MA 575 Mathematical Methods

Instructors:   S. Natesan and M.G.P. Prasad, Office: E 308/ E 207, Extn. 2613/2608

 

  Syllabus Class Timings Plan of Marks

 Policy of Attendance

Attendance in all lecture and tutorial classes is compulsory. 

Students, who do not meet 75% attendance requirement will not be allowed to write the end semester examination.

For attendance in the classes, attendance sheets will be circulated. 

Each student is expected to sign against his/her name only.

In case, any student is found marking proxy for some other student, an appropriate disciplinary action will be taken on both students involved in the proxy matter.

Random attendance will also be taken.

 

Syllabus

Power series solutions, Bessel functions, Modified Bessel functions, Legendre polynomial, Laguerre polynomial, Chebyshev polynomial, Hermite polynomials: recurrence relations, orthogonality. Concept and calculation of Green's function, Properties, Green's function method for ordinary and partial differential equations. Fourier Series, Fourier Cosine series, Fourier Sine series, Fourier integrals. Fourier transform, Laplace transform, Hankel transform, finite Hankel transform, Mellin transform. Solution of differential equations by integral transform methods. Construction of the kernels of integral transforms on a finite interval through Sturm-Liouville problem. Occurrence of integral equations, Regular and singular integral equations: Volterra integral equations, Fredholm integral equations, Volterra and Fredholm equations with different types of kernels.

Texts/References: 

  1. G. N. Watson , A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1944.
  2. G. F. Roach, Green's Functions, Cambridge University Press, 1995.
  3. A. D. Poularikas, The Transforms and Applications Handbook, CRC Press, 1996.
  4. L. Debnath and D.D. Bhatta, Integral Transforms and Their Applications, Chapman and Hall/CRC, 2011.
  5. J. W. Brown and R. Churchill, Fourier Series and Boundary Value Problems, McGraw Hill, 1993.
  6. F.G Tricomi, Integral Equations, Dover Publications Inc. New York, 1985.

 

  Lecture Timings

Tuesday 17:00 - 17:55  
Wednesday 16:00 - 16:55  
Thursday 15:00 - 15:55    

 

Venue: 2204    

  Evaluation Plan

Quiz I    10 marks
Mid-semester Examination
(Two hours exam)
  30 marks
Quiz II    10 marks
End-semester Examination
(Three hours exam)
  50 marks
Total   100 marks
 

No make up examinations will be held

Recently updated on January 1, 2025.