eBook ISBN:  9781614441045 
Product Code:  TEXT/5.E 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9781614441045 
Product Code:  TEXT/5.E 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 

Book DetailsAMS/MAA TextbooksVolume: 5; 2005; 120 ppMSC: Primary 42
This is a concise introduction to Fourier series covering history, major themes, theorems, examples and applications. It can be used to learn the subject, and also to supplement, enhance and embellish undergraduate courses on mathematical analysis.The book begins with a brief summary of the rich history of Fourier series over three centuries. The subject is presented in a way that enables the reader to appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity and convergence. The abstract theory then provides unforeseen applications in diverse areas.The author starts out with a description of the problem that led Fourier to introduce his famous series. The mathematical problems this leads to are then discussed rigorously. Examples, exercises and directions for further reading and research are provided, along with a chapter that provides materials at a more advanced level suitable for graduate students. The author demonstrates applications of the theory to a broad range of problems.The exercises of varying levels of difficulty that are scattered throughout the book will help readers test their understanding of the material.

Table of Contents

Chapters

Chapter 0. A History of Fourier Series

Chapter 1. Heat Conduction and Fourier Series

Chapter 2. Convergence of Fourier Series

Chapter 3. Odds and Ends

Chapter 4. Convergence in $L_2$ and $L_1$

Chapter 5. Some Applications

Appendix A. A Note on Normalisation

Appendix B. A Brief Bibliography


Reviews

This book is a very readable introduction to Fourier series suitable for scientists and engineers. It is sprinkled with hints about more recent developments and has a lot of nice historical comments that will intrigue the best students and math majors. The author almost talks to the readers and skillfully highlights what is important. A fair amount of the material is in the extensive set of exercises. If this very nice text had been available when I was teaching, I would have used it for a juniorsenior level course for science and math majors.
Kenneth A. Ross, University of Oregon, Eugene


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This is a concise introduction to Fourier series covering history, major themes, theorems, examples and applications. It can be used to learn the subject, and also to supplement, enhance and embellish undergraduate courses on mathematical analysis.The book begins with a brief summary of the rich history of Fourier series over three centuries. The subject is presented in a way that enables the reader to appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity and convergence. The abstract theory then provides unforeseen applications in diverse areas.The author starts out with a description of the problem that led Fourier to introduce his famous series. The mathematical problems this leads to are then discussed rigorously. Examples, exercises and directions for further reading and research are provided, along with a chapter that provides materials at a more advanced level suitable for graduate students. The author demonstrates applications of the theory to a broad range of problems.The exercises of varying levels of difficulty that are scattered throughout the book will help readers test their understanding of the material.

Chapters

Chapter 0. A History of Fourier Series

Chapter 1. Heat Conduction and Fourier Series

Chapter 2. Convergence of Fourier Series

Chapter 3. Odds and Ends

Chapter 4. Convergence in $L_2$ and $L_1$

Chapter 5. Some Applications

Appendix A. A Note on Normalisation

Appendix B. A Brief Bibliography

This book is a very readable introduction to Fourier series suitable for scientists and engineers. It is sprinkled with hints about more recent developments and has a lot of nice historical comments that will intrigue the best students and math majors. The author almost talks to the readers and skillfully highlights what is important. A fair amount of the material is in the extensive set of exercises. If this very nice text had been available when I was teaching, I would have used it for a juniorsenior level course for science and math majors.
Kenneth A. Ross, University of Oregon, Eugene