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I want to know what the prerequisites are for fully grasping Fourier analysis, and some free pdfs and such to help me with it (no videos, actual paper I can print and read/ make exercises at school).

I am asking this because I remember that I asked my math teacher when I was 13 what the prereqs were for linear algebra and he gave me a really intimidating list involving advanced calculus and such, and I decided to just continue playing video games. Then last year (at 16) I decided I was competent enough at Halo and I just started doing linear algebra and it was really easy; I didn't need anything advanced at all, and anything I needed I just learned along the way. My teacher basically misinformed me.

So, will I need calculus? For some reason I dread having the selfstudy calculus, everything I already know about it bores me and it is just so much.

Artem
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Fourier
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    You definitely need calculus. – Euler....IS_ALIVE Apr 06 '13 at 18:27
  • Will you need calculus? I'd say you will...and a lot: at least 1 whole year university level, and if you want to gett really deep into it you'll also need linear algebra and complex analysis. – DonAntonio Apr 06 '13 at 18:27
  • @Euler....IS_ALIVE But I meant will it be good if I learn it along the way? Or should it be the other way around? – Fourier Apr 06 '13 at 18:32
  • If you dread calculus, then why do you want to study Fourier analysis? Fourier analysis is (spoiler alert) a bunch of calculus! – Potato Apr 06 '13 at 18:32
  • @Fourier I just opened my Fourier Analysis book and on page 1 it talks about series. On page 2 it talks about integrals.... so... yeah. – Euler....IS_ALIVE Apr 06 '13 at 18:33
  • @Euler....IS_ALIVE Of course I do know integrals and such, but not things such as partial differential equations – Fourier Apr 06 '13 at 18:35
  • @Potato physics my friend – Fourier Apr 06 '13 at 18:38
  • @Fourier Calculus is the backbone of physics. If you want to learn physics, you're going to need to get friendly with calculus. Physicists use calculus more than any other group I know, including mathematicians. – Potato Apr 06 '13 at 18:39
  • @Potato I guess so.. perhaps calculus and me started off on a bad note.. I remember picking up a book on advanced calculus a couple of years ago and for some reason I didn't quite enjoy it... I'm guessing it was the book then – Fourier Apr 06 '13 at 18:41
  • @Fourier So what happened, did you eventually decide to learn calculus? – Bemmu Nov 05 '19 at 15:54

3 Answers3

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You'll need Single Variable Calculus and be comfortable working with sums, infinite and finite.

Here are some lecture notes from one of my professors that may be of use to you.

Robert Cardona
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Here you have the link to MIT open courseware on Fourier Series. There is lots of material. But as it has been mentioned you need Calculus. And to understand properly what you are doing you need also Real Analysis.

MIT FOURIER

Ambesh
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You would need Calculus, Series/Sequences and Complex analysis. Now, i am more familiar with numerical methods (numerical integration, numerical differentiation, numerical analaysis of sequences and series, computational complex nalysis etc), so i tend more towards the computational aspects of a type of fourier transform called "Discrete fourier Transform". It's really cool, tbh alll i've needed to help me learn it was just numerical methods really. Now, obviously if you want to delve deeper you will need much more analysis rather than numerical methods. But I am just more interested in applying stuff and computing them...since im a computer science student I enjoy comouting things more.

NXV
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