Fourier Analysis

A reader–friendly, systematic introduction to Fourier analysis

Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today′s applications.

Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of applications of Fourier analysis in the natural sciences and the enormous impact Fourier analysis has had on the development of mathematics as a whole. Systematic and comprehensive, the book:

Presents material using a cause–and–effect approach, illustrating where ideas originated and what necessitated them Includes material on wavelets, Lebesgue integration, L2 spaces, and related concepts Conveys information in a lucid, readable style, inspiring further reading and research on the subject Provides exercises at the end of each section, as well as illustrations and worked examples throughout the text

Based upon the principle that theory and practice are fundamentally linked, Fourier Analysis is the ideal text and reference for students in mathematics, engineering, and physics, as well as scientists and technicians in a broad range of disciplines who use Fourier analysis in real–world situations.

Preface.

Introduction.

1. Fourier Coefficients and Fourier Series.

2. Fourier Series and Boundary Value Problems.

3. L2 Spaces: Optimal Contexts for Fourier Series.

4. Sturm–Liouville Problems.

5. A Splat and a Spike.

6. Fourier Transforms and Fourier Integrals.

7. Special Topics and Applications.

8. Local Frequency Analysis and Wavelets.

Appendix.

References.

Index.

ERIC STADE, PhD, is Professor of Mathematics at the University of Colorado at Boulder. He received his doctorate in 1988 from Columbia University and has authored a number of refereed journal articles in number theory and physics. He is a member of the American Association of University Professors and the Mathematical Association of America.

"Eric Stade has done a great job of writing a textbook that gets across the beauty and utility of this subject." ( CMS Notes, September 2005)

"The author dies a great job of incorporating his sense of humor throughout this book...appealing to engineers and both applied and pure mathematicians " (MAA Reviews, January 20, 2006)

"Arguments are rigorous...and treatments are thorough...a very nice book for the intended audience." (CHOICE, November 2005)