Introduction, Gamma Functions, Beta Functions; Hyper geometric series, power series solution of differential equations, ordinary point, solution about singular point Frobenius method, Bessel's equation, solution of Bessel's equation; Bessel's functions, J (x), recurrence formulae, equations reducible to Bessel's equation, orthogonality of Bessel functions, a generating function of J (x), trigonometric expansion involving Bessel functions, Bessel integral, Ber and Bei functions, Legendres equation; Legendre's polynomial P_n (x); Legendre's function of the second kind; General solution of Legendre's Equation, Rodrigue's formula, Legendre polynomials, a generating function of Legendre's polynomial, Orthogonlity of Legendre polynomials; recurrence formulae for Ps(x), Fourier-Legendre expansion, Laguerres differential equation, Strum Liouville equation ; orthogonality ; orthogonality of eigen-functions.
Elementary Applied Partial Differential Equations by 
