Fourier Series and Integral Transforms

by Allan Pinkus, Samy Zafrany

This volume provides a basic understanding of Fourier series, Fourier transforms, and Laplace transforms. It is an expanded and polished version of the authors' notes for a one-semester course intended for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. The material is self contained with numerous exercises and various examples of applications.

Genres: Mathematics

200 pages, Paperback

First published July 10, 1997

Reviews

[Tomáš Ševček · Rating 5 out of 5]

I skipped the parts on Fourier series, so my comment does not apply to them. This book is an excellent choice if you want to learn how to use the Fourier and the Laplace transform in order to solve ordinary and partial differential equations, integral equations and integro-differential equations. It does actually show you more than that - applications to signal processing are included as well and you will also learn how to compute certain improper integrals with the Fourier transform, but this book primarily focuses on the applications to differential equations. Virtually all of the necessary properties of the transforms are contained (and derived) in the main text. Each subsection is concluded with exercises (no solutions given). The only prerequisite needed is the knowledge of calculus, especially multiple integrals and Fubini's theorem (although some prior knowledge of ODEs and PDEs does help to appreciate how easily/mechanically some of these equations can be solved with transform methods, without which it would take way more effort to come up with a solution). Some parts, such as the one on the inverse Laplace transform or the one on the residue theorem, do require some complex analysis as well (but these parts can be skipped if your primary goal is to solve equations). No knowledge of functional analysis is required as the main objective of the book is to provide an overview of the basic properties of the transforms and to apply them to differential equations. There are a lot of books on integral transforms on the market, but this is my go-to book every time I apply either the Fourier or the Laplace transform to differential equations.

[Natan · Rating 4 out of 5]

A good book for an introduction to Fourier series & transforms, and Laplace Transforms