Broadly organized around the applications of Fourier analysis, "Methods of Applied Mathematics with a MATLAB Overview" covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.

Inhalt

Preface.- Introduction.- Fourier Series.- Elementary Boundary Value Problems.- Sturm-Liouville Theory and Boundary Value Problems.- Functions of a Complex Variable.- Laplace Transforms.- Fourier Transforms.- Discrete Variable Transforms.- Additional Topics.- Linear Algebra Overview.- Software Resources.- Transform Tables.- Index.