DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS) · Cyclic groups- definition and examples,...

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





Department: Mathematics Paper: 2A, Abstract Algebra & Real Analysis Class: II BSc Semester: III

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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










Department: Mathematics Paper: Linear Algebra, 3A Class: III BSC Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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.


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.


Oct – 26

I Week 5 Bessel’s inequality, Practical

II Week 5 Revision

III Week 5 Revision









Department: Mathematics Paper: 4A ,Numerical Analysis Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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.


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


Nov - 10 I Week 5 SEMESTER END EXAMS







Department: Mathematics Paper: 4A ,Discrete Mathematics Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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









Department: Mathematics Paper: Differential equations&Real Analysis, 1B Class: I BSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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


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






Department: Mathematics Paper: Abstract Algebra&Real Analysis, IIB Class: II BSc Semester: 4

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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 .


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








Department: Mathematics Paper: Multiple integrals & Vector Calculus (3B) Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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


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


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








Department: Mathematics Paper: 4B ,Numerical Analysis Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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


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.








Department: Mathematics Paper: 4B ,Discrete Mathematics. Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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.







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


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










Department: Mathematics Paper: 2A Solid geometry&Real analysis Class: II BSc Semester: III

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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 .


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










Month &

No. of

working

Days

Week

No. of

periods

per

Week


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



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.


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









Department: Mathematics Paper: 4A ,Numerical Analysis. Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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.



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



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









Department: Mathematics Paper: 4A ,Discrete Mathematics. Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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.



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.




Assignment

IV Week 6

Recurrence relations ,solving recurrence relations by

substitution.

Practical.

Sep – 23


Practical.

Class Room Seminar


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









Department: Mathematics Paper: Differential equations&Real Analysis, 1B Class: I BSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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


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








Department: Mathematics Paper: 2B , Abstract Algebra & Real Analysis. Class: II BSc Semester: IV

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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 .


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.









Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13



IV Week 6

Sufficient condition for the existence of line integral, the area of a

subset .

Practical.

Dec – 24

I Week 5



rectangle of a limit of sum

Practical.

Assignment



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


III Week 3

Gradient of a scalar point function and its applications,


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








Department: Mathematics Paper: 4B, Numerical Analysis. Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13



IV Week 6

Curve fitting by a sum of exponentials ,numerical



Practical.

Dec – 24

I Week 5

Numerical integration : Trapezoidal rule , simpson’s 1/3 rule ,


Practical.

Assignment


III Week 5 Solution of linear systems :direct methods .

Practical.

Quiz


practical.

Jan – 17

I Week 5 method of factorisation ,ill – conditioned linear

systems,iterative methods .


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


Practical.

III Week 5 Runge – kutta methods . Classroom discussion


Practical.

Mar – 22

I Week 5 Milne’s method.

II Week 5 Revision.









Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13 III Week 5 Basic concepts , isomorphisms and subgraphs.


Dec – 24


Practical.

II Week 5 Binary trees .

Practical.

Assignment

III Week 5 Planar graphs, Euler’s formula.

Practical.



Practical.

Jan – 17


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.



Assignment

III Week 5 Flows.


Practical.

Class Room Seminar

Mar – 22

I Week 5 Revision.

II Week 5 Revision.








Department: Mathematics Paper: Differential Equations,IA Class: I BSC Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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








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


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










Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 22




III Week 5 Vector subspaces, algebra of subspaces


two subspaces

Jul – 25

I Week 5 Linear independence and dependence of vectors, Basis of vector

space

Assignment



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



Assignment



IV Week 6 Sylvester’s law of nullity, Characteristic values and characteristic

vectors

Sep – 23

I Week 5 Cayley-Hamilton theorem, Diagonalizable operators


vector

Assignment

III Week 5 Schwartz inequality, orthoganality, orthonormal set


orthogonalization process, Bessel’s inequality


Oct – 19

I Week 5 Revision

II Week 5 Revision

III Week 3 Revision









Department: Mathematics Paper: 4A,Numerical Analysis. Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 22



III Week 5 Errors and their computation ,Absolute , Relative and percentage

errors.


Jul – 25


II Week 5 Bisection ,the method of falsi position . Assignment


IV Week 8 Generalized Newton – Raphson method , Ramnujan’s method ,


Aug – 22



polynomial .

Class Room Seminar



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


IV Week 7 Newton’s general interpolation. Class Room discussion

Oct – 19

I Week 5 Revision.

II Week 5 Revision.

III Week 3 Revision










Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 22





Jul – 25

I Week 5 Problem Solving strategies. Assignment



IV Week 7 Methods of proof of an implication, first order logic and other

methods of proof.

Class Room Seminar

Aug – 22






substitution.

Assignlment

Sep – 23 I Week 5 Generating functions , the method of characteristic roots.


III Week 5 Relations and directed graphs ,special properties of binary

relations.

Assignment

IV Week 8 Equivalence relations , ordering relations ,lattice and

enumerations.


Oct – 19

I Week 5 Revision

II Week 5 Revision

III Week 3 Revision









Department: Mathematics Paper: Solid Geometry, 1B Class: I BSc Semester II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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


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






Department: Mathematics Paper: 2B , Abstract Algebra & Real Analysis. Class: II BSc Semester: IV

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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 .


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.









Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13



IV Week 7 Sufficient condition for the existence of line integral, the area of a

subset of

Dec – 24

I Week 5




Assignment



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


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


IV Week 7 Green’s theorem, Stoke’s theorem and its applications Assignment

Mar – 23

I Week 5 Revision

II Week 5 Revision








Department: Mathematics Paper: 4B , Numerical Analysis. Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13



IV Week 7

Curve fitting by a some of exponentials ,numerical



Assignment

Dec – 24

I Week 5 Numerical integration : Trapezoidal rule , simpson’s 1/3 rule ,



III Week 5 Solution of linear systems – direct methods .


Jan – 17

I Week 5 method of factorisation ,ill – conditioned linear systems

,iterative methods .

Assignment




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 .


III Week 5 Runge – kutta methods . Assignment


Mar – 23

I Week 5 Milne’s method. Class Room Seminar

II Week 5 Revision.









Month &

No. of

working

Days

Week

No. of

periods

per

Week




Dec – 24

I Week 5 Spanning trees , directed trees. Assignment


III Week 5

Planar graphs, Euler’s formula. Quiz


Jan – 17



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.



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.








Department: Mathematics Paper: Differential Equations Class: I BSc Semester: 1

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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




Bhimavaram, W.G.DIST. A.P


Department: Mathematics Paper: 2A, Abstract Algebra Class: II BSc Semester: 3

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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










Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 25




III Week 5 Vector subspaces, algebra of subspaces


two subspaces

Assignment

Jul – 24

I Week 5 Linear independence and dependence of vectors, Basis of vector

space



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





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


vector

III Week 5 Schwartz inequality, orthoganality, orthonormal set Assignment


orthogonalization process, Bessel’s inequality

Class Room Seminar

Oct – 18

I Week 5 Revision

II Week 0

III Week 5 Revision









Department: Mathematics Paper: 4A,Numerical Analysis. Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 25



III Week 5 Errors and their computation ,Absolute , Relative and percentage

errors.


Jul – 24



III Week 5 The iteration method , the Newton – Raphson method. Assignment

IV Week 7 Generalized Newton – Raphson method , Ramnujan’s method ,


Aug – 22



polynomial .



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 .


IV Week 7 Newton’s general interpolation. Assignment

Oct – 18

I Week 5 Revision.

II Week 0

III Week 5 Revision










Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 25





Jul – 24

I Week 5 Problem Solving strategies.


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






substitution.

Assignment

Sep – 23



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









Department: Mathematics Paper: Solid Geometry, 1B Class: I BSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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



IV Week 8 Length of the perpendicular from a givenj point to a given


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



represent a cone

II Week 4 Enveloping cone of a sphere, right circular cone, equation of the


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



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







Department: Mathematics Paper: 2B, Real Analysis Class: II BSc Semester: IV

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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


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









Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 14



IV Week 7 Sufficient condition for the existence of line integral, the area of a

subset of

Dec – 24

I Week 5






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


Class Room Seminar


III Week 3 Gradient of a scalar point function and its applications,


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


IV Week 5 Green’s theorem, Stoke’s theorem and its applications Assignment

Mar – 25

I Week 5 Revision

II Week 5 Revision








Department: Mathematics Paper: 4B , Numerical Analysis. Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 14



IV Week 7

Curve fitting by a some of exponentials ,numerical



Assignment

Dec – 24

I Week 5 Numerical integration : Trapezoidal rule , simpson’s 1/3 rule ,



III Week 5 Solution of linear systems – direct methods . Assignment


Jan – 19

I Week 5 method of factorisation ,ill – conditioned linear systems

,iterative methods .




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 .


Mar – 25

I Week 5 Milne’s method. Student Seminar

II Week 5 Revision.









Month &

No. of

working

Days

Week

No. of

periods

per

Week




Dec – 24



III Week 5 Planar graphs, Euler’s formula. Assignment

IV Week 7 Multi graphs and Euler circuits. Class Room Seminar

Jan – 19



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



III Week 5 Flows. Class Room Seminar


Mar – 25 I Week 5 Revision.

II Week 5 Revision.





Department: Mathematics Paper: Differential Equations, 1A Class: I BSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25


to linear form


variables


solvable for y

Assignment

IV Week 8



equation.

Class Room Seminar

Aug – 21

I Week 4





II Week 4



partial fractions

Assignment

III Week 5 Particular integral of f(D)y=Q when Q=be

ax,


IV Week 8

Solution of the non-homogeneous linear differential equations



Class Room Seminar

Sep – 18

I Week 5


V, where V is a



Assignment


nV, where V is a


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










Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 24



groups , examples


IV Week 7



Assignment

Jul – 25





III Week 6 Index of a subgroup of a finite group , lagrange’s theorem .



Class Room Seminar

Aug – 21


normal subgroups ,

Assignment



III Week 5



isomorphism .

IV Week 8



applications .


Sep – 18



Assignment



III Week 6

ADDITIONAL INPUT :



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









Department: Mathematics Paper: Ring Theory & Vector Calculus, 3A Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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









Department: Mathematics Paper: Linear Algebra, 4A Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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









Department: Mathematics Paper: Solid Geometry, 1B Class: I BSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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


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


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









Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 14





Dec – 23

I Week 5



sequences .

II Week 5




Assignment



IV Week 7




1. P - test

Student Seminar

Jan – 17 I Week 5

2. Cauchy’s nth root test or root test.




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




Feb – 22

I Week 6



a function.

Class Room Seminar


Role’s theorem .

III Week 6 Lagrange’s theorem , cauchy’s mean value theorem . Assignment



Mar – 23





Assignment








Department: Mathematics Paper: 3B, Numerical Analysis Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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







Bhimavaram , W.G.DIST. A.P


Department: Mathematics Paper: 4B Advanced Numerical Analysis (cluster) Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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








Department: Mathematics Paper: Special functions, 5B,( Cluster) Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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








Department: Mathematics Paper: Differential Equations, IA Class: I BSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25


to linear form


variables


solvable for y

IV Week 8



equation.

Assignment

Aug – 24

I Week 6





Class Room

Discussion

II Week 5



partial fractions

Assignment

III Week 6 Particular integral of f(D)y=Q when Q=beax

,


IV Week 7

Solution of the non-homogeneous linear differential equations



Class Room Seminar

Sep – 21

I Week 5


V, where V is a



Assignment


nV, where V is a


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










Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 22



groups , examples


IV Week 8



Assignment

Jul – 25





III Week 6 Index of a subgroup of a finite group , lagrange’s theorem . Class Room Seminar



Assignment

Aug – 24


normal subgroups ,



III Week 6



isomorphism .

IV Week 7



applications .

Class Room Seminar

Sep – 21





Assignment

III Week 5

ADDITIONAL INPUT :



IV Week 7 Elementary properties , classification of cyclic groups . Assignment

Oct – 19

I Week 5 Revision

II Week 5 Revision

III Week 0 Holidays









Department: Mathematics Paper: Ring theory&vector calculus, 3A Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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









Department: Mathematics Paper: Linear Algebra, 4A Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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









Department: Mathematics Paper: Solid Geometry, 1B Class: I BSc Semester:II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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



II Week 4 Length of the perpendicular from a givenj point to a given


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



represent a cone

IV Week 6 Enveloping cone of a sphere, right circular cone, equation of the


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



common vertex








Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13





Dec – 23

I Week 6



sequences .

II Week 6






Assignment

IV Week 6




1. P - test

Class Room Seminar

Jan – 18 I Week 5 2. Cauchy’s nth root test or root test.


Assignment



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




Class Room Seminar

Feb – 21

I Week 6



a function.


Role’s theorem .

III Week 5 Lagrange’s theorem , cauchy’s mean value theorem .



Mar – 24





Assignment








Department: Mathematics Paper: 3B, Numerical Analysis Class: III BSc Semester: V

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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







Bhimavaram , W.G.DIST. A.P .


Department: Mathematics Paper: 4B Advanced Numerical Analysis (cluster) class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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








Department: Mathematics Paper: Special functions, 5B, Cluster Class: III BSc Semester: VI

Month &

No. of

working

Days

Week

No. of

periods

per

Week


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




DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS) · Cyclic groups- definition and examples,...

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Transcript of DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS) · Cyclic groups- definition and examples,...