||G.F. Simmons, Differential Equations with Applications and Historical notes, 2nd edn, Mc Graw Hill, 1991.H. A. Hinchey, Introduction to Applicable Mathematics Part I, Wiley Eastern, 1980. G.B. Arfken, H.J.Weber, Mathematical Methods for Physicists, 4th ed., Academic Press Prism Books, 1995. P. Morse and H. Feshbach, Methods of Theoretical Physics, Vol.1, McGraw Hill Kogakusha, 1953.
||Partial differential equations and the method of separation of variables.Ordinary differential equations, second order homogeneous and inhomogeneous equations. Wronskian, general solutions, particular integral using the method of variation of parameters. Sturm separation and comparison theorems. Adjoint of a differential equation. Ordinary and singular points. Series solution. Gauss hypergeometric and confluent hyprgeometric equations. Sturm Liouville problem. Legendre, Hermite and the associated polynomials, their differential equations, generating functions. Bessel functions, spherical Bessel equations. Fourier series, Fourier and Laplace transforms with applications. Bromwich integral approach to inverse Laplace transform. Green302222s function approach to inhomogeneous differential equations.