Fourier Analysis and Its Applications (Pure and Applied Undergraduate Texts)
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.
one of the best books on the subject
By G.B.S "17" - November 25, 2001
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... read more
Simple yet Instructive and exhaustive
By A Customer - December 1, 2000
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.
Great applied mathematics book on Fourier analysis for a physicist
By Kris C. - July 29, 2012
Folland's "Fourier Analysis and Its Applications" is a great applied mathematics book for a physicist. The coverage is complete, but leaning more towards the theoretical aspects than the applications, as it should be. The topics included are Fourier series, orthogonal sets of functions, some boundary value problems, Bessel functions, orthogonal polynomials, the Fourier transform, the Laplace transform, generalized functions, and Green's functions. I particularly like the progression of the presentation of the materials and the exercises with answers of this book, making it very useful for self-learners. Also the language is very fluid. Would highly recommend to fellow physics students.