Davis J. Methods of Applied Mathematics with a Software Overview

2nd Edition. — Springer International Publishing, Switzerland, 2016. — 791 p. — (Applied and Numerical Harmonic Analysis) — ISBN: 3319433695Broadly 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.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
Appendixes
Linear Algebra Overview
Software Resources
Transform Tables