Mathematical Physics : Differential Equations and Transform Theory

A K Ghatak - Professor of Physics, IIT, Delhi.
I C Goyal - Professor of Physics, IIT, Delhi.
S J Chua - Assistant Professor and Director, Centre for Optoelectronics, Department of Electrical Engineering, National University of Singapore.

The Evolution of Differential Equations: Some Historical Notes • Ordinary Differential Equations I: With Constant Coefficients • Ordinary Differential Equations II: The Frobenius Method • Ordinary Differential Equations III: Some Specific Methods for Solving Second Order Differential Equations • Legendre Functions • Bessel Functions • Hermite Polynomials • Laguerre Polynomials • Gauss’ Hypergeometric Equations • Fourier Series • Fourier Transform Theory • Laplace Transform • The Sturm-Liouville Equation • The Dirac Delta Function • The Green’s Function • Partial Differential Equations • Airy Functions • The JWKB Approximation • Lagrange’s Equations of Motions • Calculus of Variations • Numerical Methods: Finite Differences • Numerical Solution of Second Order Differential Equations along with Computer Programs • Appendix • Index