This book presents the theory and applications of Fourier series and integrals, Laplace Transforms, eigenfunction expansions, and related topics. It deals almost exclusively with those aspects of Fourier analysis that are useful in physics and engineering. Using ideas from modern analysis, it discusses the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs. A wide variety of applications are included, in addition to discussions of integral equations and signal analysis.
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Book Description
Editorial Reviews
Review
With the same mastery as in his Real analysis, the author now offers us this excellent textbook on Fourier analysis: Fourier series, orthogonal systems, Bessel functions, Fourier and Laplace transforms, which are all very powerful mathematical tools in many a scientific domain. Without being exhaustive and without falling into a profusion of boring details, it nevertheless gives a panorama of these topics that is as complete as the framework of the book allows. Thus this text, which is designed for courses at the advanced undergraduate level and beyond, will also serve as a useful reference book. ---- Mathematical Reviews
--This text refers to an alternate
Hardcover
edition.
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Most Helpful Customer Reviews
17 of 18 people found the following review helpful:
5.0 out of 5 stars
Simple yet Instructive and exhaustive,
By A Customer
This review is from: Fourier Analysis and Its Applications (Wadsworth & Brooks/Cole Mathematics Series) (Hardcover)
Concepts are not hidden under obscure mathematical notation: they are stated explicitly in plain english and illustrated with examples. I read a couple of other books on this topic (and PDE) without really understanding the subtleties. With this book everything becomes magically clear and obvious -as you read- and don't feel like you need take another course in real analysis to understand this topic. Bonus: you get solutions to exercices.
11 of 12 people found the following review helpful:
5.0 out of 5 stars
one of the best books on the subject,
By G.B.S "17" (Europe) - See all my reviews
This review is from: Fourier Analysis and Its Applications (Wadsworth & Brooks/Cole Mathematics Series) (Hardcover)
I've been asked to teach a course on Fourier analysis,I knew nothing on the subject so I took about 15 books on this subject and went over all of them. My conclusion was that Folland's book is the best!. He explain the theory yet never forget for a minute the intuitive side of the subject. The book contains almost all the important issues and notions of the subject. If you have a solid background in vector calculus and you know some basic facts about ODE this is a very good book to learn the subject from. Moreover the book give the reader some of the important motivations to the basic ideas of functional analysis such as generating functions distrbutions it gives the connection also between linear algebra and the basic ideas that lies at the foundations for understanding normed function spaces and more. Moreover the book draw the line , in a very elegant way, between functional analysis PDE and Fourier analysis. Main subjects are:Fourier series,orthogonal sets Fourier and Laplace transforms,convolution, generating functions,Green functions, and more. Very recommended!.
10 of 15 people found the following review helpful:
5.0 out of 5 stars
Folland is The One,
By A Customer
This review is from: Fourier Analysis and Its Applications (Wadsworth & Brooks/Cole Mathematics Series) (Hardcover)
Thank God for this book. Folland is the grand-master of my life. I'm a grad student in applied math, studying for qualifying exams, and this book has been extremely helpful to me because it is perfectly rigorous and also crystal clear. When I say Folland is The One, I am referring to The Matrix. This book is that good. His treatment of distributions (otherwise known as "generalized functions") is especially nice.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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generalized functions, orthogonal polynomials, consider heat flow, second independent solution, other boundary value problems, vibrating string problem, sine series, entire analytic function, continuous superposition, allowable frequencies, inhomogeneous boundary conditions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Use Exercise, Orthogonal Sets of Functions, Proof Let, Asymptotics of Laplace, Applications of Bessel, Some Boundary Value Problems, Variants of Bessel, Proof First, Multiple Fourier, Weierstrass M-test Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
generalized functions, orthogonal polynomials, consider heat flow, second independent solution, other boundary value problems, vibrating string problem, sine series, entire analytic function, continuous superposition, allowable frequencies, inhomogeneous boundary conditions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Use Exercise, Orthogonal Sets of Functions, Proof Let, Asymptotics of Laplace, Applications of Bessel, Some Boundary Value Problems, Variants of Bessel, Proof First, Multiple Fourier, Weierstrass M-test Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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