Mathematical Methods

Code: MA575 | L-T-P-C: 3-0-0-6

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.