Mathematical Methods MA 575 (Elective Course for M. Sc students)
Three one-hour lectures per week: 6 credits
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
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:
Plan of the course:
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.