Fourier Analysis: Overview

This video presents an overview of the Fourier Transform, which is one of the most important transformations in all of mathematical physics and engineering. This series will introduce the analytic theory of the Fourier Transform, along with the Fast Fourier Transform (FFT) algorithm for efficient computations. We will explore lots of applications in image compression, audio analysis, and solving partial differential equations.

These lectures follow Chapter 2 from:

"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

This video was produced at the University of Washington

[quantabot]

I just checked your website and all the papers are free downloadable. Touched my heart, thank you. I will never forget your help

[payman_azari]

Dear Professor Brunton, you have many students around the world that besides mathematics you teach them how to share our best fruits for free.
Cordially Grateful.

[marioeuler]

You are doing god's work here, thank you so much for your effort.

[sachinr]

Thank you so much Prof. Steven L Brunton for these gem of lectures. I found your channel when i was going through one of your paper annual review of fluid mechanics with Prof. Koumoutsakos.
I think all these lecture playlist are the part of your textbook chapters, thanks for the wonderful lectures.

[enneff]

Just watched through this whole series. This is an amazing explanation. Filled in so many gaps in my understanding. Can't thank you enough! <3

[leahthegeek]

hello sir, i hope youre doing well. i just wanted to tell you how amazing this explanation was for me. because i didn't understand the importance of fourier analysis and didn't want to study it at all. i was forced to do so for my university exam and now im really intrigued by all of these amazing things it has brought to us. you made me interested in studying this topic even more than what my university demands. so thank you again for saving a desperate student.

[NineInchFailz]

Interesting reading the comments here because in my background i use the Fourier Series/Transform for frequency analysis of electrical circuits but i see a lot of people use it for mechanical systems or heat and fluid distribution. Crazy how a bunch of 17th century mathematics can model the real world around us so well!

[invinity]

you and Nathan Kutz are my favorite Mathematicians! Thank you for sharing your knowledge with such elegance!

[neilbrideau]

This blows my mind. How long did it take you to learn to write backwards?

[brunovilloria]

This might be the coolest way to give a presentation on youtube

[tianyazhang]

I become a big fan of professor Brunton after binge-watching your video lectures.

[DevRajyaguru-lxpi]

my university teacher suggested your videos before coming to learn it in the class. Amazing !

[ShaunakDe]

I discovered your channel today and I am so happy I did!

[bitterthread]

He is revealing secrets from the university he is the badass guy Thanx man. I really appreciate this as this is very very helpful.
Hope you won't stop ever.

[phamhongvinh]

This course is exactly what I need. I will find time to watch it. Please keep up what you're doing <3

[marcelbodor]

Absolutely clear presentation of a complex subject !
Excellent. Thank you very much indeed.

[PedroHenrique-buxn]

Thank you so much for all these videos. I can't describe how much your videos have been motivating me.

[jacobanderson]

I love you. We use these concepts in cryo-EM all the time. Thanks Prof. Brunton

[afaque]

Extremely thankful to you and Prof.Nathan Kutz as whatever i understand of POD is because of you both. And now I am being able to learn FT and FFT from you.
Thank you Sir.

edit : and also Hao chen's papers on POD.

[uncleroq]

Awesome. Wish this was around during my undergrad. Great review and much more clearer now.