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

- Teacher: IshratJahan Ansari
- Teacher: Naushad Shaikh

compulsory extra credit course

- Teacher: IshratJahan Ansari
- Teacher: Yashwant Madke

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

- Teacher: IshratJahan Ansari

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

- Teacher: Naushad Shaikh

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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- Teacher: IshratJahan Ansari
- Teacher: Naushad Shaikh

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)

- Teacher: IshratJahan Ansari