The Fourier Transform and Derivatives 

Correction at 8:30, right hand side of ODE should be -w^2 * c * uhat. I forgot the wavespeed "c".

Not many people can deliver with such fluency in high speed, Thank You for taking time to make these videos. Really appreciate them

Really love this episode when you get derivatives involved. Most people have very vague idea about how useful Fourier is. Now, here as soon as you bring in the derivatives, everyone gets a light bulb moment when they realize that the derivative disappears with all their life time worries about calculus. It is quite a relief knowing that algebra is useful again.

3:54 To be more precise df/dx * dx == dv and -i*w*exp(-iwx)dx == du

Is it possible that I just watched 11 lectures without actually realizing it. Now I’m too old to cause any real damage with this knowledge but boy this is riveting!

A series on stochastic calculus would be appreciated with such smooth explanations :)

Thanks for the lecture. Coded this up to get position, speed and accel out of a single measurement. Really interessting as you get smooth signals and low-pass filter by design. Might try integration as well.

Love your studio format sir .. itS amazing ..

Hello sir, your method of explaining any topic is so innovative and interesting that any difficult topic we can understand so easily. Can you please share some videos or any reference material for defining fourier transform on vector valued functions or particularly I want to define fourier transform on m×n matrix. Please suggest how to define?

Mind blown! Awesome lecture

if it is possible to you make a course on legendre and bessel equations( in general orthagonal functions).thanks

i want to go to the UofW and take all my classes with this guy.

great videos, big thanks from argentina

He looks like Harrison Wells, from The Flash show.

There is one thing I am wondering and that is how The Fourier Transform is going to be visualized geometrically . The Fourier Series is easy to imagine when we have discrete Ck but that's not the case for Fourier Transform .

Excellent explanation

Is there a video on the properties of fourier transform.

Beautiful!! Thank you!

It seems that taking the derivative of the 2nd Fourier equation also shows the transform of f'(x) is iw\hat{f}(w), is there any issue with that approach? or just an alternative?

Does anyone know what video he starts working on the spectral derivative?

Brilliant!

Doesn't Fourier transform come with some limitations? Doesn't assuming we can move the partial operator also limit the answer?

amazing！

Why the signs of integral and transformer are oppisiote? I remember reading a book that says as I said!

Math is sometimes just beautiful

what is dx if f(x) = x^2 then df(x) is x and d2f(x) is 1 then why didn't d multiplied by x equal undefined? what is df/dx

how does this board work?

4:42 I'm not sure this is correct. The only requirement to write ℱ(f) is that f must be in L¹, which doesn't mean f(x) → 0 as x → +∞. As a counterexample, consider f to be a sum of triangle functions of width 1/2 and height 2n² each centered at integers n≥1. Its integral is π²/6 but it doesn't converges to 0 as x → +∞. Edit: I thought a little bit about it and this is definitely incorrect, even if f is C¹ (just replace triangles in my previous example with smooth bells). You need to assume that f is uniformly continuous for this argument to hold.

2:44 dv = dƒ / dx * dx, so that v = ƒ

is he left handed writing on glass board filmed other side of the glass and the video is left right mirrored?

I found a goldmine.

This is insane

Wow wow wow. Many physics professors don't understand where jw comes from and just say that imaginary j is just a "mathematical device", and you just have to be force fed with third words.