Legendre's Equations and Functions; Associated Legendre's Equation and Functions; Legendre's Function of Second Kind Q n{x}; Bessel's Equations and Bessel's Functions; Hermite's Polynomials; Laguerre Polynomials; Chebyshev Polynomials; Hypergeometric Functions; Orthogonal Sets of Functions; Wave, Heat (Diffusion) and Laplace's Equations; Boundary V alue Problems.