Fourier series, convergence of Fourier series, Fourier method, Boundary value problems,orthonormal sets, Sturm Liouville problems, Bessel functions , Legendre polynomials and applications,

Prescribed Book

R.V. Churchill and J. Brown.: Fourier Series and Boundary Value Problems (7th

edition)(Publisher: Tata McGraw-Hill Book Company)(2011) Chapters 1,2,4,5, 7,8,9,10

compulsory extra credit course

MT 805 Operations Research
Unit I - Kuhn – Tucker conditions of Optimality – Quadratic Programming
(Sections 19.2.2B, 20.2.2)
Unit II - Inventory Models
(Sections 14.1 to 14.3)
Unit III - Queuing Models
(Section 15.1, 15.2, 15.4, 15.5)
Unit IV - Project Scheduling By PERT – CPM
(Sections 13.1 to 13.4)
Unit V - Simulation Modeling with SIMNET – II
(Sections 17.1 to 17.10)
Prescribed Book :
Hamy A.Taha, Operations Research, Fifth Edition, Prentice Hall of India


MT803 Fourier Analysis and boundary value problems
Fourier series, convergence of Fourier series, Fourier method, Boundary value problems,
orthonormal sets, Sturm Liouville problems, Bessel functions , Legendre polynomials
and applications,
Prescribed Book
R.V. Churchill and J. Brown.: Fourier Series and Boundary Value Problems (7th
edition)(Publisher: Tata McGraw-Hill Book Company)(2011) Chapters 1,2,4,5, 7,8,9,10


MT 802 Differential Geometry
Graphs and level sets, vector fields, tangent spaces, surfaces, vector fields on surfaces,
orientation, gauss map, geodesics, parallel transport, Weingarten map, curvature, arc
length and line integrals, curvature of surfaces, parametrised surfaces, local equivalence
of surfaces and parametrised surfaces.
Prescribed Book :
John A. Thorpe : Elementary topics in differential Geometry , Springer (2004 ) Chapters :
1-12, 14, 15.
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MT 801 Number theory
1. Revision :- Divisibility in integers, Division algorithm, G.C.D., L.C.M. Fundamental
theorem of arithmetic. The number of primes. Mersene numbers and Fermat's numbers.
2. Congruences :- Properties of congruence relation. Resicle classes their properties
Fermat'sand Euler's theorems. Wilson's Theorem. The congruence
≡      −1    (
     )
has solution iff p is the form 4n+1 where p is prime. Linear congruences of degree one.
Chinese remainder Theorem.
3. Arithmetic functions : Euler function, Greatest integer function, Divisor function d(n),
Mobius function m(n). Properties and their inter relation.
4. Quadratic Reciprocity :- Quadratic residue, Legendre's symbol, Its properties,
Quadratic reciprocity law, Jacobi symbol, Its properties. Sums of Two Squares.
5. Some Diophantine Equations :
The equation ax + by = c , simultaneous linear equations.
6. Algebraic Numbers :- Algebraic Numbers, Algebraic number fields. Algebraic
integers, Quadratic fields. Units in Quadratic fields. Primes in Quadratic fields. Unique
factorization Primes in quadratic fields having the unique factorization property.
Prescribed book : Ivan Niven & H.S. Zuckerman, An introduction to number theory
(Wiley Eastern Limited)
Sections: 2.1 to 2.4, 3.1 to 3.3, 3.6, 4.1 to 4.3, 5.1, , and 9.1 to 9.9
Reference Books :-
1. T.M. Apostol, An Introduction to Analytical Number Theory
(Springer International Student's Edition)
2. David M Burton, Elementary Number Theory (Universal Book Stall, New Delhi)
3. S. G. Telang, Number Theory (Tata Macgrow Hill)4. G. H. Hardy and E. M. Wright, Introduction to Number Theory
(The English language book society and oxford university press)