Description
Book SynopsisTrade ReviewHugh 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, USA
"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, USA
"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, USA, Author of
Wavelets Through a Looking GlassTable of Contents
- Background
- Complex numbers
- The discrete Fourier transform
- Fourier coefficients and first Fourier series
- Summability of Fourier series
- Fourier series in mean square
- Trigonometric polynomials
- Absolutely convergent Fourier series
- Convergence of Fourier series
- Applications of Fourier series
- The Fourier transform
- 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
- Index
