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Fourier Analysis and Its Applications by Gerald B. Folland

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This book is intended for students of mathematics, physics, and engineering at the advanced undergraduate level or beyond. It is primarily a text for a course at the advanced undergraduate level, but I hope it will also be useful as a reference for people who have taken such a course and continue to use Fourier analysis in their later work. The reader is presumed to have (i) a solid background in calculus of one and several variables, (ii) knowledge of the elementary theory of linear ordinary differential equations (i.e., how to solve first-order linear equations and second-order ones with constant coefficients), and (iii) an acquaintance with the complex number system and the complex exponential function ex+iy = ex(cosy + isiny). In addition, the theory of analytic functions (power series, contour integrals, etc.) is used to a slight extent in Chapters 5, 6, 7, and 9 and in a serious way in Sections 8.2, 8.4, 8.6, 10.3, and 10.4. I have written the book so that lack of knowledge of complex analysis is not a serious impediment; at the same time, for the benefit of those who do know the subject, it would be a shame not to use it when it arises naturally. (In particular, the Laplace transform without analytic functions is like Popeye without his spinach.) At any rate, the facts from complex analysis that are used here are summarized in Appendix 2. The subject of this book is the whole circle of ideas that includes Fourier series, Fourier and Laplace transforms, and eigenfunction expansions for differential operators.
(Gerald B. Folland)

Book Detail :-
Title: Fourier Analysis and Its Applications
Edition:
Author(s): Gerald B. Folland
Publisher: Thomson Brooks-Cole
Series: The Wadsworth and Brooks Cole Mathematics Series
Year: 1992
Pages: 441
Type: PDF
Language: English
ISBN: 0130652652
Country: US

Author Gerald Budge Folland is an American mathematician and a professor of mathematics at the University of Washington. His areas of interest are harmonic analysis (on both Euclidean space and Lie groups), differential equations, and mathematical physics. The title of his doctoral dissertation at Princeton University (1971) is "The Tangential Cauchy-Riemann Complex on Spheres".
He is the author of several textbooks in mathematical analysis. In 2012 he became a fellow of the American Mathematical Society.

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Book Contents :-
Fourier Analysis and Its Applications written by Gerald B. Folland cover the following topics.
1. Overture
2. Fourier Series
3. Orthogonal Sets of Functions
4. Some Boundary Value Problems
5. Bessel Functions
6. Orthogonal Polynomials
7. The Fourier Transform
8. The Laplace Transform
9. Generalized Functions
10. Green's Functions
Appendex 1. Some physical derivations
Appendex 2. Summary of complex variable theory
Appendex 3. The gamma function
Appendex 4. Calculations in polar coordinates
Appendex 5. The fundamental theorem of ordinary differential equations
References
Index of Symbols
Index

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Fourier Analysis by Gerald Folland
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