Pure and Applied Undergraduate Texts
Volume: 22;
2014;
390 pp;
Hardcover
MSC: Primary 42;
Print ISBN: 978-1-4704-1560-0
Product Code: AMSTEXT/22
List Price: $82.00
AMS Member Price: $65.60
MAA Member Price: $73.80
Electronic ISBN: 978-1-4704-2038-3
Product Code: AMSTEXT/22.E
List Price: $77.00
AMS Member Price: $61.60
MAA Member Price: $69.30
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Supplemental Materials
Early Fourier Analysis
Share this pageHugh L. Montgomery
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 Wisconsin-Madison
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
junior-senior 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.
Readership
Undergraduate and graduate students interested in learning Fourier analysis.
Reviews & Endorsements
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, well-known number-theorist, 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
Table of Contents
Table of Contents
Early Fourier Analysis
- Cover Cover11 free
- Title page i2 free
- Contents v6 free
- Preface ix10 free
- Chapter 0. Background 112 free
- Chapter 1. Complex numbers 920
- Chapter 2. The discrete Fourier transform 3344
- Chapter 3. Fourier coefficients and first Fourier series 5364
- Chapter 4. Summability of Fourier series 91102
- Chapter 5. Fourier series in mean square 135146
- Chapter 6. Trigonometric polynomials 149160
- Chapter 7. Absolutely convergent Fourier series 183194
- Chapter 8. Convergence of Fourier series 195206
- Chapter 9. Applications of Fourier series 211222
- Chapter 10. The Fourier transform 249260
- Chapter 11. Higher dimensions 279290
- Appendix B. The binomial theorem 291302
- Appendix C. Chebyshev polynomials 299310
- Appendix F. Applications of the fundamental theorem of algebra 309320
- Appendix I. Inequalities 319330
- Appendix L. Topics in linear algebra 339350
- Appendix O. Orders of magnitude 349360
- Appendix T. Trigonometry 351362
- References 377388
- Notation 383394
- Index 385396 free
- Back Cover Back Cover1402