
Nov - 09 I Week 5 SEMESTER END EXAMS
II Week 4 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16 .
Department: Mathematics Paper: 2A Solid Geometry &Real analysis Class: II BSc Semester: III
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 22
I Week 3 Coordinates of a point in IR
3,Distance between two points
,section formula.
II Week 5 Angle between two lines ,equation of a plane ,shortest
distance from a point to a plane and related results .
III Week 6 Angle between two planes ,plane bisecting the angles
between two planes ,joint equation of two planes .
IV Week 8 Projection on a plane ,symmetric form of equation of a line
changing ,the equations of a line in to symmetric form .
Assignment
Jul – 25
I Week 6 Angle between a line and a plane incidence and coplanarity
,skew lines and the shortest distance between them .
II Week 5 Length of the perpendicular from a point to a line ,equation of
sphere ,plane sections ,circle .
III Week 5 Tangent planes and tangent lines ,polar plane , and
intersection of two spheres radical plane .
Assignment
IV Week 9 Coaxial systems ,algebraic operations on functions ,Bounded
and unbounded functions ,limit of a function .
Class Room Seminar
Aug – 22 I Week 6 Algebra of limits ,one sided limits ,right handed and left
handed limits .
II Week 5 Limits at infinity and infinite limits ,continuous functions
,discontinuity of functions .
III Week 5 Algebra of continuous functions ,criteria for continuity .
IV Week 6 some properties of continuity of functions at a point Assignment
Sep – 23
I Week 5 Properties of functions continuous in closed finite intervals
uniform continuity
II Week 5 Derivability of a function ,A necessary condition for the
existence of a finite derivative .
III Week 5 Algebra of derivative , Geometrical meaning of the derivative
.
Assignment
IV Week 8 Meaning of the sign of derivative at a point Class Room discussion
Oct – 19
I Week 5 Dorboux’s theorem Class Room Seminar
II Week 5 Revision.
III Week 3 Revision
IV Week 6 SEMESTER END EXAMS
Nov - 09 I Week 5 SEMESTER END EXAMS
II Week 4 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16.
Department: Mathematics Paper: Linear Algebra, 3A Class: III BSC Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 22
I Week 3 Vector spaces, general properties of vector spaces
II Week 5 n-dimensional vectors, addition and scalar multiplication of
vectors,Internal and external composition
III Week 5 Vector subspaces, algebra of subspaces
IV Week 7 Linear combination of vectors, linear span of a set,linear sum of
two subspaces
Jul – 25
I Week 5 Linear independence and dependence of vectors, Basis of vector
space
Assignment
II Week 5 Finite dimensional vector spaces,dimension of vector space,
dimension of subspace
III Week 5 Homomorphism of vector spaces, Isomorphism of vector spaces,
quotient space,dimension of quotient space
IV Week 8 Linear transformations,properties of linear transformations,range
and null space of linear transformation
Class Room Seminar
Aug – 22
I Week 5 Rank and nullity of linear transformations and its applications
II Week 5 Linear transformation as vectors, product of linear
transformations, invertible linear transformations
Assignment
III Week 5 Singular and non singular transformations, Matrix of a linear
transformation,the adjoint of a linear transformation,
IV Week 6 Sylvester’s law of nullity, Characteristic values and characteristic
vectors
Sep – 23
I Week 5 Cayley-Hamilton theorem, Diagonalizable operators
II Week 5 Inner product spaces, Euclidean and unitary spaces, length of a
vector
Assignment
III Week 5 Schwartz inequality, orthoganality, orthonormal set
IV Week 7 Complete orthonormal set, orthonormal basis, Gram-schmidt
orthogonalization process, Bessel’s inequality
Class Room discussion
Oct – 19
I Week 5 Revision
II Week 5 Revision
III Week 3 Revision
IV Week 5 SEMESTER END EXAMS
Nov - 09 I Week 5 SEMESTER END EXAMS
II Week 4 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16.
Department: Mathematics Paper: 4A,Numerical Analysis. Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 22
I Week 3 Errors in numerical computations.
II Week 5 Numbers and their accuracy.
III Week 5 Errors and their computation ,Absolute , Relative and percentage
errors.
IV Week 7 A general error formula , error in a series approximation.
Jul – 25
I Week 5 Solution of algebraic and transcendental equations.
II Week 5 Bisection ,the method of falsi position . Assignment
III Week 5 The iteration method , the Newton – Raphson method.
IV Week 8 Generalized Newton – Raphson method , Ramnujan’s method ,
interpolatrion , forward differences.
Aug – 22
I Week 5 Backward differences , central differences , symbolic relations.
II Week 5 Detection of errors by use of D – tables ,differences of
polynomial .
Class Room Seminar
III Week 5 Newton’s forward interpolation formula ,Newton’s backward
interpolation formula .
IV Week 5 Gauss’s central difference formula ,stirling’s difference formula. Assignment
Sep – 23 I Week 5 Divided differences and their properties .
II Week 5 Lagrange’s formula ,errors in Lagrange’s formula . Assignment
III Week 5 Derivation of governing equations , end conditions.
IV Week 7 Newton’s general interpolation. Class Room discussion
Oct – 19
I Week 5 Revision.
II Week 5 Revision.
III Week 3 Revision
IV Week 5 SEMESTER END EXAMS
Nov - 09 I Week 5 SEMESTER END EXAMS
II Week 4 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16.
Department: Mathematics Paper: 4A ,Discrete Mathematics Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 22
I Week 3 Sets and operations of sets.
II Week 5 Sets and operations of sets.
III Week 5 Relations and functions.
IV Week 6 Some methods of proof .
Jul – 25
I Week 5 Problem Solving strategies. Assignment
II Week 5 Fundamentals of logic.
III Week 5 Logical inference.
IV Week 7 Methods of proof of an implication, first order logic and other
methods of proof.
Class Room Seminar
Aug – 22
I Week 5 Rules of inference for quantified propositions.
II Week 5 Mathematical induction ,the principle of inclusion-exclusion.
III Week 5 Generating functions of sequences , calculating coefficients
of generating functions.
IV Week 5 Recurrence relations ,solving recurrence relations by
substitution.
Assignlment
Sep – 23 I Week 5 Generating functions , the method of characteristic roots.
II Week 5 Solutions of inhomogeneous recurrence relations .
III Week 5 Relations and directed graphs ,special properties of binary
relations.
Assignment
IV Week 8 Equivalence relations , ordering relations ,lattice and
enumerations.
Class Room discussion
Oct – 19
I Week 5 Revision
II Week 5 Revision
III Week 3 Revision
IV Week 5 SEMESTER END EXAMS
Nov - 09 I Week 5 SEMESTER END EXAMS
II Week 4 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16
Department: Mathematics Paper: Solid Geometry, 1B Class: I BSc Semester II
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Co-ordinates of a point in , Distance between two points, section
formula, angle between two lines
IV Week 8
Equation of a plane in terms of it’s intercepts on the axis,
equation of the plane through the given points Length of
perpendicular from a given point to a given plane, bisector of
angle between planes
Dec – 24
I Week 6 Combined equation of two planes, orthogonal projection on a
plane, Equation of a line, angle between a line and a plane
Assignment
II Week 5
the condition that a given line may lie in a given plane, The
condition that two given lines are coplanar, number of arbitrary
constants in the equations of straight line
III Week 6
Sets of conditions which determine a line, the shortest distance
between two lines, the length and equation of the short distance
between two straight lines
Class Room discussion
IV Week 7 Length of the perpendicular from a givenj point to a given
line,definition and equation of the sphere
Class Room seminar
Jan – 17
I Week 5
Equation of the sphere through four point,Plane section of a
sphere, Intersection of two spheres, equation of a circle, sphere
through a given circle,
II Week 1
intersection of a sphere and a line, tangent plane, plane of
contact,polar plane, Pole of a plane, conjucate points, conjucate
planes
III Week 4 angle of intersection of two spheres
IV Week 7
conditions for two spheres to be orthogonal, power of a point,
radical plane, Co-axial system of spheres, simplified form of the
equation of two spheres, definition of a cone
Assignment
Feb – 23
I Week 6
Equationof cones with vertex at origin are homogeneous,
condition that the general equation of the second degree should
represent a cone
II Week 5 Enveloping cone of a sphere, right circular cone, equation of the
right circular cone with a given vertex
III Week 5
Axis and semi vertical angle, condition that a cone may have
three mutually perpendicular generators, intersection of a line and
a quadric cone
Class Room Seminar
IV Week 7
Tangent lines, tangent plane at a point, condition that a plane may
touch the cone, reciprocal cones, intersection of two cones with a
common vertex
Mar – 23
I Week 5 Right circular cone, equation of the right circular cone with a
given vertex,axis and semi-vertical angle,definition of cylinder
Assignment
II Week 5
Equation to the cylinder whose generators intersect a given conic
and are parallel to a given line, enveloping cylinder of a sphere,
the right circular cylinder, equation of the right circular cylinder
with a given axis and radius
III Week 6 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16.
Department: Mathematics Paper: 2B , Abstract Algebra & Real Analysis. Class: II BSc Semester: IV
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Rings and elementary properties : Definition and example
,Divisors of zero and cancellation laws .
IV Week 8
Integral domains and fields ,The characteristic of a ring non –
commutative rings matrices over a field ,Ideals and
homomorphism .
Dec – 24
I Week 6 Ideals ,factor rings ,Maximal Ideal and prime Ideals . Assignment
II Week 5 Homomorphism of rings ,prime fields ,polynomial rings
,Definition of polynomial ring .
III Week 6 Mean value theorem ,Role’s theorem ,Geometrical interpretation
of Rolle’s theorem .
Class Room discussion
IV Week 7
Increasing and decreasing functions ,monotonic functions
,Cauchy’s mean value theorem ,Generalized mean value theorem
.
Jan – 17
I Week 5 Taylor’s theorem with schlomitch and Roche , Cauchy’s
Lagranges form of remainders ,Cauchy’s .
II Week 1 Lagrange’s form of remainders , maclaurin’s Infinte series Class Room Seminars
III Week 4 Infinite series .power series expansions of some standard
functions .
IV Week 7
Riemann integrability : Introduction ,partitions and Riemann
sums and some properties of Darboux ,Upper and Lower
Riemann integrals .
Feb – 23
I Week 6 Riemann integral another equivalent definition of integrability
and integral , Second definition of Riemann integrability .
Assignment
II Week 5 necessary and sufficient condition for integrability particular
classes of bounded ,Integrable functions .
III Week 5
Integrability of the modulus of a bounded integrable functions ,
definition of if b≤a , Inequalities for an integral
functions defined by definite integrals.
IV Week 7 fundamental theorem of integral calculus , Generalised mean
value theorem.
Assignment
Mar – 23
I Week 5 Abel’s lemma , second mean value theorem change of variable
in integral , integration by parts.
Class Room Seminar
II Week 5 Revision.
III Week 6 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16.
Department: Mathematics Paper: Multiple integrals & Vector Calculus (3B) Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Introduction, the concept of a plane curve, Introduction to line
integrals, properties of line integrals, examples
IV Week 7 Sufficient condition for the existence of line integral, the area of a
subset of
Dec – 24
I Week 5
Introduction to double integrals, Darboux’s theorem, necessary
and sufficient condition for integrability, double integral over a
rectangle of a limit of sum
Assignment
II Week 5 Problems on double integrals, integration over non
rectangular,change of order of integration and its applications
III Week 5 Fubini’s theorem, Jordan’s theorem,change of variable in a
double integration
IV Week 6 Introduction to length of the curves, Rectifiability of a curve,
property of recdtifiable curves, surface areas
Jan – 17
I Week 5 Introduction to vector differentiation, derivative of a vecdtor
function, theorems,partial differentiation
II Week 1 Differential operator-directional derivative at a point Class Room Seminar
III Week 4 Gradient of a scalar point function and its applications, Assignment
divergence of a vecddtor,solenoidal vecdtor,laplacian operator,
curl of a vecdtor
IV Week 7 Irrotational vector, problems on divergence and curl of a vector Class Room discussion
Feb – 23
I Week 5 Vector identities, theorems, Introduction to vector integration,
definite integrals, line integrals and its applications
II Week 5 Surface integrals, Volume integrals and its applications
III Week 5 Gauss divergence theorem and its applications
IV Week 7 Green’s theorem, Stoke’s theorem and its applications Assignment
Mar – 23
I Week 5 Revision
II Week 5 Revision
III Week 5 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16.
Department: Mathematics Paper: 4B , Numerical Analysis. Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Curve Fitting : Least squares curve fitting procedures ,fitting
a straight line ,non linear curve fitting .
IV Week 7
Curve fitting by a some of exponentials ,numerical
differentiation , errors in numerical differentiation , maximum
and minimum values of a tabulated functions.
Assignment
Dec – 24
I Week 5 Numerical integration : Trapezoidal rule , simpson’s 1/3 rule ,
simpson’s 3/8 rule.
II Week 5 Boole’s rule and weddle’s rule , linear systems of equations.
III Week 5 Solution of linear systems – direct methods .
IV Week 6 matrix inversion method ,Gauss elimination method .
Jan – 17
I Week 5 method of factorisation ,ill – conditioned linear systems
,iterative methods .
Assignment
II Week 1 Jacobi’s method.
III Week 4 Gauss siedal method ,numerical solution of ordinary
differential equations : Introduction
Class Room Seminar
IV Week 6 Solution by Taylor’s series.
Feb – 23 I Week 5 Solution by Taylor’s series , picards method of successive
approximations .
II Week 5 Euler’s method ,modified Euler’s method.
III Week 5 Runge – kutta methods . Assignment
IV Week 7 Predictor-corrector methods .
Mar – 23
I Week 5 Milne’s method. Class Room Seminar
II Week 5 Revision.
III Week 6 SEMESTER-END EXAMS
IV Week 6 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2015 – 16.
Department: Mathematics Paper: 4B ,Discrete Mathematics. Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13 III Week 5 Basic concepts , isomorphisms and subgraphs.
IV Week 7 Trees and their properties.
Dec – 24
I Week 5 Spanning trees , directed trees. Assignment
II Week 5 Binary trees .
III Week 5
Planar graphs, Euler’s formula. Quiz
IV Week 6 Multi graphs and Euler circuits.
Jan – 17
I Week 5 Hamiltonian graphs.
II Week 1 Chromatic numbers .
III Week 4 the four color problem ,Introduction .
IV Week 6 Boolean algebras ,Switching mechanisms. Class Room Seminar
Feb – 23
I Week 5 Boolean functions ,Minimization of Boolean functions.
II Week 5 Additional input:
Network flows: graphs as model of flow of commodities.
Class Room Seminar
III Week 5 Flows.
IV Week 6 Maximal flows and minimal cuts. Assignment
Mar – 23
I Week 5 Revision.
II Week 5 Revision.
III Week 6 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2016 – 17.
Department: Mathematics Paper: Differential Equations Class: I BSc Semester: 1
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
July – 24
I Week 5 Linear differential equations; Differential equations reducible
to linear form
II Week 5 Exact differential equations; Integrating factors; Change of
variables
III Week 6 Orthogonal trajectories, Equations solvable for p; Equations
solvable for y
IV Week 8
Equations solvable for x; Equations that do not contain x
(or y); Equations of the first degree in x and y - Clairaut's
equation.
Assignment
Aug – 22
I Week 6
Solution of homogeneous linear differential equations of
order n with constant coefficients.Solution of the non-
homogeneous linear differential equations with constant
coefficients by means of polynomial operators.
II Week 4
General Solution of f(D)y=0, General solution of
f(D)y=Q when Q is a function of x, 1/f(D) is expressed as
partial fractions
III Week 4 Particular integral of f(D)y=Q when Q=be
ax,
particular integral of f(D)y=Q when Q=bsinax, bcosax
Assignment
IV Week 8 Solution of the non-homogeneous linear differential equations
with constant coefficients by means of polynomial operators,
Class Room Seminar
particular integral of f(D)y=Q when Q=bxk.
Sept – 23
I Week 5
Particular integral of f(D)y=Q, when Q=eax
V, where V is a
function of x, particular integral of f(D)y=Q, when Q=xV,
where V is a function of x.
Assignment
II Week 4 Particular integral of f(D)y=Q, when Q=x
nV, where V is a
function of x. Method of variation of Parameters.
III Week 6 Linear Differential equations with non-constant coefficients,
The Cauchy - Euler equations
Assignment
IV Week 8 Method of undetermined coefficients. Class Room Seminar
Oct – 18
I Week 6 Revision
II Week 0
III Week 5 Revision
IV Week 7 Semester-End Examinations
Nov - 11 I Week 6 Semester-End Examinations
II Week 5 Semester-End Examinations
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P
Teaching Plan for the Academic Year: 2016 – 17
Department: Mathematics Paper: 2A, Abstract Algebra Class: II BSc Semester: 3
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 25
I Week 6 Binary operations , Algebraic structure , semi – group , Monoid .
II Week 5 Group definition and elementary properties , finite and infinte
groups , examples
III Week 6 Order of a group , composition tables with examples .
IV Week 8
Subgroups : complex definition , multiplication of two complexes
, inverse of a complex , subgroup definition , examples .
Jul – 24
I Week 5 Criterion for a complex to be a subgroup , criterion for the
product of two subgroups to be a subgroup .
II Week 5 Union and intersection of subgroups , cosets and lagrange’s
theorem : cosets definition , properties of cosets .
Assignment
III Week 6 Index of a subgroup of a finite group , lagrange’s theorem .
IV Week 8 Normal subgroups : definition of normal subgroup , proper and
improper normal subgroups and Hamilton group .
Class Room Seminar
Aug – 22
I Week 6 Criterion subgroup to be a normal subgroup , intersection of two
normal subgroups ,
II Week 4 Subgroups of index2 is a normal subgroup , simple group ,
quotient group , criterion for the existence of a quotient group .
III Week 4
Homomorphism : definition of homomorphism , image of
homomorphism , elementary properties of homomorphism ,
isomorphism .
IV Week 8
Automorphism definition and elementary properties , kernel of a
homomorphism , fundamental theorem on homomorphism and
applications .
Assignment
Sep – 23
I Week 5 Permutations and Cyclic groups : definition of permutation ,
permutation multiplication , inverse of a permutation .
Class Room Seminar
II Week 4 Cyclic permutations , transposition , even and odd permutations ,
cayley’s theorem .
III Week 6
ADDITIONAL INPUT :
Construction of finite non abelian group , symmetries of
geometrical figures , Cyclic groups : definition of cyclic group
Assignment
IV Week 8 Elementary properties , classification of cyclic groups .
Oct – 18
I Week 6 Revision
II Week 0 Holidays
III Week 5 Revision
IV Week 7 SEMESTER END EXAMS
Nov - 11 I Week 6 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2016 – 17.
Department: Mathematics Paper: Linear Algebra, 3A Class: III BSC Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 25
I Week 5 Vector spaces, general properties of vector spaces
II Week 5 n-dimensional vectors, addition and scalar multiplication of
vectors,Internal and external composition
III Week 5 Vector subspaces, algebra of subspaces
IV Week 7 Linear combination of vectors, linear span of a set,linear sum of
two subspaces
Assignment
Jul – 24
I Week 5 Linear independence and dependence of vectors, Basis of vector
space
II Week 5 Finite dimensional vector spaces,dimension of vector space,
dimension of subspace
III Week 5 Homomorphism of vector spaces, Isomorphism of vector spaces,
quotient space,dimension of quotient space
IV Week 7 Linear transformations,properties of linear transformations,range
and null space of linear transformation
Class Room Seminar
Aug – 22
I Week 5 Rank and nullity of linear transformations and its applications Assignment
II Week 4 Linear transformation as vectors, product of linear
transformations, invertible linear transformations
III Week 4 Singular and non singular transformations, Matrix of a linear
transformation,the adjoint of a linear transformation,
IV Week 7 Sylvester’s law of nullity, Characteristic values and characteristic Class Room discussion
vectors
Sep – 23
I Week 5 Cayley-Hamilton theorem, Diagonalizable operators
II Week 4 Inner product spaces, Euclidean and unitary spaces, length of a
vector
III Week 5 Schwartz inequality, orthoganality, orthonormal set Assignment
IV Week 7 Complete orthonormal set, orthonormal basis, Gram-schmidt
orthogonalization process, Bessel’s inequality
Class Room Seminar
Oct – 18
I Week 5 Revision
II Week 0
III Week 5 Revision
IV Week 7 SEMESTER END EXAMS
Nov - 11 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2016 – 17.
Department: Mathematics Paper: 4A,Numerical Analysis. Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 25
I Week 5 Errors in numerical computations.
II Week 5 Numbers and their accuracy.
III Week 5 Errors and their computation ,Absolute , Relative and percentage
errors.
IV Week 7 A general error formula , error in a series approximation.
Jul – 24
I Week 5 Solution of algebraic and transcendental equations.
II Week 5 Bisection ,the method of falsi position .
III Week 5 The iteration method , the Newton – Raphson method. Assignment
IV Week 7 Generalized Newton – Raphson method , Ramnujan’s method ,
interpolatrion , forward differences.
Aug – 22
I Week 5 Backward differences , central differences , symbolic relations.
II Week 4 Detection of errors by use of D – tables ,differences of
polynomial .
III Week 4 Newton’s forward interpolation formula ,Newton’s backward
interpolation formula .
IV Week 7 Gauss’s central difference formula ,stirling’s difference formula. Student Seminar
Sep – 23 I Week 5 Divided differences and their properties . Assignment
II Week 4 Lagrange’s formula ,errors in Lagrange’s formula .
III Week 5 Derivation of governing equations , end conditions.
IV Week 7 Newton’s general interpolation. Assignment
Oct – 18
I Week 5 Revision.
II Week 0
III Week 5 Revision
IV Week 6 SEMESTER END EXAMS
Nov - 11 I Week 5 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2016 – 17.
Department: Mathematics Paper: 4A ,Discrete Mathematics Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 25
I Week 5 Sets and operations of sets.
II Week 5 Sets and operations of sets.
III Week 5 Relations and functions.
IV Week 7 Some methods of proof .
Jul – 24
I Week 5 Problem Solving strategies.
II Week 5 Fundamentals of logic.
III Week 5 Logical inference. Assignment
IV Week 7 Methods of proof of an implication, first order logic and other
methods of proof.
Class Room Seminar
Aug – 22
I Week 5 Rules of inference for quantified propositions.
II Week 4 Mathematical induction ,the principle of inclusion-exclusion.
III Week 4 Generating functions of sequences , calculating coefficients
of generating functions.
IV Week 7 Recurrence relations ,solving recurrence relations by
substitution.
Assignment
Sep – 23
I Week 5 Generating functions , the method of characteristic roots.
II Week 4 Solutions of inhomogeneous recurrence relations .
III Week 5 Relations and directed graphs ,special properties of binary
relations.
IV Week 7 Equivalence relations , ordering relations ,lattice and
enumerations.
Class Room Seminar
Oct – 18
I Week 5 Revision
II Week 0
III Week 5 Revision
IV Week 7 SEMESTER END EXAMS
Nov - 11 I Week 6 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2016 – 17
Department: Mathematics Paper: Solid Geometry, 1B Class: I BSc Semester: II
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14
III Week 6 Co-ordinates of a point in, Distance between two points, section
formula, angle between two lines
IV Week 8
Equation of a plane in terms of it’s intercepts on the axis,
equation of the plane through the given points Length of
perpendicular from a given point to a given plane, bisector of
angle between planes
Assignment
Dec – 24
I Week 6 Combined equation of two planes, orthogonal projection on a
plane, Equation of a line, angle between a line and a plane
II Week 4
the condition that a given line may lie in a given plane, The
condition that two given lines are coplanar, number of arbitrary
constants in the equations of straight line
III Week 6
Sets of conditions which determine a line, the shortest distance
between two lines, the length and equation of the short distance
between two straight lines
IV Week 8 Length of the perpendicular from a givenj point to a given
line,definition and equation of the sphere
Class Room Seminar
Jan – 19 I Week 5 Equation of the sphere through four point,Plane section of a Assignment
sphere, Intersection of two spheres, equation of a circle, sphere
through a given circle,
II Week 3
intersection of a sphere and a line, tangent plane, plane of
contact,polar plane, Pole of a plane, conjucate points, conjucate
planes
III Week 3 angle of intersection of two spheres
IV Week 8
conditions for two spheres to be orthogonal, power of a point,
radical plane, Co-axial system of spheres, simplified form of the
equation of two spheres, definition of a cone
Class Room Seminar
Feb – 20
I Week 5
Equationof cones with vertex at origin are homogeneous,
condition that the general equation of the second degree should
represent a cone
II Week 4 Enveloping cone of a sphere, right circular cone, equation of the
right circular cone with a given vertex
Assignment
III Week 6
Axis and semi vertical angle, condition that a cone may have 3
mutually perpendicular generators, intersection of a line and a
quadric cone
Class Room Seminar
IV Week 5
Tangent lines, tangent plane at a point, condition that a plane may
touch the cone, reciprocal cones, intersection of two cones with a
common vertex
Mar – 25
I Week 6 Right circular cone, equation of the right circular cone with a
given vertex,axis and semi-vertical angle,definition of cylinder
II Week 5
Equation to the cylinder whose generators intersect a given conic
and are parallel to a given line, enveloping cylinder of a sphere,
the right circular cylinder, equation of the right circular cylinder
with a given axis and radius
Assignment
III Week 6 SEMESTER-END EXAMS
IV Week 8 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P
Teaching Plan for the Academic Year: 2016 – 17
Department: Mathematics Paper: 2B, Real Analysis Class: II BSc Semester: IV
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14
III Week 6 Real Numbers : The algebraic and order properties of IR ,
absolute value and real line , the completeness properties of IR .
IV Week 8 Applications of Supremum property , Intervals .
Real sequences : sequences and their limits .
Dec – 24
I Week 6
Range and Boundedness of sequences , limit of a sequence and
convergent sequence , The cauchy’s criterion , properly divergent
sequences .
II Week 4
Monotone sequences , necessary and sufficient condition for
convergence of monotone sequences , limit point of a sequence ,
sub-sequences and Bolzano – Weierstress theorem .
Assignment
III Week 6 Cauchy’s sequences Cauchy’s general principle .of converges
theorem, series; Introduction to series.
IV Week 8
Convergence of series , Cauchy’s general principle of
convergence for series , tests for convergence of series , series of
non – negative terms .
1. P - test
Class Room discussion
Jan – 19 I Week 5 2. Cauchy’s nth root test or root test.
3. D- Alembert’s test or ratio test.
4. Alternating series, Leibnitz test.
5. Absolute convergence and conditional convergence, semi
convergence .
Assignment
II Week 3 Continuity : limits , real valued functions , boundedness of a
function , limits of functions .
III Week 3 Some extensions of the limit concept.
IV Week 8
Infinite limits, limits at infinity .
continuous functions : continuous function , combination of
continuous function .
Assignment
Feb – 20
I Week 5
Differentiation and mean value theorems : The derivability of a
function on an interval , at a point , derivability and continuity of
a function.
II Week 4 Graphical meaning of the derivative mean value theorems :
Role’s theorem .
III Week 6 Lagrange’s theorem , cauchy’s mean value theorem . Class Room Seminar
IV Week 5 Riemann Integration : Riemann integral , Riemann integral
functions , Darboux theorem .
Mar – 25
I Week 6 Necessary and sufficient for R – integrability properties of
integrable functions.
II Week 5 Fundamental theorem of integral calculus , Integral as a limit of a
sum , Mean value theorems.
Assignment
III Week 6 SEMESTER-END EXAMS
IV Week 8 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2016 – 17.
Department: Mathematics Paper: Multiple integrals & Vector Calculus (3B) Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14
III Week 5 Introduction, the concept of a plane curve, Introduction to line
integrals, properties of line integrals, examples
IV Week 7 Sufficient condition for the existence of line integral, the area of a
subset of
Dec – 24
I Week 5
Introduction to double integrals, Darboux’s theorem, necessary
and sufficient condition for integrability, double integral over a
rectangle of a limit of sum
II Week 4 Problems on double integrals, integration over non
rectangular,change of order of integration and its applications
Assignment
III Week 5 Fubini’s theorem, Jordan’s theorem,change of variable in a
double integration
IV Week 7 Introduction to length of the curves, Rectifiability of a curve,
property of recdtifiable curves, surface areas
Jan – 19
I Week 5 Introduction to vector differentiation, derivative of a vecdtor
function, theorems,partial differentiation
Class Room Seminar
II Week 3 Differential operator-directional derivative at a point
III Week 3 Gradient of a scalar point function and its applications,
divergence of a vector,solenoidal vector,laplacian operator, curl
of a vector
IV Week 7 Irrotational vector, problems on divergence and curl of a vector Class Room Seminar
Feb – 20
I Week 5 Vector identities, theorems, Introduction to vector integration,
definite integrals, line integrals and its applications
II Week 4 Surface integrals, Volume integrals and its applications
III Week 5 Gauss divergence theorem and its applications
IV Week 5 Green’s theorem, Stoke’s theorem and its applications Assignment
Mar – 25
I Week 5 Revision
II Week 5 Revision
III Week 5 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2016 – 17.
Department: Mathematics Paper: 4B , Numerical Analysis. Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14
III Week 5 Curve Fitting : Least squares curve fitting procedures ,fitting
a straight line ,non linear curve fitting .
IV Week 7
Curve fitting by a some of exponentials ,numerical
differentiation , errors in numerical differentiation , maximum
and minimum values of a tabulated functions.
Assignment
Dec – 24
I Week 5 Numerical integration : Trapezoidal rule , simpson’s 1/3 rule ,
simpson’s 3/8 rule.
II Week 4 Boole’s rule and weddle’s rule , linear systems of equations.
III Week 5 Solution of linear systems – direct methods . Assignment
IV Week 7 matrix inversion method ,Gauss elimination method .
Jan – 19
I Week 5 method of factorisation ,ill – conditioned linear systems
,iterative methods .
II Week 3 Jacobi’s method.
III Week 3 Gauss siedal method ,numerical solution of ordinary
differential equations : Introduction
IV Week 7 Solution by Taylor’s series. Student Seminar
Feb – 20 I Week 5 Solution by Taylor’s series , picards method of successive
approximations .
II Week 4 Euler’s method ,modified Euler’s method. Assignment
III Week 5 Runge – kutta methods .
IV Week 5 Predictor-corrector methods .
Mar – 25
I Week 5 Milne’s method. Student Seminar
II Week 5 Revision.
III Week 5 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2016 – 17.
Department: Mathematics Paper: 4B ,Discrete Mathematics. Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14 III Week 5 Basic concepts , isomorphisms and subgraphs.
IV Week 7 Trees and their properties.
Dec – 24
I Week 5 Spanning trees , directed trees.
II Week 4 Binary trees .
III Week 5 Planar graphs, Euler’s formula. Assignment
IV Week 7 Multi graphs and Euler circuits. Class Room Seminar
Jan – 19
I Week 5 Hamiltonian graphs.
II Week 3 Chromatic numbers .
III Week 3 the four color problem ,Introduction .
IV Week 7 Boolean algebras ,Switching mechanisms.
Feb – 20
I Week 5 Boolean functions ,Minimization of Boolean functions. Assignment
II Week 4 Additional input:
Network flows: graphs as model of flow of commodities.
III Week 5 Flows. Class Room Seminar
IV Week 5 Maximal flows and minimal cuts.
Mar – 25 I Week 5 Revision.
II Week 5 Revision.
III Week 6 SEMESTER-END EXAMS
IV Week 8 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2017 – 18.
Department: Mathematics Paper: Differential Equations, 1A Class: I BSc Semester: I
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jul – 25
I Week 6 Linear differential equations; Differential equations reducible
to linear form
II Week 5 Exact differential equations; Integrating factors; Change of
variables
III Week 6 Orthogonal trajectories, Equations solvable for p; Equations
solvable for y
Assignment
IV Week 8
Equations solvable for x; Equations that do not contain x
(or y); Equations of the first degree in x and y - Clairaut's
equation.
Class Room Seminar
Aug – 21
I Week 4
Solution of homogeneous linear differential equations of
order n with constant coefficients.Solution of the non-
homogeneous linear differential equations with constant
coefficients by means of polynomial operators.
II Week 4
General Solution of f(D)y=0, General solution of
f(D)y=Q when Q is a function of x, 1/f(D) is expressed as
partial fractions
Assignment
III Week 5 Particular integral of f(D)y=Q when Q=be
ax,
particular integral of f(D)y=Q when Q=bsinax, bcosax
IV Week 8
Solution of the non-homogeneous linear differential equations
with constant coefficients by means of polynomial operators,
particular integral of f(D)y=Q when Q=bxk.
Class Room Seminar
Sep – 18
I Week 5
Particular integral of f(D)y=Q, when Q=eax
V, where V is a
function of x, particular integral of f(D)y=Q, when Q=xV,
where V is a function of x.
Assignment
II Week 5 Particular integral of f(D)y=Q, when Q=x
nV, where V is a
function of x. Method of variation of Parameters.
III Week 6 Linear Differential equations with non-constant coefficients
IV Week 2 The Cauchy-Euler Equations Assignment
Oct – 22
I Week 5 Method of undetermined coefficients
II Week 5 Revision
III Week 4 Revision
IV Week 8 Semester-End Examinations
Nov - 11 I Week 6 Semester-End Examinations
II Week 5 Semester-End Examinations
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P
Teaching Plan for the Academic Year: 2017 – 18
Department: Mathematics Paper: 2A, Abstract Algebra Class: II BSc Semester: 3
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 24
I Week 6 Binary operations , Algebraic structure , semi – group , Monoid .
II Week 5 Group definition and elementary properties , finite and infinte
groups , examples
III Week 6 Order of a group , composition tables with examples .
IV Week 7
Subgroups : complex definition , multiplication of two complexes
, inverse of a complex , subgroup definition , examples .
Assignment
Jul – 25
I Week 6 Criterion for a complex to be a subgroup , criterion for the
product of two subgroups to be a subgroup .
II Week 5 Union and intersection of subgroups , cosets and lagrange’s
theorem : cosets definition , properties of cosets .
III Week 6 Index of a subgroup of a finite group , lagrange’s theorem .
IV Week 8 Normal subgroups : definition of normal subgroup , proper and
improper normal subgroups and Hamilton group .
Class Room Seminar
Aug – 21
I Week 4 Criterion subgroup to be a normal subgroup , intersection of two
normal subgroups ,
Assignment
II Week 4 Subgroups of index2 is a normal subgroup , simple group ,
quotient group , criterion for the existence of a quotient group .
III Week 5
Homomorphism : definition of homomorphism , image of
homomorphism , elementary properties of homomorphism ,
isomorphism .
IV Week 8
Automorphism definition and elementary properties , kernel of a
homomorphism , fundamental theorem on homomorphism and
applications .
Class Room discussion
Sep – 18
I Week 5 Permutations and Cyclic groups : definition of permutation ,
permutation multiplication , inverse of a permutation .
Assignment
II Week 5 Cyclic permutations , transposition , even and odd permutations ,
cayley’s theorem .
III Week 6
ADDITIONAL INPUT :
Construction of finite non abelian group , symmetries of
geometrical figures , Cyclic groups : definition of cyclic group
Assignment
IV Week 2 Elementary properties
Oct – 22
I Week 5 Classification of cyclic groups Class Room Seminar
II Week 5 Revision
III Week 4 Revision
IV Week 8 SEMESTER END EXAMS
Nov - 11 I Week 6 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2017 – 18.
Department: Mathematics Paper: Ring Theory & Vector Calculus, 3A Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 24
I Week 5 Abstract algebra : Introduction, basics
II Week 5 Revision of groups, subgroups, cosets and lagrange’s
theorem, normal subgroups ,cyclic groups
III Week 5 Definition of a ring and basic properties, Boolean rings,
divisors of zero, cancellation laws
IV Week 6 Integral domains, division ring, field, the characteristic of a
ring, the characteristic of a field, subrings
Jul – 25
I Week 5 Ideals, principal ideals, quotient rings, Euclidean rings Assignment
II Week 5 Definition of a homorphism, homorphic image, elementary
properties of homomorphism
III Week 5 Kernel of a homomorphism, fundamental theorem of
homomorphism
Class Room Seminar
IV Week 7 Maximal ideals, prime ideals Assignment
Aug – 21
I Week 4 Vector differentiation, ordinary derivatives of vectors
II Week 4 Differentiability, gradient, divergence, curl
III Week 5 Formulae involving these operators, vector integration
IV Week 7 Line integral, surface integral
Sep – 18 I Week 5 Volume integral with examples, Assignment
II Week 5 Gauss divergence theorem and applications
III Week 5 Green’s theorem and applications
IV Week 2 Stoke’s theorem Class room seminar
Oct – 22
I Week 5 Applications of stoke’s theorem Assignment
II Week 5 Revision
III Week 4 Revision
IV Week 8 SEMESTER END EXAMS
Nov - 11 I Week 6 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P
Teaching Plan for the Academic Year: 2017 – 18
Department: Mathematics Paper: Linear Algebra, 4A Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 24
I Week 5 Vector spaces, General properties of vector spaces, n-dimentional
vectors,addition and scalar multiplication of vectors
II Week 5 Internal and external composition, null space, Vecdtor subspaces,
Algebra of subspaces
III Week 5 Linear sum of two subspaces, linear combination of vectors,
linear span
IV Week 6 Linear independence and linear dependence of vectors Assignment
Jul – 25
I Week 5 Basis of vector space, Finite dimensional vector spaces
II Week 5 Basis extension, coordinates
III Week 5 Dimension of a vector space, dimension of a subspace
IV Week 7 Quotient space and dimension of quotient space Class Room Seminar
Aug – 21
I Week 4
Linear transformations, linear operators, properties of linear
transformations,sum and product of linear
transformations,Algebra of linear operators
II Week 4 Range and null space of linear transformation, Rank and nullity
of linear transformation
Assignment
III Week 5 Rank-nullity theorem, linear equations
IV Week 7 Characteristic roots, characteristic values& vectors of square Class Room discussion
matrix, cayley-Hamilton theorem
Sep – 18
I Week 5 Innerproduct spaces, Euclidean and unitary spaces, norm of a
vector, Schwarz inequality
Assignment
II Week 5 Triangle inequality, parallelogram law, orthogonality
III Week 5 Orthonormal set, complete orthonormal set
IV Week 2 Gram-schmidt orthogonalisation process Assignment
Oct – 22
I Week 5 Bessel’s inequality, Parseval’s identity
II Week 5 Revision
III Week 4 Revision
IV Week 7 SEMESTER END EXAMS
Nov - 11 I Week 6 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2017 – 18.
Department: Mathematics Paper: Solid Geometry, 1B Class: I BSc Semester: II
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14
III Week 6 Co-ordinates of a point in , Distance between two points,
section formula, angle between two lines
IV Week 8 Equation of a plane in terms of it’s intercepts on the axis,
equation of the plane through the given points
Dec – 23
I Week 5 Length of perpendicular from a given point to a given plane,
bisector of angle between planes
II Week 5 Combined equation of two planes, orthogonal projection on a
plane
Assignment
III Week 6 Equation of a line, angle between a line and a plane, the
condition that a given line may lie in a given plane
IV Week 7 The condition that two given lines are coplanar, number of
arbitrary constants in the equations of straight line
Student Seminar
Jan – 17
I Week 5
Sets of conditions which determine a line, the shortest
distance between two lines, the length and equation of the
short distance between two straight lines
II Week 3 Length of the perpendicular from a givenj point to a given
line,definition and equation of the sphere
III Week 3 Equation of the sphere through four point,Plane section of a
sphere
Assignment
IV Week 6
Intersection of two spheres, equation of a circle, sphere
through a given circle, intersection of a sphere and a line,
tangent plane, plane of contact,polar plane
Feb – 22
I Week 6
Pole of a plane, conjucate points, conjucate planes, angle of
intersection of two spheres, conditions for two spheres to be
orthogonal, power of a point, radical plane
II Week 4
Co-axial system of spheres, simplified form of the equation of
two spheres, definition of a cone, vertex, guiding curve,
generators, equation of the cone with a given vertex and
guiding curve
Assignment
III Week 6
Equationof cones with vertex at origin are homogeneous,
condition that the general equation of the second degree
should represent a cone
IV Week 6 Enveloping cone of a sphere, right circular cone, equation of
the right circular cone with a given vertex
Student Seminar
Mar – 23
I Week 5
Axis and semi vertical angle, condition that a cone may have
3 mutually perpendicular generators, intersection of a line and
a quadric cone
II Week 5
Tangent lines, tangent plane at a point, condition that a plane
may touch the cone, reciprocal cones, intersection of two
cones with a common vertex
Assignment
III Week 6 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P
Teaching Plan for the Academic Year: 2017 – 18
Department: Mathematics Paper: 2B, Real Analysis Class: II BSc Semester: IV
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14
III Week 6 Real Numbers : The algebraic and order properties of IR ,
absolute value and real line , the completeness properties of IR .
IV Week 8 Applications of Supremum property , Intervals .
Real sequences : sequences and their limits .
Dec – 23
I Week 5
Range and Boundedness of sequences , limit of a sequence and
convergent sequence , The cauchy’s criterion , properly divergent
sequences .
II Week 5
Monotone sequences , necessary and sufficient condition for
convergence of monotone sequences , limit point of a sequence ,
sub-sequences and Bolzano – Weierstress theorem .
Assignment
III Week 6 Cauchy’s sequences Cauchy’s general principle .of converges
theorem, series; Introduction to series.
IV Week 7
Convergence of series , Cauchy’s general principle of
convergence for series , tests for convergence of series , series of
non – negative terms .
1. P - test
Student Seminar
Jan – 17 I Week 5
2. Cauchy’s nth root test or root test.
3. D- Alembert’s test or ratio test.
4. Alternating series, Leibnitz test.
5. Absolute convergence and conditional convergence, semi
Assignment
convergence .
II Week 3 Continuity : limits , real valued functions , boundedness of a
function , limits of functions .
III Week 3 Some extensions of the limit concept.
IV Week 6
Infinite limits, limits at infinity .
continuous functions : continuous function , combination of
continuous function .
Feb – 22
I Week 6
Differentiation and mean value theorems : The derivability of a
function on an interval , at a point , derivability and continuity of
a function.
Class Room Seminar
II Week 4 Graphical meaning of the derivative mean value theorems :
Role’s theorem .
III Week 6 Lagrange’s theorem , cauchy’s mean value theorem . Assignment
IV Week 6 Riemann Integration : Riemann integral , Riemann integral
functions , Darboux theorem .
Mar – 23
I Week 5 Necessary and sufficient for R – integrability properties of
integrable functions.
II Week 5 Fundamental theorem of integral calculus , Integral as a limit of a
sum , Mean value theorems.
Assignment
III Week 6 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2017 – 18.
Department: Mathematics Paper: 3B, Numerical Analysis Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 24
I Week 5 Bridge Course, Errors in numerical computations
II Week 5 Numbers and their accuracy, Errors and their computation,
Absolute,relative and percentage errors
III Week 5
A general error formula, error in a series approximation,
Solution of Algebraic and transcendental equations, Bisection
method and Regula –falsi method
IV Week 6
The iteration method, The Newton-Raphson method,
Generalised Newton-Raphson method, Ramanujan method,
Muller’s method
Assignment
Jul – 25
I Week 5 Interpolation: Forward differences, Backward differences,
Central differences
Class Room Seminar
II Week 5 Symbolic relations, Detection of errors by use of D-tables
III Week 5 Differences of a polynomial, Newton’s forward interpolation
formula
IV Week 7 Newton’s backward interpolation formula-Examples Assignment
Aug – 21
I Week 4 Gauss’s central difference formulae
II Week 4 Stirling’s difference formula,
III Week 5 Bessel’ formula Assignment
IV Week 7 Everett’s formula Class Room Seminar
Sep – 18 I Week 5 Divided differences and their properties
II Week 5 Relation between divided differences and forward
differences, Backward differences , central differences
III Week 5 Lagrange’s formula Assignment
IV Week 2 Error in Lagrange’s formula,Newton’s general interpolation
formula
Oct – 22
I Week 5 Inverse interpolation
II Week 5 Revision
III Week 4 Revision
IV Week 7 SEMESTER END EXAMS
Nov - 11 I Week 6 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram , W.G.DIST. A.P
Teaching Plan for the Academic Year: 2017 – 18
Department: Mathematics Paper: 4B Advanced Numerical Analysis (cluster) Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14 III Week 5
Curve fitting : least squares curve fitting procedures ,fitting a
straight line.
IV Week 7 Non linear curve fitting , curve fitting by a sum of exponentials.
Dec – 23
I Week 5 Numerical differentiation : Derivatives using Newton’s forward
difference formula , Newton’s backward difference formula .
Assignment
II Week 5 Derivatives using central difference formula : Stirling’s
interpolation formula ,Newton’s divided difference formula
III Week 5 Maximum and Minimum values of a tabulated functions .
IV Week 6 Numerical integration : General quadrature formula , Trapezoidal
rule , Simpson’s 1/3 – rule .
Class Room Seminar
Jan – 17
I Week 5 Simpson’s 3/8 – rule , Boole’s rule and Weddle’s rule .
II Week 3 Euler – Maclaurin formula of summation and quadrature , the
Euler transformation .
Assignment
III Week 3 Solutions of simultaneous linear systems of equations .
IV Week 5
Solutions of simultaneous linear systems of equations : solution
of linear systems – Direct methods , matrix inversion method ,
Gaussian elimination methods .
Feb – 22 I Week 5 Gauss – Jordan method , method of factorization , solution of tri Class Room Seminar
diagonal systems , iterative methods .
II Week 4 Jacobi’s method , Gauss Seidal method
III Week 5
Numerical solution of ordinary differential equations : Solution
by Taylor’s series , Picard’s method of successive
approximations .
Assignment
IV Week 5 Euler’s method , modified Euler’s method , Runge – Kutta
second and fourth order methods .
Assignment
Mar – 23
I Week 5 Revision
II Week 5 Revision
III Week 5 SEMESTER-END EXAMS
IV Week 6 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2017 – 18.
Department: Mathematics Paper: Special functions, 5B,( Cluster) Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 14
III Week 5 Hermite polynomial: Hermite differential equation, solution
of Hermite equation,
IV Week 7 Hermite polynomials, generating functions, other forms for
Hermite polynomials
Dec – 23
I Week 5 To find first few Hermite polynomials, orthogonal properties
of Hermite polynomials,
Assignment
II Week 5 Recurrence formulae for Hermite polynomials, problems
III Week 5
Laguerre polynomials- Lagurre’s differential equations,
solution of Laguerre’s equation, Laguerre’s polynomials
,generating functions
IV Week 6
Other forms of laguerre’s polynomial, to find first few
Laguerre’s polynomials, orthogonal properties of laguerre’s
polynomials, recurrence formulae
Class Room Seminar
Jan – 17 I Week 5
Associated laguerre equation, Legendre’s equation-
definition, solution of legendre’s equation, definition of
,general solution of legendre’s equation
Assignment
II Week 3 To show that is the coefficient of in the expansion of
Orthogonal properties of legendre’s equation, recurrence
formula
III Week 3 Rodrigue’s formula, problems
IV Week 5 Bessel’s equation-Definition, solution of Bessel’s general
differential equation, general solution of Bessel’s equation
Class Room
Discussion
Feb – 22
I Week 5
Integration of Bessel’s equation in series for n=0, definition
of
Recurrence formula for
Assignment
II Week 4
Generating function for , Beta and gamma functions-
Euler’s integrals, Beta and gamma functions, Elementary
properties
III Week 5 Transformations of gamma functions, another form of Beta
function
Assignment
IV Week 5 Relation between Beta and gamma functions, other
transformations
Mar – 23
I Week 5 Revision
II Week 5 Revision
III Week 5 SEMESTER-END EXAMS
IV Week 6 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P
Teaching Plan for the Academic Year: 2018 – 19
Department: Mathematics Paper: Differential Equations, IA Class: I BSc Semester: I
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jul – 25
I Week 6 Linear differential equations; Differential equations reducible
to linear form
II Week 5 Exact differential equations; Integrating factors; Change of
variables
III Week 6 Orthogonal trajectories, Equations solvable for p; Equations
solvable for y
IV Week 8
Equations solvable for x; Equations that do not contain x
(or y); Equations of the first degree in x and y - Clairaut's
equation.
Assignment
Aug – 24
I Week 6
Solution of homogeneous linear differential equations of
order n with constant coefficients.Solution of the non-
homogeneous linear differential equations with constant
coefficients by means of polynomial operators.
Class Room
Discussion
II Week 5
General Solution of f(D)y=0, General solution of
f(D)y=Q when Q is a function of x, 1/f(D) is expressed as
partial fractions
Assignment
III Week 6 Particular integral of f(D)y=Q when Q=beax
,
particular integral of f(D)y=Q when Q=bsinax, bcosax
IV Week 7
Solution of the non-homogeneous linear differential equations
with constant coefficients by means of polynomial operators,
particular integral of f(D)y=Q when Q=bxk.
Class Room Seminar
Sep – 21
I Week 5
Particular integral of f(D)y=Q, when Q=eax
V, where V is a
function of x, particular integral of f(D)y=Q, when Q=xV,
where V is a function of x.
Assignment
II Week 4 Particular integral of f(D)y=Q, when Q=x
nV, where V is a
function of x. Method of variation of Parameters.
III Week 5 Linear Differential equations with non-constant coefficients,
The Cauchy - Euler equations
Assignment
IV Week 7 Method of undetermined coefficients. Class Room Seminar
Oct – 19
I Week 5 Revision
II Week 5 Revision
III Week 0 Holidays
IV Week 9 Semester-End Examinations
Nov - 09 I Week 4 Semester-End Examinations
II Week 5 Semester-End Examinations
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2018 – 19.
Department: Mathematics Paper: 2A, Abstract Algebra Class: II BSc Semester: 3
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 22
I Week 4 Binary operations , Algebraic structure , semi – group , Monoid .
II Week 5 Group definition and elementary properties , finite and infinte
groups , examples
III Week 5 Order of a group , composition tables with examples .
IV Week 8
Subgroups : complex definition , multiplication of two complexes
, inverse of a complex , subgroup definition , examples .
Assignment
Jul – 25
I Week 6 Criterion for a complex to be a subgroup , criterion for the
product of two subgroups to be a subgroup .
II Week 5 Union and intersection of subgroups , cosets and lagrange’s
theorem : cosets definition , properties of cosets .
III Week 6 Index of a subgroup of a finite group , lagrange’s theorem . Class Room Seminar
IV Week 8 Normal subgroups : definition of normal subgroup , proper and
improper normal subgroups and Hamilton group .
Assignment
Aug – 24
I Week 6 Criterion subgroup to be a normal subgroup , intersection of two
normal subgroups ,
II Week 5 Subgroups of index2 is a normal subgroup , simple group ,
quotient group , criterion for the existence of a quotient group .
III Week 6
Homomorphism : definition of homomorphism , image of
homomorphism , elementary properties of homomorphism ,
isomorphism .
IV Week 7
Automorphism definition and elementary properties , kernel of a
homomorphism , fundamental theorem on homomorphism and
applications .
Class Room Seminar
Sep – 21
I Week 5 Permutations and Cyclic groups : definition of permutation ,
permutation multiplication , inverse of a permutation .
II Week 4 Cyclic permutations , transposition , even and odd permutations ,
cayley’s theorem .
Assignment
III Week 5
ADDITIONAL INPUT :
Construction of finite non abelian group , symmetries of
geometrical figures , Cyclic groups : definition of cyclic group
IV Week 7 Elementary properties , classification of cyclic groups . Assignment
Oct – 19
I Week 5 Revision
II Week 5 Revision
III Week 0 Holidays
IV Week 9 SEMESTER END EXAMS
Nov - 09 I Week 4 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2018 – 19.
Department: Mathematics Paper: Ring theory&vector calculus, 3A Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 22
I Week 4 Abstract algebra : Introduction, basics
II Week 5 Revision of groups, subgroups, cosets and lagrange’s theorem,
normal subgroups ,cyclic groups
III Week 5 Definition of a ring and basic properties, Boolean rings, divisors
of zero, cancellation laws
IV Week 7 Integral domains, division ring, field, the characteristic of a ring,
the characteristic of a field, subrings
Assignment
Jul – 25
I Week 5 Ideals, principal ideals, quotient rings, Euclidean rings
II Week 5 Definition of a homorphism, homorphic image, elementary
properties of homomorphism
III Week 5 Kernel of a homomorphism, fundamental theorem of
homomorphism
Assignment
IV Week 7 Maximal ideals, prime ideals Class Room Seminar
Aug – 24
I Week 5 Vector differentiation, ordinary derivatives of vectors
II Week 5 Differentiability, gradient, divergence, curl
III Week 5 Formulae involving these operators, vector integration
IV Week 6 Line integral, surface integral Assignment
Sep – 21
I Week 5 Volume integral with examples,
II Week 4 Gauss divergence theorem and applications Class Room Seminar
III Week 5 Green’s theorem and applications
IV Week 6 Stoke’s theorem and applications Assignment
Oct – 19
I Week 5 revision
II Week 5 revision
III Week 0 Holidays
IV Week 8 SEMESTER END EXAMS
Nov - 09 I Week 4 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2018 – 19.
Department: Mathematics Paper: Linear Algebra, 4A Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 22
I Week 4 Vector spaces, General properties of vector spaces, n-dimentional
vectors,addition and scalar multiplication of vectors
II Week 5 Internal and external composition, null space, Vector subspaces,
Algebra of subspaces
III Week 5 Linear sum of two subspaces, linear combination of vectors,
linear span
IV Week 7 Linear independence and linear dependence of vectors Assignment
Jul – 25
I Week 5 Basis of vector space, Finite dimensional vector spaces
II Week 5 Basis extension, coordinates
III Week 5 Dimension of a vector space, dimension of a subspace
IV Week 7 Quotient space and dimension of quotient space Class Room Seminar
Aug – 24
I Week 5
Linear transformations, linear operators, properties of linear
transformations,sum and product of linear
transformations,Algebra of linear operators
II Week 5 Range and null space of linear transformation, Rank and nullity
of linear transformation
Assignment
III Week 5 Rank-nullity theorem, linear equations
IV Week 6 Characteristic roots, characteristic values& vectors of square
matrix, cayley-Hamilton theorem
Assignment
Sep – 21 I Week 5 Innerproduct spaces, Euclidean and unitary spaces, norm of a
vector, Schwarz inequality
II Week 4 Triangle inequality, parallelogram law, orthogonality
III Week 5 Orthonormal set, complete orthonormal set Class Room Seminar
IV Week 6 Gram-schmidt orthogonalisation process, Bessel’s inequality,
Parseval’s identity
Assignment
Oct – 19
I Week 5 Revision
II Week 5 Revision
III Week 0 Holidays
IV Week 8 SEMESTER END EXAMS
Nov - 09 I Week 4 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2018 – 19.
Department: Mathematics Paper: Solid Geometry, 1B Class: I BSc Semester:II
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Co-ordinates of a point in , Distance between two points,
section formula, angle between two lines
IV Week 8 Equation of a plane in terms of it’s intercepts on the axis,
equation of the plane through the given points
Dec – 23
I Week 6 Length of perpendicular from a given point to a given plane,
bisector of angle between planes
II Week 6 Combined equation of two planes, orthogonal projection on a
plane
Assignment
III Week 5 Equation of a line, angle between a line and a plane, the condition
that a given line may lie in a given plane
IV Week 6 The condition that two given lines are coplanar, number of
arbitrary constants in the equations of straight line
Class Room Seminar
Jan – 18 I Week 5 Sets of conditions which determine a line, the shortest distance
between two lines, the length and equation of the short distance
between two straight lines
II Week 4 Length of the perpendicular from a givenj point to a given
line,definition and equation of the sphere
Assignment
III Week 1 Equation of the sphere through four point,Plane section of a
sphere
IV Week 8
Intersection of two spheres, equation of a circle, sphere through a
given circle, intersection of a sphere and a line, tangent plane,
plane of contact,polar plane
Feb – 21
I Week 6
Pole of a plane, conjucate points, conjucate planes, angle of
intersection of two spheres, conditions for two spheres to be
orthogonal, power of a point, radical plane
II Week 4
Co-axial system of spheres, simplified form of the equation of
two spheres, definition of a cone, vertex, guiding curve,
generators, equation of the cone with a given vertex and guiding
curve
Assignment
III Week 5
Equationof cones with vertex at origin are homogeneous,
condition that the general equation of the second degree should
represent a cone
IV Week 6 Enveloping cone of a sphere, right circular cone, equation of the
right circular cone with a given vertex
Class RoomSeminar
Mar – 24
I Week 5
Axis and semi vertical angle, condition that a cone may have 3
mutually perpendicular generators, intersection of a line and a
quadric cone
Assignment
II Week 5
Tangent lines, tangent plane at a point, condition that a plane may
touch the cone, reciprocal cones, intersection of two cones with a
common vertex
III Week 6 SEMESTER-END EXAMS
IV Week 8 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2018 – 19.
Department: Mathematics Paper: 2B, Real Analysis Class: II BSc Semester: IV
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Real Numbers : The algebraic and order properties of IR ,
absolute value and real line , the completeness properties of IR .
IV Week 8 Applications of Supremum property , Intervals .
Real sequences : sequences and their limits .
Dec – 23
I Week 6
Range and Boundedness of sequences , limit of a sequence and
convergent sequence , The cauchy’s criterion , properly divergent
sequences .
II Week 6
Monotone sequences , necessary and sufficient condition for
convergence of monotone sequences , limit point of a sequence ,
sub-sequences and Bolzano – Weierstress theorem .
III Week 5 Cauchy’s sequences Cauchy’s general principle .of converges
theorem, series; Introduction to series.
Assignment
IV Week 6
Convergence of series , Cauchy’s general principle of
convergence for series , tests for convergence of series , series of
non – negative terms .
1. P - test
Class Room Seminar
Jan – 18 I Week 5 2. Cauchy’s nth root test or root test.
3. D- Alembert’s test or ratio test.
Assignment
4. Alternating series, Leibnitz test.
5. Absolute convergence and conditional convergence, semi
convergence .
II Week 4 Continuity : limits , real valued functions , boundedness of
a function , limits of functions .
III Week 1 Some extensions of the limit concept. Assignment
IV Week 8
Infinite limits, limits at infinity .
continuous functions : continuous function , combination of
continuous function .
Class Room Seminar
Feb – 21
I Week 6
Differentiation and mean value theorems : The derivability of a
function on an interval , at a point , derivability and continuity of
a function.
II Week 4 Graphical meaning of the derivative mean value theorems :
Role’s theorem .
III Week 5 Lagrange’s theorem , cauchy’s mean value theorem .
IV Week 6 Riemann Integration : Riemann integral , Riemann integral
functions , Darboux theorem .
Mar – 24
I Week 5 Necessary and sufficient for R – integrability properties of
integrable functions.
II Week 5 Fundamental theorem of integral calculus , Integral as a limit of a
sum , Mean value theorems.
Assignment
III Week 6 SEMESTER-END EXAMS
IV Week 8 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P
Teaching Plan for the Academic Year: 2018 – 19
Department: Mathematics Paper: 3B, Numerical Analysis Class: III BSc Semester: V
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Jun – 22
I Week 4 Bridge Course
II Week 5
Errors in Numerical computations, Numbers and their accuracy,
Errors and their computation, Absolute,relative and percentage
errors
III Week 5
A general error formula, error in a series approximation, Solution
of Algebraic and transcendental equations, Bisection method and
Regula –falsi method
IV Week 7
The iteration method, The Newtonj-Raphson method,
Generalised Newtonj-Raphson method, Ramanujan method,
Muller’s method
Assignment
Jul – 25
I Week 5 Interpolation: Forward differences, Backward differences,
Central differences
Class Room Seminar
II Week 5 Symbolic relations, Detection of errors by use of D-tables
III Week 5 Differences of a polynomial, Newton’s forward interpolation
formula
IV Week 7 Newton’s backward interpolation formula-Examples Assignment
Aug – 24
I Week 5 Gauss’s central difference formulae
II Week 5 Stirling’s difference formula,
III Week 5 Bessel’ formula Class Room Seminar
IV Week 6 Everett’s formula Assignment
Sep – 21
I Week 5 Divided differences and their properties
II Week 4 Relation between divided differences and forward differences,
Backward differences , central differences
III Week 5 Lagrange’s formula, error in Lagrange’s formula
IV Week 6 Newton’s general interpolation formula, Inverse interpolation Assignment
Oct – 19
I Week 5 Revision
II Week 5 Revision
III Week 0 Holidays
IV Week 8 SEMESTER END EXAMS
Nov - 09 I Week 4 SEMESTER END EXAMS
II Week 5 SEMESTER END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram , W.G.DIST. A.P .
Teaching Plan for the Academic Year: 2018 – 19.
Department: Mathematics Paper: 4B Advanced Numerical Analysis (cluster) class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13 III Week 5
Curve fitting : least squares curve fitting procedures ,fitting a
straight line.
IV Week 7 Non linear curve fitting , curve fitting by a sum of exponentials.
Dec – 23
I Week 5 Numerical differentiation : Derivatives using Newton’s forward
difference formula , Newton’s backward difference formula .
Assignment
II Week 5 Derivatives using central difference formula : Stirling’s
interpolation formula ,Newton’s divided difference formula
III Week 5 Maximum and Minimum values of a tabulated functions .
IV Week 5 Numerical integration : General quadrature formula , Trapezoidal
rule , Simpson’s 1/3 – rule .
Jan – 18
I Week 5 Simpson’s 3/8 – rule , Boole’s rule and Weddle’s rule . Assignment
II Week 4 Euler – Maclaurin formula of summation and quadrature , the
Euler transformation .
III Week 1 Solutions of simultaneous linear systems of equations .
IV Week 7
Solutions of simultaneous linear systems of equations : solution
of linear systems – Direct methods , matrix inversion method ,
Gaussian elimination methods .
Class Room Seminar
Feb – 21 I Week 5
Gauss – Jordan method , method of factorization , solution of tri
diagonal systems , iterative methods .
Class Room Seminar
II Week 4 Jacobi’s method , Gauss Seidal method Assignment
III Week 5
Numerical solution of ordinary differential equations : Solution
by Taylor’s series , Picard’s method of successive
approximations .
IV Week 5 Euler’s method , modified Euler’s method , Runge – Kutta
second and fourth order methods .
Assignment
Mar – 24
I Week 5 Revision
II Week 5 Revision
III Week 5 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal
DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)
(A College with Potential for Excellence)
Bhimavaram, W.G.DIST. A.P.
Teaching Plan for the Academic Year: 2018 – 19.
Department: Mathematics Paper: Special functions, 5B, Cluster Class: III BSc Semester: VI
Month &
No. of
working
Days
Week
No. of
periods
per
Week
Topics to be covered Co-Curricular Activity
Nov – 13
III Week 5 Hermite polynomial: Hermite differential equation, solution of
Hermite equation,
IV Week 7 Hermite polynomials, generating functions, other forms for
Hermite polynomials
Dec – 23
I Week 5 To find first few Hermite polynomials, orthogonal properties of
Hermite polynomials,
Assignment
II Week 5 Recurrence formulae for Hermite polynomials, problems
III Week 5
Laguerre polynomials- Lagurre’s differential equations, solution
of Laguerre’s equation, Laguerre’s polynomials ,generating
functions
IV Week 5
Other forms of laguerre’s polynomial, to find first few Laguerre’s
polynomials, orthogonal properties of laguerre’s polynomials,
recurrence formulae
Assignment
Jan – 18
I Week 5
Associated laguerre equation, Legendre’s equation- definition,
solution of legendre’s equation, definition of ,general
solution of legendre’s equation
Class Room Seminar
II Week 4 To show that is the coefficient of in the expansion of
Orthogonal properties of legendre’s equation, recurrence formula
III Week 1 Rodrigue’s formula, problems
IV Week 7 Bessel’s equation-Definition, solution of Bessel’s general
differential equation, general solution of Bessel’s equation
Class Room Seminar
Feb – 21
I Week 5 Integration of Bessel’s equation in series for n=0, definition of
Recurrence formula for
Assignment
II Week 4 Generating function for , Beta and gamma functions- Euler’s
integrals, Beta and gamma functions, Elementary properties
III Week 5 Transformations of gamma functions, another form of Beta
function
IV Week 5 Relation between Beta and gamma functions, other
transformations
Assignment
Mar – 24
I Week 5 Revision
II Week 5 Revision
III Week 5 SEMESTER-END EXAMS
IV Week 7 SEMESTER - END EXAMS
Signature of the Lecturer Signature of the HOD Signature of the Principal