What are the best textbooks for learning Fourier analysis and its applications?

[dcrisci]

Hello all, I'm a third year university physics major. I haven't read much on Fourier analysis however I have had been introduced to it through an oscillations and waves class. My professor was saying that it can be applied to many different areas and is extremely helpful tool to have under your belt for many reasons. Since I have been introduced to Fourier integrals and transforms and what they mean in terms of oscillations, I am seeking an introductory to slightly advanced text to buy on the topic. Could anyone recommend a specific text for Fourier analysis that applies it to many areas, such as physics, business, etc?

More or less looking to get a good summer reader, so I can keep the brain cells working. Any other suggestions on books that are worth reading (not only
On Fourier analysis) that will help me out in the future would be taken into account too! Thanks!

 

[vanhees71]

My all-time favorite on Fourier analysis is

M. J. Lighthill, Introduction to Fourier Analysis and Generalised Functions, Cam. Uni. Press (1959)

 

[Incand]

I really like https://www.amazon.com/dp/0821847902/?tag=pfamazon01-20 which I'm currently using for self study (and I will take a class in it using the book next year).
It is however a math book and not a book on applications and it mostly covers the aspects relevant to physics and engineering so it may not be what you looking for but definitively check it out!
All you need for it is calculus & linear algebra (at the level of linear algebra done wrong). Some of the later chapters also use some concepts from complex analysis.