Mathematical Methods MA 575 (Elective Course for M. Sc students)

 

Three one-hour lectures per week: 6 credits

 

Course Contents:

 

1. (Review of series solution of ordinary differential equations, singularities of ODEs.)

 

2. General solution of Bessel equation, recurrence relations, orthogonal sets of Bessel functions, modified Bessel functions, applications.

 

3. General solution of Legendre equation, Legendre polynomials, associated Legendre polynomials, Rodrigues’ formula, orthogonality of Legendre

Polynomials, applications.

 

4. Fourier series, generalized Fourier series, Fourier cosine series, Fourier sine series, Fourier integrals.

 

5. Fourier transform, Laplace transform, Hankel transform, Mellin transform, Z-transform.

 

6. Solution of differential equations by using transforms.

 

7. (Some ideas of Dirac delta functions, unit step function, Green’s function.)

 

Textbooks and References:

 

  1. G.N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press.
  2. G.F. Roach, Green’s Functions, CUP, 1995.
  3. A.D. Poularikas, The Transforms and Applications-Handbook, CRC Press, 1996.
  4. J.W. Brown and R. Churchill, Fourier Series and Boundary Value Problems, McGraw Hill, 1993.

 

Plan of the course:

 

  1. One  assignment: 10 marks (72 hours for submission).
  2. Two class quizzes: 7.5 marks each (45 minutes).
  3. Mid semester examination: 25 marks (Two hours)
  4. Viva: 5 marks.
  5. End semester examination: 45 marks (Three hours).

 

Important Dates:

 

Quiz I: 8:00 AM, 3rd February.

Assignment I: Distribution - 10th March, Submission - 14th March.

Quiz II: 12:00 noon, 4th April.

Viva: 12:00 noon, 11th April.