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Fourier Analysis

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Synopses & Reviews

Publisher Comments:

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.

Book News Annotation:

Writing primarily for advanced undergraduate or graduate students in mathematics, engineering and physics or for "real life" users of Fourier analysis, Stade (mathematics, U. of Colorado, Boulder) assumes readers have background in calculus in one and several variables. Stade gives weight both to applications in the natural sciences and to the impact Fourier analysis has had on mathematics. He uses a systematic, cause-and-effect approach to his topics, beginning with Fourier coefficients and series, then applying Fourier series to boundary value problems. He then proceeds to the vector space, Sturm-Liouville problems, convolution and the delta function ("a splat and a spike"), Fourier transforms and integrals, local frequency analysis and wavelets. He includes special topics and applications such as the discrete Fourier transform, Fraunhofer diffraction and Fourier optics. Stade includes exercises with each chapter.
Annotation 2004 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

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.

Synopsis:

This pioneering resource tells the full story of Fourier analysis-its history, its impact on the development of modern mathematical analysis, and today's applications. The topics are presented using a cause-and-effect approach, illustrating where ideas originated and what necessitated them. Rich in both theory and application, Fourier Analysis is an unique, thorough approach to this key topic in advanced calculus.

About the Author

"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)

Table of Contents

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.

Product Details

ISBN:
9780471669845
Author:
Stade, Eric
Publisher:
Wiley-Interscience
Subject:
Advanced
Subject:
Infinity
Subject:
Fourier analysis
Subject:
Functional Analysis
Subject:
Mathematics - General
Subject:
Applied
Subject:
Applied Mathematics in Science
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Series Volume:
69
Publication Date:
20050331
Binding:
Online electronic file accessible through online networks
Grade Level:
General/trade
Language:
English
Illustrations:
Y
Pages:
520
Dimensions:
9.36x6.70x1.12 in. 1.80 lbs.

Related Subjects

Business » General
Business » Management
Business » Writing
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General

Fourier Analysis New Hardcover
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Product details 520 pages Wiley-Interscience - English 9780471669845 Reviews:
"Synopsis" by , 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.
"Synopsis" by , This pioneering resource tells the full story of Fourier analysis-its history, its impact on the development of modern mathematical analysis, and today's applications. The topics are presented using a cause-and-effect approach, illustrating where ideas originated and what necessitated them. Rich in both theory and application, Fourier Analysis is an unique, thorough approach to this key topic in advanced calculus.
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