Fourier Analysis (eBook)

Eric Stade (Autor)

eBook Download: PDF

2011 | 1. Auflage
520 Seiten
John Wiley & Sons (Verlag)
9781118165515 (ISBN)

Infos

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.

Autor

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.

Inhalt

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.

Rezensionen

"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)

Produkt-Details

• Erscheint lt. Verlag: 7.10.2011
• Reihe/Serie: Wiley Series in Pure and Applied Mathematics
• Reihe/Serie: Wiley Series in Pure and Applied Mathematics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• Schlagworte: Applied Mathematics in Engineering • Applied Mathematics in Science • Applied Mathmatics in Engineering • Complex & Functional Analysis • Diskrete Mathematik • Fourieranalyse • Komplexe Analysis u. Funktionalanalysis • Mathematics • Mathematik • Mathematik in den Ingenieurwissenschaften • Mathematik in den Naturwissenschaften
• ISBN-13: 9781118165515 / 9781118165515