(mathematics) pass/hons ug 1

1

COURSES OF STUDIES

for

Bachelor Degree Examination: 2014-2017

MATHEMATICS

Ravenshaw University

Cuttack

2

B.Sc.(Mathematics) Pass/Hons

UG 1st year :

First Semester Subject Code

Calculus I (Pass and Hons) 1.1.1 Pass/Hons

Matrix Algebra (Pass and Hons) 1.1.2 Pass/Hons

Number Theory ( Hons) 1.1.3 Hons

Second Semester

Calculus II (Pass and Hons) 1.2.3(Pass) & 1.2.4(Hons)

Ordinary Differential Equation (Pass and Hons) 1.2.4(Pass) & 1.2.5(Hons)

Discrete Mathematics (Hons) 1.2.6.( Hons)

UG 2nd

year :

Third Semester

Calculus III (Pass and Hons) 2.3.5(Pass) & 2.3.7(Hons)

Algebra-I (Pass and Hons) 2.3.6(Pass) & 2.3.8(Hons)

Probability Theory (Hons) 2.3.9(Hons)

Fourth Semester

Numerical Analysis-I (Pass and Hons) 2.4.7(Pass) & 2.4.10(Hons)

Linear Programming (Pass and Hons) 2.4.8(Pass) & 2.4.11(Hons)

Algebra-II (Hons) 2.4.12(Hons)

3

B.Sc.(Mathematics)

UG 3rd

year :

Fifth Semester Subject Code

Algebra-III (Hons) 3.5.13(Hons)

Mechanics (Hons) 3.5.14(Hons)

Differential Geometry (Hons) 3.5.15(Hons)

Programming in C (Hons) 3.5.16(Hons)

Topology of Metric Spaces (Hons) 3.5.17(Hons)

Practical using C-Language (Hons) 3.5.18(Hons)

Sixth Semester

Analysis of Several Variables (Hons) 3.6.19(Hons)

Numerical Analysis-II (Hons) 3.6.20(Hons)

Calculus of Variations (Hons) 3.6.21(Hons)

Ordinary and Partial Differential Equation (Hons) 3.6.22(Hons)

Complex Analysis (Hons) 3.6.23(Hons)

Problem Comprehensive (Hons) 3.6.24(Hons)

4

UG 1st year

MATHEMATICS (PASS /HONS)

First Semester Paper-1.1.1 (P & H)

CALCULUS-I

Full marks: 10+40 Time : 2 Hours

Unit-I

Real numbers : Algebra of real numbers, order, Completeness(continuum), Upper and

Lower Bounds, Least Upper Bounds and Greatest Lower Bounds, Density, Archimedean

Principle, One- to- one correspondence, Cardinality, Countability, Uncountability.

Unit-II

Convergence of Sequence and Series: Convergence, Limit theorem, Weierstrass’s

completeness principle, Cantor’s completeness principle, Subsequences and Bolzano-

Weierstrass theorem, Cauchy’s completeness principle, Convergence of series, Series of

positive terms, Absolute convergence, Conditionally convergent series.

Unit-III

Limit and Continuity : Limit of function, Left and right limit, Continuity, Discontinuity,

Further properties of continuous function defined on closed intervals, Uniform continuity.

Differentiation : Left and right derivative, Mean value theorems, Higher derivatives and

Taylor’s theorem.

Book Prescribed:

Fundamentals of Mathematical Analysis by G.Das and S.Pattanayak ( Tata McGraw-Hill

Publishing Company LTD).

Chapters : 2(2.1-2.4, 2.6), 3(3.1-3.4), 4(4.1-4.7, 4.10-4.13), 6(6.1-6.6, 6.9),

7(7.1-7.4, 7.6, 7.7).

Book for reference:

Mathematical Analysis by S. C. Mallick and S. Arora (New Age International).

5

Paper-1.1.2 (P & H)

MATRIX ALGEBRA Full marks: 10+40 Time : 2 Hours

Unit-I

Introduction to vectors: Vectors and linear combinations, length and dot products,

matrices, Solving linear equations: Vectors and linear equations, the idea of elimination,

elimination using matrices, Rules of matrix operations, inverse matrices, factorization,

Transposes and Permutations

UNIT-II

Vector spaces and subspaces: The space of vectors, the nullspace of , solving

homogeneous system of linear equations, rank and row reduced form, complete solution

to non-homogeneous system of linear equations, independence, basis and dimension,

Determinants: properties of determinants, permutations and cofactors, Cramer’s rule,

inverses and volumes

UNIT-III

Eigen values and Eigen vectors: Introduction to Eigen values, Diagonalizing a matrix,

Applications to differential equations, symmetric matrices, positive definite matrices, similar

matrices, Complex matrices: Hermitian and Unitary matrices

1. Book Prescribed: An Introduction to Linear Algebra, 4th Ed., Gilbert Strang (Wellesley

Cambridge Press). Chapters: 1, 2, 3(3.1-3.5), 5, 6(6.1-6.6), 10(10.1-10.2)

Books for reference:

2. Linear Algebra, S. Kumarsen (PHI).

3. Hoffman and Kunze, Linear Algebra, 2nd

Ed., (PHI).

4. V. Krishnamurthy, Linear Algebra (East West Press)

6

Paper-1.1.3 (Hons)

NUMBER THEORY


Unit-I

Divisibility theory in the integers, Primes and their distribution, Theory of congruences, Euler’s

Phi-function, Euler’s theorem.

Unit-II

Quadratic reciprocity, Number theoretic functions, Arithmatic functions, Mobius inversion

formula, Greatest Integer function.

Unit-III

Diophantine equations, The equations x2+y

2=z

2, the equation x

4+y

4=z

2, the sum of four and five

squares, Fermat’s last theorem, sum of fourth powers.

Book Prescribed:

Elementary number theory- David M. Burton (Tata MC-Graw Hill).

Chapters: 2 (2.2-2.5), 3 (3.1, 3.2), 4 (4.2-4.4), 6 (6.2, 6.3), 7 (7.2, 7.3), 9 (9.2-9.4), 12 (12.1, 12.2)

Book for reference:

An Introduction to the Theory of Numbers- Ivan Niven & H. S. Zuckerman (Wiley).

7

UG 1st year

MATHEMATICS (PASS /HONS)

Second Semester

Paper-1.2.3(Pass) & 1.2.4(Hons)

CALCULUS-II


Unit-I

Riemann Integration : Riemann integral, Continuity and Integrability, Properties

of Riemann integral, Fundamental theorem of calculus.

Unit-II

Sequences and Series of Functions : Pointwise convergence, Uniform

convergence, Uniform convergence and continuity, Term-by-term integration of

series, Term-by-term differentiation of series, Power series, Taylor’s series.

Unit-III

Improper integrals, Beta and Gamma functions.

Books Prescribed:

1. Fundamentals of Mathematical Analysis by G.Das and S.Pattanayak ( Tata McGraw-

Hill Publishing Company LTD).

Chapters : 8(8.1-8.5), 9(9.1-9.7)

2. Mathematical Analysis by S. C. Mallick and Sabita Arora (New Age International).

Chapter : 11, Appendix-I

8


ORDINARY DIFFERENTIAL EQUATIONS


Unit-I

Ordinary differential equations of first order and first degree, Exact equation, Integrating factor,

Equation reducible to linear form, Equation of first order of higher degree, Equation solvable for

p, y and x, Equation homogeneous in x and y, Clairaut’s and Lagrange’s Equation.

Unit-II

Linear equations with Constant Co-efficient and with variable co-efficient.

Unit-III

Laplace transforms and Applications to ODE.

Book Prescribed:

A course on Ordinary and Partial Differential Equation with Application- J. Sinha Roy and

S. Padhy (Kalyani Publishers).

Chapters: 2 (2.4 to 2.7), 3, 4 (4.1 to 4.7), 5, 9 (9.1, 9.2, 9.5, 9.10, 9.11, 9.13)

9

Paper-1.2.6(Hons)

DISCRETE MATHEMATICS


Unit –I

The Foundations: Logic and proofs: Propositional logic, Propositional equivalences, predicates

and quantifiers, nested Quantifiers, rules of inference, Introduction to proofs, Normal forms.

Mathematical Induction: Mathematical Induction, strong Induction and well ordering

Unit-II

Advanced Counting techniques: recurrence relations, solving linear recurrence relations,

generating functions, Inclusion-Exclusion, Applications of Inclusion-Exclusion

Unit-III

Relations: Relations and their properties, n-ary relations and their applications, representing

relations, closure of relations, equivalence relations, partial orderings

Book Prescribed:

1. Discrete Mathematics and its Applications, Kenneth H. Rosen, Tata Mc-Graw Hill

Education private Limited, Seventh Edition (Indian adaptation by Kamala Krithivasan),

2012

Chapter 1 (1.1-1.7), 4 (4.1-4.2), 6(6.1-6.6, Excluding 6.3), 7(7.1-7.6)

Book Recommended:

1. Discrete Mathematical structures with Application to Computer Science – J. P. Tremblay

and R. Monohar.

10

UG 2nd

year MATHEMATICS (PASS /HONS)

Third Semester


CALCULUS-III Full marks: 10+40 Time : 2 Hours

Unit-I

Analytical Properties of R and C : Open sets, Closed sets, Limit points, Bolzano-Weirstrass

theorem, Closure, Interior and Boundary, Compactness, Sequential compactness, Heine-Borel

theorem(Statement only).

Unit-II

Function of several variable, Limit of a function, Algebra of limits, Repeated limits, Partial

derivatives, Differentiability, Equality of cross derivatives, Derivatives of composite functions,

Derivatives of implicit functions, Change of variables, Homogeneous functions, Mean value

theorem, Taylor’s theorem, Maclaurin’s theorem, Jacobians, Maxima/Minima, Lagrange’s

multipliers.

Unit-III

Differential operator : Scalar and vector point functions, Gradient, Tangent plane and normal line,

Divergence and curl.

Integral Theorem : Line integrals, Surface integrals, Volume integrals, Volume integrals, Integral

theorems (Gauss, Stoke’s, Green’s theorems).

Books Prescribed:

1. Topics in Calculus – by R. K. Panda & P. K. Satapathy

Chapters: 3, 4(4.1-4.6, 4.10, 4.12-4.16), 5, 9

2. Fundamental of Mathematical Analysis- by G. Das & S. Pattanayak

Chapters- 5(5.1-5.6)

11


ALGEBRA-I


Unit-I

Symmetries: Motivation for the definition of a group, Dihedral groups.

Groups : Binary operation on a set, Axiomatic definition of a group, examples, these to include

general and special linear groups over familiar fields, the group of units of integers modulo n and

connection with Euler’s function.

Elementary properties : Uniqueness of identity and inverse, cancellation, etc; subgroups; order of

a group; order of an element; finite groups.

Unit-II

Cyclic groups : Classification; the structure of subgroups of a cyclic group. Permutation groups :

Definition; cycle notation; representation as a product of disjoint cycles; generation by transpositions;

sign of a permutation; alternating group. Cayley’s theorem.

Unit-III

Cosets : Lagrange’s theorem; theorem of Fermat and Euler from number theory to be seen as

special cases. Homomorphism, Isomorphisms, Normal subgroups, kernels and images; kernels

and normal subgroups. Quotient groups. Conjugation; inner and outer automorphisms.

Books Prescribed:

Contemporary Abstract Algebra- Gallian, 4th edition, Narosa.

Chapters : 1,2,3,4,5,6,7,9,10

12

Paper-2.3.9(Hons)

PROBABILITY THEORY


Unit –I

Probability: Examples of probability, Deduction from the axioms, independent events,

arithmetical density, Counting-fundamental rules, Diverse ways of sampling, allocation models,

Binomial coefficients.

Unit-II

Random variables-What is random variable. How do random variables come about , Distribution

and expectation, integer valued random variables with densities, Conditioning and independence,

Example of conditioning , basic formulas, sequential sampling.

Unit-III

Mean variance,: basic properties of expectation, the density case, multiplication theorems,

Poisson and normal distribution, Models for Poisson’s distributions, normal distributions.

Book Prescribed:

Elementary Probability Theory with Stochastic process by Kai Lai Chung.

Chapters: 2(2.1-2.5), 3(3.1-3.4), 4(4.1-4.5), 5(5.1-5.3), 6(6.1-6.3), 7(7.1-7.4).

13

UG 2nd

year MATHEMATICS (PASS /HONS)

Fourth Semester


NUMERICAL ANALYSIS-I

(Scientific non-programmable calculators are allowed in Examination Hall)


Unit-I

Computer Arithmetic, Octal and Hectadecimal systems, Floating point Arithmetic, Errors,

Significant digits and Numerical Stability. Transcendental and Algebraic Equations, Bisection

Methods, Iterative Methods based on First Degree Approximations, Rates of Convergence.

Unit-II

System of Linear Algebraic Equations, Direct Method, Crammer’s Rule, Gauss Elimination

Method, Gauss Jordan Method, Triangularisation Method, Cholesky Method.

Unit-III

Interpolation, Lagrange’s and Newton’s Interpolations, Finite Differences, Numerical

Integrations, Methods based on Undetermined Co-efficient.

Book Prescribed:

Numerical Methods for Scientific and Engineering Computation by M. K. Jain, S. R. K. Iyegar

and R. K. Jain (Willy Eastern Ltd.)

Chapters: 1(1.2, 1.3), 2(2.1, 2.2, 2.3, 2.5, 2.6), 3(3.2), 4(4.1 to 4.4), 5(5.6, 5.7, 5.8.1)

14


LINEAR PROGRAMMING


Unit- I

Pre-requisites: Vectors, Vector-inequalities, Linear combination of vectors, Hyper plane

and Hyper spheres, Convex sets and their properties, supporting and separating hyper

planes, convex functions, local and global extrema, Quadratic form.

LPP- Mathematical formulation, graphical solutions.

Unit-II

General LPP, Canonical and standard forms, Simplex method- Introduction, Simple

algorithm, Use of artificial variables, Two phase method, Big M method or method of

penalties.

Unit-III

Duality in LPP : Introduction, primal dual conversion, duality and simplex method, dual

simplex method.

Transportation problem: Introduction, basic concepts, finding initial basic feasible

solutions by NWC, LCM and VAM, Test of optimality by MODI method, some

exceptional cases.

Assignment problem: Introduction, Hungarian’s method, special cases.

Book Prescribed:

Operation Research- Kanti Swarup, P.K Gupta & Man Mohan (Sultan Chand & Sons),

Ninth Edition 2001.

Chapters : 0(0.9-0.17), 2(2.2), 3(3.2, 3.4, 3.5), 4(4.1, 4.3, 4.4, 4.5, 4.6), 5(5.1-5.4, 5.7,

5.9), 10(10.1-10.6, 10,8-10.12, 10.14), 11(11.1-11.4).

15

Paper-2.4.12(Hons)

ALGEBRA-II


Unit-I

Rings : Motivation, definition, examples, basic properties; sub rings.

Ideals and factor rings : one and two sided ideals; factor rings; prime and maximal

ideals in commutative rings: characterization in terms of properties of quotients.

Zero divisors : integral domains; fields; finite domains are fields; the finite field

Z/pZ Field of quotients of an Integral domain.

Unit II

Ring homeomorphisms : kernels are ideals; first isomorphism theorem.

Polynomial ring over a ring : division algorithm; remainder theorem; polynomial in F[X]

of degree n has at most n roots.

Principal ideal domains : Z and F[X]; prime ideals and maximal ideals in PIDs.

Unit-III

Factorization of polynomials: irreducible; Z[X]: content of a polynomial, primitive

polynomials, Gauss’s lemma: product of primitives is primitive; primitive and irreducible

over Q is irreducible; Irreducibility tests: reading modulo primes; Eisenstein’s criterion;

cyclotomic polynomials; irreducibility of a polynomial over F[X] being equivalent to it

generating a prime ideal; Unique factorization in Z[X].

Book Prescribed:

Contemporary Abstract Algebra-Gallian, 4th

edition, Narosa.

Chapters : 12 to 18.

16

UG 3rd

year MATHEMATICS (HONS)

Fifth Semester

Paper-3.5.13(Hons)

ALGEBRA-III


Unit –I

Vector spaces : fields and vector spaces; linear combinations; subspaces; span of a set of vectors;

linear independence; finite dimensional vector spaces, bases and dimension; coordinates.

Linear transformation: Definition, linear functional, composition of transformations; the

endomorphism algebra; invertible transformations; isomorphism: there is only one vector space

up to isomorphism of a given dimension; representation of transformations by matrices;

correspondence between the algebra of transformations and the algebra of matrices; how the

representing matrix changes with choice of bases: similarity transformations; the rank-nullity

theorem: row-rank equals column-rank.

Unit-II

Dual Vector Space: The dual V* of a vector space V, dimension of the dual and the dual basis,

the double dual and isomorphism of a vector space with its double dual. Linear equations and

matrices Revisited in the light of the abstract definition of vector spaces and transformations.

Eigenvalue: review of the material under this heading in the Matrix algebra course: eigenvalues,

eigenvectors of a linear transformation, linear independence of eigenvectors corresponding to

different eigenvalues, characteristic polynomial. Cayley-Hamilton theorem, Minimum

polynomial.

Unit-III

Geometry of Inner Product Spaces : (over the fields of real numbers and complex numbers,

separately) inner products, Schwarz inequality, Gram-Schmidt orthogonalization, linear

functional on an inner product space, orthogonality, existence of orthogonal basis, orthogonal

projections, Linear functional and Adjoints.

Book Prescribed:

Linear Algebra by Kenneth Hoffman and Ray Kunze. PHI Learning PVT. Ltd.

Chapters: 2(2.1-2.6), 3(3.1-3.7), 6(6.1-6.4), 8(8.1-8.3)

17

Paper-3.5.14(Hons)

MECHANICS


Unit –I

Methods of Plane Statics, Applications of plane statics, Plane kinematics.

Unit-II

Methods and applications in plane Dynamics

Unit-III

Plane impulsive motion. The equation of Lagrange and Hamilton

Book Prescribed:

Principles of Mechanics, J.L. Synge and B. A. Griffith, Mc. Graw Hill

Chapters: 2(2.1-2.4), 3(3.1,3.2), 4(4.1),8,15

18

Paper-3.5.15(Hons)

DIFFERENTIAL GEOMETRY


Unit –I

Curve with torsion, Tangent, Principal normal, Curvature, Binomial torsion, Locus of

center of spherical curvature, Intrinsic equation Heloics, Spherical indicatrix.

Unit-II

Involute, Evolute, Bertrand curves, Surfaces, Tangent plane, Normal, Envelope

characteristics, Edge of regression, Developable surfaces.

Unit-III

Curvilinear co-ordinates, First order magnitudes, Direction on a surface, Second order

magnitude, Derivation of n.

Books Prescribed:

Differential Geometry of Three Dimensional by C. E. Weatherbun (ELDS)

Chapter : 1, 2(2.13-2.17), 3(3.22-3.27)

19

Paper-3.5.16(Hons)

PROGRAMMING IN ‘C’


Unit –I

Overview of C, Constants, variables and data types, operations and Expressions, Managing Input

and output operation. Writing simple programs

Unit-II

Decision making and branching.

Unit-III

Arrays

Recommended Books

Programming in ANSIC(2nd

Edn.), E.Balaguruswamy(Tata Mc. Graw Hill) Ch.1,2,3, 4, 5,6,7

20

Paper-3.5.17(Hons)

TOPOLOGY OF METRIC SPACES


Unit –I

Introductory concepts: Definition and examples of metric space, Open sphere and Closed

sphere, Neighborhoods’, Open sets, Equivalent metrics, Interior points, closed set,

Limit points and Isolated points, Closure of a set, Boundary points, Distance between sets

and diameter of a set, Subspace of a metric space, Product metric spaces and basis.

Unit-II

Completeness: Convergent Sequences, Cauchy-Sequence, Complete spaces, Dense

sets and separable spaces, no-where dense sets, Baire’s theorem, Completion.

Continuous functions: Definition and Characteristics, Extension theorem, Uniform

continuity, Homeomorphism, Uniformly equivalent metrics

Unit-III

Compactness: Compact space and Compact set, Sequentially Compactness, totally

boundedness, Equivalence of compactness and sequential compactness, Compactness

and finite intersection property, Continuous functions and compact spaces, Fixed point

theorems.

Recommended Books:

1. Metric spaces by Pawan K. Jain and Khalil Ahmad (Narosa Publishing House), 2nd

Edition, 2012

Chapter : 2(2.1-2.14), 3(3.1-3.7), 4 (4.1-4.5), 5(5.1-5.6), 7(7.1)

21

Paper-3.5.18(Hons)


Practical Using ‘C’LANGUAGE

1. Solutions of a Quadratic Equation.

2. Generate Fibonacci sequence.

3. Find factorial of a number using recursion.

4. Sorting.

5. Test whether a number is an Armstrong Prime.

6. Evaluation of Integrals by Trapezoidal and Simpson’s method.

7. Solving an ODE by Runge-Kutta method.

8. Matirx multiplication.

9. Count number of vowels in a word.

10. Reverse a string or a number.

22

UG 3rd

year MATHEMATICS (HONS)

Sixth Semester

Paper-3.6.19(Hons)

ANALYSIS OF SEVERAL VARIABLES


Unit-I

Mutivariate Differential Calculus

Introduction,The directional derivative, Directional derivatives and continuity, total derivative, total

derivative expressed in terms of partial derivatives, an application to complex-valued functions, matrix of

a linear function, Jacobian matrix , chain rule, Matrix form of the chain rule

Unit-II

Implicit Functions and Extremum Problems

Introduction , Functions with nonzero Jacobian determinant , The inverse function theorem , The implicit

function theorem, Extrema of real-valued functions of one variable, Extremum problems with side

conditions

Unit-III

Multiple Riemann Integrals

Introduction, The measure of a bounded interval in Rn , The Riemann integral of a bounded function

defined on a compact interval in R", Sets of measure zero and Lebesgue's criterion for existence of a

multiple Riemann integral, Evaluation of a multiple integral by iterated integration

Recommended Books:

1. Tom M Apostol: Mathematical Analysis, 2nd

edition, Narosa Publishing House

Chapter 12 (12.1-12.10), Chapter 13, Chapter 14 (14.1-14.5)

23

Paper-3.6.20.(Hons)

NUMERICAL ANALYSIS-II


(Scientific non-programmable calculators are allowed in Examination Hall)

Unit-I

System of Linear Algebraic Equations, Iteration Methods, Jacobi Iteration Method, Gauss-Seidel Method,

SOR Method, Eigen values and Eigen vectors, Given’s Method, Power method.

Unit-II

Ordinary differential Equations, Euler method, Backward Euler Method, Mid-Point Method, Single Step

Method, Taylor series Method.

Unit-III

Runge-Kutta method, Second Order Method, Fourth Order Method, Explicit and Implicit Runge Kutta

Method.

Recommended Books:

1. Numerical Methods for Scientific and Engineering Computation by M. K. Jain, S. R. K. Iyengar

and R. K. Jain (Wiley Eastern Ltd.)

Chapter 3 (3.4, 3.5), 6 (6.2, 6.3, 6.4)

24

Paper-3.6.21(Hons)

CALCULUS OF VARIATIONS


Unit –I

The concept of variation and its properties, Euler’s equation, variational problem for functional of

the form, Functional dependent on higher order derivatives, Functional dependent on functions of

several independent variables.

Unit-II

Variational problem in parametric form, some applications to problems of mechanics, variational

problems leading to an integral equation or a differential difference equation. Theorem of du

bois-Reymond strocastic Calculus of variations.

Unit-III

Variational problem with moving Boundaries, Functional of the form [y(x)=x], variational

problem with a movable boundary for a functional dependent on two functions one sided

variation reflection and refraction of internals, diffraction of light rays.

Recommended Books:

Calculus of variation with Application by A.S. Gupta.

Chapters: 1(1.1-1.10), 2(2.1-2.5)

25

Paper-3.6.22(Hons)

ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS


Unit-I

Ordinary differential Equation in more than two variables, Partial differential Equations of First

order.

Unit-II

Partial differential equation of the second and higher order.

Unit-III

Series solutions and Special functions.

Recommended Books:

1. A course on Ordinary and Partial Differential Equation with Application- J. Sinha Roy and S.

Padhy (Kalyani Publishers)

Chapter 7, 11, 12, 13

26

Paper-3.6.23(Hons)

COMPLEX ANALYSIS


Unit –I

Analytic functions : Functions of a complex variable, Limit, Continuity,

Differentiability, Analytic functions, Cauchy-Riemann Equations, Harmonic

functions, Periodic functions, Exponential functions, Trigonometric functions,

Hyperbolic functions.

Unit-II

Complex Integration : Contour integral, Primitives, Cauchy-Goursat theorem and its

extensions, Winding number, Cauchy-integral formula, some subsequences of the

Cauchy integral formula, Maximum moduli of functions.

Unit-III

Series Expansions : Taylor series, Zero’s of Analytic functions, Laurent series.

Singularities and Residue : Classification of singularities, Residue, Poles and Zeros.

Recommended Books

1. Complex variables : Theory and Applications by H. S. Kasana

Chapter 2(2.1-2.7), 3(3.1-3.4), 4(4.1-4.9), 6(6.3-6.5), 7(7.1-7.3)

27

Paper-3.6.24(Hons)

Problem Comprehensive


Unit-I

Problems pertaining to Differential Equations

Unit-II

Problems pertaining to Calculus-I, Calculus-II, Calculus-III

Unit-III

Problems pertaining to Algebra-I, Algebra-II, Algebra-III

Reference Books:

1. Mathematical Analysis by S. C. Mallick and S. Arora (New Age International).

2. Contemporary Abstract Algebra- Gallian, 4th edition, Narosa.

3. Hoffman and Kunze, Linear Algebra, 2nd

Ed., (PHI).

4. V. Krishnamurthy, Linear Algebra (East West Press)

5. Fundamentals of Mathematical Analysis by G.Das and S.Pattanayak ( Tata McGraw-Hill

Publishing Company LTD).

6. A course on Ordinary and Partial Differential Equation with Application- J. Sinha Roy and

S. Padhy (Kalyani Publishers).

(mathematics) pass/hons ug 1

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