In case it is helpful, here are all my PDE videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrFvek-n1MKhFaDARSdKWPnx.html. Please let me know what you think in the comments. Thanks for watching!
I'm fourth year engineering and up until now, I got away with barely understanding how to solve PDE's. I've used many resources in the past to learn the topic but I never got a true understanding of it. In my recent classes, I require having a rigorous understanding of how to solve PDE's as I'm working with the wave equation in depth. Your series of videos helped me finally feel comfortable with the topic and actually understand it, thank you so much!
I'm glad it was helpful. There are several other videos on the channel regarding the wave equation as well as PDEs in general. Feel free to check them out and let me know what you think. Please share with your classmates if you think it would be useful. Thanks for watching!
Hi, First let me say thank you for your generous support of the channel, it is very much appreciated! Do you have any particular interests in terms of videos or topics? I try to prioritize request made by interested parties as much as possible as I plan future videos. I've also got several other videos on the channel focusing on PDEs, I hope they are useful to you. If you are interested, I interact personally with all Patreon members at www.patreon.com/christopherwlum. Given your interest in the topic, I'd love to have you as a Patron. In any event, I want to again say thank you for your contribution and for supporting the channel. I hope to hear from you at a future UA-cam video or on Patreon! -Chris
@@ChristopherLum Thanks for the reply! If it's possible, videos on different Fourier topics (e.g. series, integrals, and transform) would be a great help
AE 501 - Thanks for breaking down this example into more digestible steps (especially with reminders on the left side of the board). The concepts taught from the past weeks are coming together.
This lecture is amazing, professor Lum. I'm genuinely excited following the procedure and it's extremely helpful the way you explain in great detail each and every step. Thank you very much :)
AE 501. This video is really helpful. The step-by-step approach allows me to easily follow on how to tackle a 1D Wave PDE problem. The example also consolidates my understanding of this topic. Thank you!
AE 501: This was interesting to learn, it's something that seems simple but seeing the culmination of the topics we've been learning the past weeks all come into play is a really awesome sight
Thanks for the positive feedback. Feel free to subscribe to the channel if you'd like to see more of these videos, several will be release over the next few days.
AE501: Great helpful video! This was super helpful for the homework and was easy to digest as all your other videos! I like how you show the verification of each step in mathematica as well.
This just saved my entire IB Extended Essay. I can't thank you enough for making such a detailed explanation of every step. Keep doing that and THANK YOU!
Hi, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris
@@azizsametzorlu1355 Hahha someone else with the same nightmare 😅🥲. For mine I was doing: “How to solve a linear homogenous one dimensional wave equation using Fourier series”. I hope yours is going well!!
AE 501 amazing video into figuring out the solution of the 1d wave equation. In reality, it is very tricky and more complicated than solving ODEs but your explanation made it easier.
AE501 - Great set of videos on this, I really like that the derivation gets its own video and the applications are separate, makes it easier to consume (and to have open in two tabs to jump between). Thanks!
AE501 - Solving for the separation constant had me flipping through notes I made in class just a few weeks back. It's cool to see what we've learned so far continue to build on each other.
AE501: Really interesting topic and definitely eye opening to be able to digest how a 1D wave equation works with detailed step by step walkthrough, amazing explanation!!
Hi, Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris
I like how you said "not gonna show, k has to be negative" while my mind was like "let's hope k can be negative cause that's gonna make this a breeze" at 33 min and then left it to your students to show k MUST be negative. Me who barely knows enough about ODEs to want k to be negative "jack pot. With the initial condition that should be sine. now to mess it up so it's zeroes land on L. sin(sqrt(k)*pi/L x)?" I admit that was a wild guess. i know it needs to be square root of k thanks to the chain rule but I completely forgot to adjust the period of a sine function^^ on a sidenot mad respect for the german pronunciation. You don't believe how some people die (or kill German ears) with words like "Eigenfunktion"
Hi Goutam, Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris
AE501 Thank you for this lecture. This is a lot of content but I was able to follow along and I believe that I am able to walk away with a great understanding.
Great lectures, really easy to follow. Just one thing needs to be corrected, the Fourier series formula used here should be with period 2L, instead of L.
Regarding 34:00: If k were a positive value, wouldn't the solutions be non-trivial and non-periodic? I.e. the solution would be an increasing exponential function, rather than damped or undamped oscillation. Of course this also isn't the sort of solution we're looking for, but I don't think it's a "trivial" solution in which u(x,t) is identically zero. It's been a while since I studied ODE's, though, so please do correct me if I'm mistaken.
I agree. Actually k can be positive or negative, and we end up with a trig function or an exponential function. However, Euler's identity connects them ...
AE501: This video draws on a lot of different concepts we have touched in AE501 including recent topics like Fourier series. This is really getting complex.
If it makes you feel better, this is for a university class that I teach :) There are other similar videos on the channel, please let me know what you think and thanks for watching!
@@NuzzywtheWuzzy Feel free to share it with your classmates or anyone you think might benefit. I'm trying to share knowledge that was once passed to me in a similar fashion.
AE501 - This is a dumb question...but in this lecture, you determine solution for ODEs that satisfies boundary conditions, then use F''(x) ODE to find specific P value. If you solve G double dot ODE first, can you still get same specific P value?
Hi Nicolas, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer questions or discuss video topics on Patreon. Thanks for watching! -Chris
Hi Eme, Thanks for reaching out. If you have questions or would like to request a video, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris
08:03 Hmm... _What_ class? I mean, what are the _exact_ conditions that has to be met for the separation of variables to work, and when does it break? Sure, we can always just try and see if it will work, but it wouldn't be cool if after hours of arduous work it would turn out that all that work is wasted because the separation of variables doesn't apply to that particular problem, right? :q
I'm glad it was helpful. There are other similar videos on the channel. Please feel free to check them out and let me know what you think. Thanks for watching!
Matlab has the "Symbolic Math Toolbox" that will allow you to do symbolic manipulations similar to Mathematica. Alternatively, if you have numerical values for your problem then you can do it in Matlab just as easily as Mathematica. I like to use Mathematica for symbolic manipulation and problem setup/analysis and then use Matlab for the actual numerical solution/simulation of the problem.
Hi. What would happen if the string was only fixed at x=0 but free at x=L? I know the boundary conditions would be different but I'm unsure in what way
Hi Alicia, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on UA-cam due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris
AE501: For separation of variables, are there any PDEs where the solution cannot be written as the product of single-variable functions? If so, how do you know when that product assumption will not be valid?
In case it is helpful, here are all my PDE videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrFvek-n1MKhFaDARSdKWPnx.html. Please let me know what you think in the comments. Thanks for watching!
Your lectures are awesome sir, but can you upload more solved problems with 1D equation? It will be really helpful to us!
which text book you have used?
I am in AA519 this quarter, but am watching this for my CFD class, and it explains so much that I had forgotten about solving PDEs!! Thanks Prof
I'm fourth year engineering and up until now, I got away with barely understanding how to solve PDE's. I've used many resources in the past to learn the topic but I never got a true understanding of it. In my recent classes, I require having a rigorous understanding of how to solve PDE's as I'm working with the wave equation in depth. Your series of videos helped me finally feel comfortable with the topic and actually understand it, thank you so much!
Your video is 10 times better than my prof's lecture. Thank you!! salute
I'm glad it was helpful. There are several other videos on the channel regarding the wave equation as well as PDEs in general. Feel free to check them out and let me know what you think. Please share with your classmates if you think it would be useful. Thanks for watching!
This is the first time I've felt that I genuinely owe a teacher money for the quality of their tutorials. Thanks for the great videos
Hi,
First let me say thank you for your generous support of the channel, it is very much appreciated!
Do you have any particular interests in terms of videos or topics? I try to prioritize request made by interested parties as much as possible as I plan future videos. I've also got several other videos on the channel focusing on PDEs, I hope they are useful to you.
If you are interested, I interact personally with all Patreon members at www.patreon.com/christopherwlum. Given your interest in the topic, I'd love to have you as a Patron.
In any event, I want to again say thank you for your contribution and for supporting the channel. I hope to hear from you at a future UA-cam video or on Patreon!
-Chris
@@ChristopherLum Thanks for the reply! If it's possible, videos on different Fourier topics (e.g. series, integrals, and transform) would be a great help
AE 501 - Thanks for breaking down this example into more digestible steps (especially with reminders on the left side of the board). The concepts taught from the past weeks are coming together.
This lecture is amazing, professor Lum. I'm genuinely excited following the procedure and it's extremely helpful the way you explain in great detail each and every step. Thank you very much :)
AE501: This video in particular was the most helpful for the homework. I added a lot of pictures from the lecture to my homework for future reminders.
AE 501. This video is really helpful. The step-by-step approach allows me to easily follow on how to tackle a 1D Wave PDE problem. The example also consolidates my understanding of this topic. Thank you!
AE501: This was a great video on the 1-D wave equation. I'd long forgotten most of this information so this was great!
AE501 : Easy to follow solution, especially having watched the previous Fourier analysis videos. And a great example with the plucked string!
This was a really helpful video. Thanks for being so detailed Chris!
AE501: This step by step solution really helped me understand the physical phenomena being modeled. Thanks!
Thank you for covering this solution so thoroughly, solving these kinds of problems is far more understood.
AE 501: This was interesting to learn, it's something that seems simple but seeing the culmination of the topics we've been learning the past weeks all come into play is a really awesome sight
this is extremely well done cannot thank you enough cannot comprehend why this has so few views
Thanks for the positive feedback. Feel free to subscribe to the channel if you'd like to see more of these videos, several will be release over the next few days.
A huge thank you from across the pond, you're incredibly concise and I use your video to supplement some of my less "concise" lecturers
I'm glad it was helpful thanks for watching!
AE501: super glad I could watch the Fourier transform video before this. This is super cool and makes a lot of sense!!
AE 501: Your demos are always so engaging and really help explain the diagrams.
AE501 - Really good in-depth video of the 1-D wave equation. Extremely helpful thanks
AE501: Great helpful video! This was super helpful for the homework and was easy to digest as all your other videos! I like how you show the verification of each step in mathematica as well.
This just saved my entire IB Extended Essay. I can't thank you enough for making such a detailed explanation of every step. Keep doing that and THANK YOU!
Hi,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!
-Chris
bruh 💀 I am writing an extended essay too, what did you do in yours?
@@azizsametzorlu1355 Hahha someone else with the same nightmare 😅🥲. For mine I was doing: “How to solve a linear homogenous one dimensional wave equation using Fourier series”. I hope yours is going well!!
AE 501 amazing video into figuring out the solution of the 1d wave equation. In reality, it is very tricky and more complicated than solving ODEs but your explanation made it easier.
AE501 - Great set of videos on this, I really like that the derivation gets its own video and the applications are separate, makes it easier to consume (and to have open in two tabs to jump between). Thanks!
Glad you like them!
AE501: Thank you for the thorough explanation and walk-through of the solution in Mathematica!
The visualization and verification in mathematica helped a lot to provide confidence in the solution to the 1D wave equation.
AE501 - Solving for the separation constant had me flipping through notes I made in class just a few weeks back. It's cool to see what we've learned so far continue to build on each other.
Great, also feel free to download the lecture notes to help follow along if that is helpeful
I really like the walk thorough in mathematica... a visual always helps me understand the topic
You make this easier to follow than what I remember from years ago... Thanks.
The outline of the different steps was clear and easy to follow, thanks!
AE501: Really interesting topic and definitely eye opening to be able to digest how a 1D wave equation works with detailed step by step walkthrough, amazing explanation!!
Glad you found the step-by-step breakdown helpful!
Thanks for the video. After several weeks of other material, eigenvalues and eigenvectors return. It's the "proper" thing to cover.
AE501: The animation part is really awesome, and it is incredibly helpful.
This single video is so much better than my entire semester at university
Hi,
Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!
-Chris
Thank you for providing examples. It really help me understand the 1D wave equation concept.
I keep referring to this video for later HW problems. Very informative lecture. Thank you. #AE501
Thank you for this! I like the way your videos are so comprehensive.
AE 501: I really like the manipulate command in Mathematica, makes things really easy to visualize
AE501: Showing the computation in mathematic for the 1D wave equations was very helpful!
AE 501 This lecture is great! Thanks for breaking every step down so it is easy to understand.
A lot of content, but clearly presented. Really helpful!
I like how you said "not gonna show, k has to be negative" while my mind was like "let's hope k can be negative cause that's gonna make this a breeze" at 33 min and then left it to your students to show k MUST be negative. Me who barely knows enough about ODEs to want k to be negative "jack pot. With the initial condition that should be sine. now to mess it up so it's zeroes land on L. sin(sqrt(k)*pi/L x)?" I admit that was a wild guess. i know it needs to be square root of k thanks to the chain rule but I completely forgot to adjust the period of a sine function^^
on a sidenot mad respect for the german pronunciation. You don't believe how some people die (or kill German ears) with words like "Eigenfunktion"
AE501: Great overview of the wave equation. The example was really helpful.
I really like your teaching style. Thanks for this video!
Thank you so much Professor Lum for posting these videos--explaining every step. I am going to complete this whole course.
Hi Goutam,
Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!
-Chris
AE501: Very thorough derivation of the solution to the 1D Wave Equation
AE501: Thank you for simplifying the 1D wave equation. I learned this in the context of "particle in a box" which always confused me.
Wow, you are a fantastic lecturer, clear and concise
Thanks for watching and for the comment!
Thanks for the great video professor Lum.!
Thanks! The examples were especially helpful
AE 501: Thanks for the video! Pretty helpful!
thanks sir ....u really work hard for these vids ...really appreciate it
Our is my pleasure, I hope it was helpful, thanks for watching!
[AE501] Very thorough treatment of the topic!
Great video, a really good explanation of the wave Equation.
Very clear layout. Thank you!
Very much enjoy these videos, keep up the great work
Amazing series of lectures! Thank you!
Found this very helpful, thank you!
Systematic & comprehendible. Thumbs up!
AE501: Great video, really helped me bring it all together.
Great explanation! Will help quite a bit with the homework!
you're my favorite tutor now !
I'll just skip all the lectures cause my professor is boring af.
Thanks, I'm glad it was helpful. Feel free to share with your classmates. Thanks for watching!
AE 501: Great video thank you!
Good examples that help explain the topic! thanks!
AE501 Thank you for this lecture. This is a lot of content but I was able to follow along and I believe that I am able to walk away with a great understanding.
[AE501] Showing how the math corresponds with the Mathematica was great to show how they relate
Great lectures, really easy to follow. Just one thing needs to be corrected, the Fourier series formula used here should be with period 2L, instead of L.
Regarding 34:00: If k were a positive value, wouldn't the solutions be non-trivial and non-periodic? I.e. the solution would be an increasing exponential function, rather than damped or undamped oscillation. Of course this also isn't the sort of solution we're looking for, but I don't think it's a "trivial" solution in which u(x,t) is identically zero. It's been a while since I studied ODE's, though, so please do correct me if I'm mistaken.
I agree. Actually k can be positive or negative, and we end up with a trig function or an exponential function. However, Euler's identity connects them ...
AE501:
This video draws on a lot of different concepts we have touched in AE501 including recent topics like Fourier series. This is really getting complex.
Thank you very very much, I start understanding wave eq!!
Glad it was helpful, thanks for watching!
Best explanation, I wish you were my tutor
AE 501: Thanks Professor
Frustrating when you learn more watching free online videos than you do from university.
If it makes you feel better, this is for a university class that I teach :) There are other similar videos on the channel, please let me know what you think and thanks for watching!
Christopher Lum Thank you! Your lesson was far more digestible than those given by my professor.
@@NuzzywtheWuzzy Feel free to share it with your classmates or anyone you think might benefit. I'm trying to share knowledge that was once passed to me in a similar fashion.
Very thorough solution discussion
AE501 - This is a dumb question...but in this lecture, you determine solution for ODEs that satisfies boundary conditions, then use F''(x) ODE to find specific P value. If you solve G double dot ODE first, can you still get same specific P value?
Ae501: This is definitely something that requires a worked through example to nail down the details. We will see???
Thanks for these, videos, they're excellent.
Helped a lot. Thank you sir !!!
Manipulate in mathematica is a really cool feature.
This video is absolutely amazing.
Hi Nicolas,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer questions or discuss video topics on Patreon. Thanks for watching!
-Chris
AE501 Is there a way to determine beforehand if a particular PDE can be solved using the three step process without going through the entire process?
AE501: Great video, super useful
thank you dr for this video. how do you handle the wave equation of 4th order (cantilever beam equation) forced damped case?
Hi Eme,
Thanks for reaching out. If you have questions or would like to request a video, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching!
-Chris
08:03 Hmm... _What_ class? I mean, what are the _exact_ conditions that has to be met for the separation of variables to work, and when does it break?
Sure, we can always just try and see if it will work, but it wouldn't be cool if after hours of arduous work it would turn out that all that work is wasted because the separation of variables doesn't apply to that particular problem, right? :q
Yeah if you practice PDE solutions ,this is only a subset of methods to solve where the variables in those equations actually can be separated.
Thanks for the great videos!
Well done ... But I was hoping you would explain why lambda_n are called eigenvalues ....
DIVINE TEACHING
Thank you , very helpful
Really great lecture. Just curious, did you neglect the -ve sign of ODE intentionally or was it a mistake? at time 50:00
It is a positive quantity
[AE501] I love this series
Thanks for the great video!
Hi I'm new to PDEs and terminology. Is this method an eigenfunction expansion and is it equivalent to 'spectral methods'? 🤔
Great video
great video, This is Martin Gonzalez, credit plz
Awesome! Thank you!
I'm glad it was helpful. There are other similar videos on the channel. Please feel free to check them out and let me know what you think. Thanks for watching!
Thanks for the very informative video. Can the demonstrations you made be done in the MATLAB as easy as in Mathhematica?
Matlab has the "Symbolic Math Toolbox" that will allow you to do symbolic manipulations similar to Mathematica. Alternatively, if you have numerical values for your problem then you can do it in Matlab just as easily as Mathematica. I like to use Mathematica for symbolic manipulation and problem setup/analysis and then use Matlab for the actual numerical solution/simulation of the problem.
Thanks for the quick and informative answer.
Hi. What would happen if the string was only fixed at x=0 but free at x=L? I know the boundary conditions would be different but I'm unsure in what way
Hi Alicia,
Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on UA-cam due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching!
-Chris
AE501: For separation of variables, are there any PDEs where the solution cannot be written as the product of single-variable functions? If so, how do you know when that product assumption will not be valid?
Hi Beni, yes, there are PDEs where separation of variables does not work. We'll take a look at these in week 8.
Many Thanks
I'm glad it was helpful, thanks for watching!
Thank you professor!