I've gotta say. Your lessons are excellent. Extremely clear, accurate, and helpful. Thank you for taking the time to teach to make up for the lack of teaching ability on many professors' part.
I recently saw in another RUclipsr’s video (A professor called Steve Brunton at the University of Washington) how you can derive the Fourier transform by taking the Fourier series of a function with compact support and simply extending the domain to positive and negative infinity. Once that made sense, this video just clicked magically for me. I wanted to solve for the electromagnetic response of a wire due to an external E field (you assume the current density equals the material conductivity times the external E field) and solve the hyperbolic pdes of Maxwells equations. I knew you have to use Fourier series because they have a tendency of reducing pdes to odes and algebraic systems of equations, but I couldn’t quite see how. Your video example was the perfect demonstration of how useful the approach can be. Many thanks Professor Tisdell, you’re doing the Lords work! 🙌🏽☺️ Best wished with everything.
Your videos are amazing. For months I've been trying to understand Fourier Transform method in vain. But today it sunk as I watched this video. It is helpful as tomorrow I have a PDE exam.
Wow, I have been having the hardest time figuring this stuff out and this video really brought it all into focus. Thank you for making this video, and I look forward to watching other videos of yours for future assistance
Hey Chris, Thanks a lot for your video, it is very informative. I just finished a graduate introductory course in applied mathematics, and one of the topics was Fourier transforms, but I didn't have enough time to solve any actual PDE's using them, so thank you for sharing this knowledge! Alex
Awesome video! Thank you, Professor Tisdell. I found this useful to refresh my Fourier Transform knowledge, in pursuit of the Inverse scattering transform for the KdV.
THANK YOU, it's simply absurd how hard it was for me to find a simple, objective, didatic tutorial on Fourier Transform as applied to Differential Eqs.
hello. i come from the future. i had a similar problem, but solving the klein-gordon equation. your solution is excellent and helped me understand wth im doing. this is a 1am comment. thanks again
Dr chris: your lecture is excellent . But if don't mine can interpret in physical manner,that mean what we are transforming from one to another. THANK YOU
Thank you so much Dr Chris.You have been a great help for revising the course. May I ask you as to how do we apply Fourier Transform do solve the 4th order PDE? U''''(x,t)= Utt(x,t)
My math book on PDEs is terrible at explaining things - it's "one of those books" that goes on about proofs and formal theorems in a stiff manner all the time and almost never gives any intuitive example problems. These videos are a million times easier to understand.
Hi, thanks so much for posting these videos. Have you got any where the Fourier transform is applied to ordinary differential equations? Would love to see some examples on those if you could ? :) thanks
getting confused at 4:39 , my book said that ux=-iwU(w,t) and uxx=(-iw)^2U(w,t). however, by differential by part, I got the same answer as you did. But, I find out that use the formula in the book has no problem at all. So, I don't know why.
I've gotta say. Your lessons are excellent. Extremely clear, accurate, and helpful. Thank you for taking the time to teach to make up for the lack of teaching ability on many professors' part.
a tip : watch series on flixzone. Been using them for watching all kinds of movies recently.
@Azariah Keith Yup, been watching on flixzone for months myself :D
2020 and still the only relevant video that I could find on this topic
Thank you so so much for these videos... You're the best teacher!!! So clear and easy to follow
I recently saw in another RUclipsr’s video (A professor called Steve Brunton at the University of Washington) how you can derive the Fourier transform by taking the Fourier series of a function with compact support and simply extending the domain to positive and negative infinity. Once that made sense, this video just clicked magically for me. I wanted to solve for the electromagnetic response of a wire due to an external E field (you assume the current density equals the material conductivity times the external E field) and solve the hyperbolic pdes of Maxwells equations. I knew you have to use Fourier series because they have a tendency of reducing pdes to odes and algebraic systems of equations, but I couldn’t quite see how. Your video example was the perfect demonstration of how useful the approach can be. Many thanks Professor Tisdell, you’re doing the Lords work! 🙌🏽☺️ Best wished with everything.
Your videos are amazing. For months I've been trying to understand Fourier Transform method in vain. But today it sunk as I watched this video. It is helpful as tomorrow I have a PDE exam.
Wow, I have been having the hardest time figuring this stuff out and this video really brought it all into focus. Thank you for making this video, and I look forward to watching other videos of yours for future assistance
Hey Chris,
Thanks a lot for your video, it is very informative. I just finished a graduate introductory course in applied mathematics, and one of the topics was Fourier transforms, but I didn't have enough time to solve any actual PDE's using them, so thank you for sharing this knowledge!
Alex
Thank you professor! This is quite clear and very easy to follow!
Absolutely awesome teaching Dr. Chris Tisdell. I just love your teaching method. Thanks a lot.
Awesome video! Thank you, Professor Tisdell. I found this useful to refresh my Fourier Transform knowledge, in pursuit of the Inverse scattering transform for the KdV.
Thank you, Im learning this material by myself, and the textbook skips lots of steps, and is very hard to follow.
You make it so much easier : )
THANK YOU, it's simply absurd how hard it was for me to find a simple, objective, didatic tutorial on Fourier Transform as applied to Differential Eqs.
My pleasure!
You're the best teacher I never had.
hello. i come from the future. i had a similar problem, but solving the klein-gordon equation. your solution is excellent and helped me understand wth im doing. this is a 1am comment. thanks again
Dr. Chris...thank you for this excellent video. you are a life saver
Thanks for your effort. It is helping me alot especially these hard days with online education.
Dr chris: your lecture is excellent .
But if don't mine can interpret in physical manner,that mean what we are transforming from one to another.
THANK YOU
Thank you so much Dr Chris.You have been a great help for revising the course. May I ask you as to how do we apply Fourier Transform do solve the 4th order PDE? U''''(x,t)= Utt(x,t)
My math book on PDEs is terrible at explaining things - it's "one of those books" that goes on about proofs and formal theorems in a stiff manner all the time and almost never gives any intuitive example problems.
These videos are a million times easier to understand.
Hi, thanks so much for posting these videos. Have you got any where the Fourier transform is applied to ordinary differential equations? Would love to see some examples on those if you could ? :) thanks
Thanku for such excellent explanation. Appreciation from Quaid-i-Azam University Pakistan !!!
Hi Chris, great videos! Quick question, when would you use the sin or cosine transforms instead of the complex transform?
Is it possible include the boudary conditions with the Fourier transform? Because you showed that it is possible using a Fourier's serie tecnique..
Hi, can you prove existence and smoothness of the Navier-Stokes solutions on R^3 for me please? Thank you!
+Blahblahblahblahblah Now that really is a million dollar question.
But really though, could you do it for us please? That would be awesome.
thank you!!! but where have you used the boundary conditions u going to 0 as mod(x) goes to infinity??? please reply, ive an exam in a week!!!
Yes, it is theoretically possible to do this. You must really like transform methods! :-)
getting confused at 4:39 , my book said that ux=-iwU(w,t) and uxx=(-iw)^2U(w,t). however, by differential by part, I got the same answer as you did. But, I find out that use the formula in the book has no problem at all. So, I don't know why.
Please can you tell me ....This type of example equation-P.D. what it means (practical application) in physics?
Life saver! Thank you very much sir.
What if we have Neumann boundary condition?
Can you only use the Fourier transform on PDes when they are on an infinite spatial domain?
You are so smart and helpful , thanks so much.
Can you do an inhomogeneous problem?
this guy's a legend
do you have PDFs of your lecture slides? They are often quite good and I cant be bothered to copy them by hand!
Awesome video! Thank you!
I am lost infinitely expressing the solution of a differential equation (with epsilon) using Fourier series.
When you say that we assume w is positive (10:30) wouldn't it still work if w is negative? Does w just have to be real?
Thank you very much Dr Chris.
Thank you! Helped me a lot with my assignment!
Amazing Doctor...
Perfect and Thank you
Thank you so much Dr, really helpful and useful
Thank you so much!!!!!!!!! It's really helpful!!!!!!!!!
When solving the ODE in Fourier space, would it be possible to solve that with another laplace/fourier transform?
Thank you Chris love your videos.
What about if u sub t (x,0) is not zero?
very informative thank you
Thank you.
Excellent thank you!
very good
wait at 13:50 it is u-hat(w,0)=A(w) right ?
Yes. Well spotted.
thank you!
15:29 sounds like "I'll never find my solution", hah.
Lol 😂
Thank you so much :)
How can you rewrite sin(wt) as a power of e?
Akshayan Manivannan Euler's formula.
love your vids!
thanks alot
1:54
"here, or here...or somewhere else".
lol, seems like a very adventuous factor. =D
solve poiseuille equation by fourier transform?!!
yea!
came for the fourier tansform - stayed for the ASMR
what even is w. He just writes it and never explains
Ahmed Janjua w is a dummy variable.