Mathematical Methods MA 575 (Elective Course for M. Sc 2nd Yr.  and B.Tech. 4th Yr. students)

 

Three one-hour lectures per week: 6 credits

Class Timing: 09:00-9:55, Wednesday; 10:00-10:55, Thursday; 11:00-11:55, Friday

           Reserve Slot: 08:00-08:55, Tuesday.

Room Number: 1104

First Day of Instruction: Thursday, July 28, 2017

Last day of Instruction: Wednesday, November 22, 2017

Course Instructor: Swaroop Nandan Bora

Office: E-306 or HOD Chamber (SNB)

Phone: 2604  and 2601

Email: swaroop@iitg.ernet.in

 

Change of time-table: 

 

Classes with Tuesday time-table

17 August 2017, Thursday

Classes with Thursday Time table

 17 October 2017, Tuesday

NO Classes

25 (Monday)-27 (Wednesday) September, 2017

 

Course Contents:  

 

MA575 Mathematical Methods [3-0-0-6] Prerequisites: Nil

Total number of lectures: 42

Power series solutions, Bessel functions, Modified Bessel functions, Legendre polynomial, Laguerre polynomial, Chebyshev polynomial, Hermite polynomials: recurrence relations, orthogonality. (Tentative 14 lectures)

Concept and calculation of Green's function, Properties, Green's function method for ordinary and partial differential equations. (Tentative 6 lectures)

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. (Tentative 14 lectures)

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 (Tentative 8 lectures)

 

Suggested Books:

  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.

 

Plan of the course:

 

  1. Two quizzes: 25 marks.
  2. Mid semester examination: 28 marks.
  3. End semester examination: 47 marks.

 

Important Dates:

 

*Quiz I: Wednesday, August 29, 2017 (15 Marks)

Mid Semester Exam: 14:00-16:00 hrs, Friday, September 22, 2017

*Quiz II: Wednesday, November 1 (15 Marks) - Tentative

End Semester Exam: 14:00-17:00 hrs, Tuesday, November 28, 2017

*Total of quizzes will be scaled to 25 marks.