Prerequisites for Stein and Shakarchi Fourier Analysis

Question

I'm currently taking Fourier Analysis that uses Stein and Shakarchi Fourier Analysis textbook. I only have experience in multivariable calculus and linear algebra, and since they were the only prerequisites for the course, I decided to take the course.

However, the textbook is too difficult to understand, and I'm spending more than 15 hours/week to read a section of the chapter. Does anyone have any suggestions about which subjects I should study to get a better understanding of Fourier Analysis? I already read some basic textbook about Fourier Transform, and I'm confident with those calculations.

Answer 1

I think firm understanding of introductory analysis is a requisite for Stein & Shakarchi's tough series. If you have not read any analysis textbook, I recommend you to find one and at least get used to the properties of series of complex numbers, series of functions and rigorous understanding of differentiation and integration.

My personal choice was Rudin, and I suppose the material is already an overkill if your primary aim is to read Stein & Shakarchi's first book. For a beginner Stein is quite difficult to read, I think, but logically the only prerequisites are analysis, calculus, and linear algebra.

Answer 2

A few notes in addition to Hyeongmuk's answer:

Instead of Rudin, you might choose one of the many gentler introductions out there to single variable real analysis (Abbott's Understanding Analysis is a popular choice). If you need additional support, pick up a copy of Alcock's How to Think about Analysis.

Aside from that, you do not mention having studied differential equations. The motivational background in the opening chapter of Stein & Shakarchi may make more sense if you have some background in differential equations and physics. Also, reading an introductory book on partial differential equations (e.g. Borthwick or Olver) at the same time as Stein & Shakarchi may provide some additional perspectives.