This BookWare Companion book integrates analytical and computer solutions of problems that lead to understanding of advanced mathematical techniques with applications in engineering, physics and mathematics. Each chapter begins with a preview, and in addition to the text, contains numerous examples, exercises and problems, a bibliography, and answers to exercises. Major topics covered are vector and matrix algebra, differential equations, Fourier analysis, advanced calculus, and partial differential equations. MATLAB is the primary programming language utilized in the text; MATLAB scripts accompanying each chapter are provided on a bound-in disk. A Maple notebook also ships on the disk--the Maple scripts serve the same purpose as the MATLAB scripts for Maple users.