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eBook ISBN:  9781470420383 
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AMS Member Price:  $68.00 
Hardcover ISBN:  9781470415600 
eBook: ISBN:  9781470420383 
Product Code:  AMSTEXT/22.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 
Hardcover ISBN:  9781470415600 
Product Code:  AMSTEXT/22 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470420383 
Product Code:  AMSTEXT/22.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470415600 
eBook ISBN:  9781470420383 
Product Code:  AMSTEXT/22.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsPure and Applied Undergraduate TextsVolume: 22; 2014; 390 ppMSC: Primary 42
Hugh Montgomery has written a book which both students and faculty should appreciate. I wish it had been written 15 years ago so I could have shared it with students. It is a gem.
—Richard Askey, University of WisconsinMadison
Montgomery has written an exquisite text combining basic material, exciting examples, advanced topics, wonderful historical notes, and excellent exercises. It is absolutely compelling and masterful!
—John Benedetto, University of Maryland
This nice book is likely to be especially successful. l feel that the author has managed admirably to bring to light both the beauty and the usefulness of Fourier's idea, thus making the first introduction to Fourier analysis a joy for undergraduates. All the details are included in a way that is both attractive and easy for students to follow.
—Palle Jorgensen, University of Iowa, author of “Wavelets Through a Looking Glass”
Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three most classical settings: The Discrete Fourier Transform for periodic sequences, Fourier Series for periodic functions, and the Fourier Transform for functions on the real line.
The presentation is accessible for students with just three or four terms of calculus, but the book is also intended to be suitable for a juniorsenior course, for a capstone undergraduate course, or for beginning graduate students. Material needed from real analysis is quoted without proof, and issues of Lebesgue measure theory are treated rather informally. Included are a number of applications of Fourier Series, and Fourier Analysis in higher dimensions is briefly sketched. A student may eventually want to move on to Fourier Analysis discussed in a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting.
ReadershipUndergraduate and graduate students interested in learning Fourier analysis.

Table of Contents

Cover

Title page

Contents

Preface

Chapter 0. Background

Chapter 1. Complex numbers

Chapter 2. The discrete Fourier transform

Chapter 3. Fourier coefficients and first Fourier series

Chapter 4. Summability of Fourier series

Chapter 5. Fourier series in mean square

Chapter 6. Trigonometric polynomials

Chapter 7. Absolutely convergent Fourier series

Chapter 8. Convergence of Fourier series

Chapter 9. Applications of Fourier series

Chapter 10. The Fourier transform

Chapter 11. Higher dimensions

Appendix B. The binomial theorem

Appendix C. Chebyshev polynomials

Appendix F. Applications of the fundamental theorem of algebra

Appendix I. Inequalities

Appendix L. Topics in linear algebra

Appendix O. Orders of magnitude

Appendix T. Trigonometry

References

Notation

Index

Back Cover


Additional Material

Reviews

This is a very good book, and the publishers may feel proud to publish it. It is of interest and usefulness both for instructors and for students of all levels and various specialties. I believe that researchers will also find enough interesting points in the text.
Zentralblatt fur Mathematik 
This is a polished introduction to classical Fourier analysis designed for students early in their undergraduate career, perhaps even just after a third term of calculus. The author, wellknown numbertheorist, Hugh Montgomery, says that such students will find in his book '... a gentle introduction to the art of writing proofs and will be better prepared for advanced calculus and complex variables.' ...portions of the book might work very well for a capstone course or independent study.
MAA Reviews


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 Book Details
 Table of Contents
 Additional Material
 Reviews
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Hugh Montgomery has written a book which both students and faculty should appreciate. I wish it had been written 15 years ago so I could have shared it with students. It is a gem.
—Richard Askey, University of WisconsinMadison
Montgomery has written an exquisite text combining basic material, exciting examples, advanced topics, wonderful historical notes, and excellent exercises. It is absolutely compelling and masterful!
—John Benedetto, University of Maryland
This nice book is likely to be especially successful. l feel that the author has managed admirably to bring to light both the beauty and the usefulness of Fourier's idea, thus making the first introduction to Fourier analysis a joy for undergraduates. All the details are included in a way that is both attractive and easy for students to follow.
—Palle Jorgensen, University of Iowa, author of “Wavelets Through a Looking Glass”
Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three most classical settings: The Discrete Fourier Transform for periodic sequences, Fourier Series for periodic functions, and the Fourier Transform for functions on the real line.
The presentation is accessible for students with just three or four terms of calculus, but the book is also intended to be suitable for a juniorsenior course, for a capstone undergraduate course, or for beginning graduate students. Material needed from real analysis is quoted without proof, and issues of Lebesgue measure theory are treated rather informally. Included are a number of applications of Fourier Series, and Fourier Analysis in higher dimensions is briefly sketched. A student may eventually want to move on to Fourier Analysis discussed in a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting.
Undergraduate and graduate students interested in learning Fourier analysis.

Cover

Title page

Contents

Preface

Chapter 0. Background

Chapter 1. Complex numbers

Chapter 2. The discrete Fourier transform

Chapter 3. Fourier coefficients and first Fourier series

Chapter 4. Summability of Fourier series

Chapter 5. Fourier series in mean square

Chapter 6. Trigonometric polynomials

Chapter 7. Absolutely convergent Fourier series

Chapter 8. Convergence of Fourier series

Chapter 9. Applications of Fourier series

Chapter 10. The Fourier transform

Chapter 11. Higher dimensions

Appendix B. The binomial theorem

Appendix C. Chebyshev polynomials

Appendix F. Applications of the fundamental theorem of algebra

Appendix I. Inequalities

Appendix L. Topics in linear algebra

Appendix O. Orders of magnitude

Appendix T. Trigonometry

References

Notation

Index

Back Cover

This is a very good book, and the publishers may feel proud to publish it. It is of interest and usefulness both for instructors and for students of all levels and various specialties. I believe that researchers will also find enough interesting points in the text.
Zentralblatt fur Mathematik 
This is a polished introduction to classical Fourier analysis designed for students early in their undergraduate career, perhaps even just after a third term of calculus. The author, wellknown numbertheorist, Hugh Montgomery, says that such students will find in his book '... a gentle introduction to the art of writing proofs and will be better prepared for advanced calculus and complex variables.' ...portions of the book might work very well for a capstone course or independent study.
MAA Reviews