Fourier Analysis

1. Auflage 2005
ISBN: 978-0-471-66984-5
Verlag: Wiley

Buch, Englisch, 520 Seiten, Format (B × H): 162 mm x 242 mm, Gewicht: 833 g

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.

Autoren/Hrsg.

Stade, Eric

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.

Über Autor(innen)

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.