Preface. Introduction. (1) Vector Analysis.(2) Vector Analysis In Curved Coordinates And Tensors. (3) Determines and Matrices. (4) Group Theory. (5) Infinite Series. (6) Functions of a Complex Variable I: Analytic Properties Mapping.(7) Functions of A Complex Variable II: Calculus of Residues. (8) Differntial Equations. (9) Sturm-Liouville Theory-Orthogonal Functions. (10) The Gamma Function (Factorial Function) (11) Bessel Functions. (12) Legendre Functions. (13) Special Functions. (14) Fourier Series. (15) Integral Transforms. (16) Intergal Equations. (17) Calculus of Variations. (18) Nonlinear Methods and Chaos.Appendix 1. Real Zeros of a Function.Appendix 2 Gaussian QuadratureGeneral ReferencesIndex * This revised Fourth Edition includes:* Modernized technology* Group theoretic methods brought together and expanded in a new chapter* An entirely new chapter on nonlinear mathematical physics* Significant revisions of the differential equations and complex variables chapters* Many new or improved exercises* Forty new or improved figures* An update of computational techniques for today's contemporary tools, such as microcomputers, Numerical Recipes, and Mathematica, among others.