Fourier Analysis and Its Applications (Pure and Applied Undergraduate Texts)

I've been asked to teach acourse on fourier analysis,Iknew nothing on the subject so I took abut 15 books on the subject I went over all of them and my conclusion was thatfollands book is the best!.He explains the theory yet never forget for a minute the intuitive part 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 elementry notions of ODE this is the best book to learn the subject.One more thing:the book also give the reader some of the important motivations to functional analysis such as generating function and distrbutions the conection between linear algebera and the basic ideas that lies at the foundations of understanding function spaces (with norm on it)and more in short it gives you in a kind of magic the conections between functional analysis fourier analysis and even PDE .main subjects are:fourier series,orthogonal sets of functions,fourier and laplace transforms ,convolution,generating function green functions and more.raed it and enjoy it!.

A remarkable book. It strikes the perfect balance between rigor and usefullness. The author explains intuitively most all the theorems and physics, and the rigor goes only as far as is necessary for most every real application.