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!
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
Hey man just discover your videos recently, I gotta say thank you so much! Recently learning PDEs and struggling a lot with my books... your videos help me a lot and I love it, also learn some skills for The Wolfram Math programming thing you using to check solution in the video, it's actually kinda fun, maybe I should also learn it
I'm glad they are helpful. There are more videos on Mathematica on the channel, please feel free to check them out and let me know what you think. Thanks for watching!
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!
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!
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 - 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.
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.
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!!
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.
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 ...
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 - 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.
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
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!!
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.
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
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
@ 51:09 you mention a textbook you are using. What textbook? I'm using Boyce & DiPrima, which uses somewhat different notation. Also B&D skip steps like mad, especially in Laplace's equation. Another book would be helpful.
Hi John, 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. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris
Hi John, I usually cannot keep up with the amount of comments I receive via UA-cam. As such, I like to encourage people to interact via Patreon as I'm able to interact more closely with them and answer questions on that platform. If it helps, the textbook I recommend to students is Advanced Engineering Mathematics by Kreyszig.
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
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!
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: 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.
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.
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.
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
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.
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?
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
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
Hey man just discover your videos recently, I gotta say thank you so much! Recently learning PDEs and struggling a lot with my books... your videos help me a lot and I love it, also learn some skills for The Wolfram Math programming thing you using to check solution in the video, it's actually kinda fun, maybe I should also learn it
I'm glad they are helpful. There are more videos on Mathematica on the channel, please feel free to check them out and let me know what you think. Thanks for watching!
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!
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!
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 - 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 was a really helpful video. Thanks for being so detailed Chris!
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!
Thank you for covering this solution so thoroughly, solving these kinds of problems is far more understood.
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
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.
AE501: This was a great video on the 1-D wave equation. I'd long forgotten most of this information so this was great!
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!!
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.
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.
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 : Easy to follow solution, especially having watched the previous Fourier analysis videos. And a great example with the plucked string!
Thank you for this! I like the way your videos are so comprehensive.
AE501: This step by step solution really helped me understand the physical phenomena being modeled. Thanks!
The outline of the different steps was clear and easy to follow, thanks!
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: 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.
AE501: The animation part is really awesome, and it is incredibly helpful.
I really like the walk thorough in mathematica... a visual always helps me understand the topic
AE501 - Really good in-depth video of the 1-D wave equation. Extremely helpful thanks
Wow, you are a fantastic lecturer, clear and concise
Thanks for watching and for the comment!
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
AE501: Thank you for the thorough explanation and walk-through of the solution in Mathematica!
You make this easier to follow than what I remember from years ago... Thanks.
Thanks! The examples were especially 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: Great overview of the wave equation. The example was really helpful.
Very clear layout. Thank you!
AE501: Showing the computation in mathematic for the 1D wave equations was very helpful!
I really like your teaching style. Thanks for this video!
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
Thanks for the video. After several weeks of other material, eigenvalues and eigenvectors return. It's the "proper" thing to cover.
AE 501: Thanks for the video! Pretty helpful!
Thank you for providing examples. It really help me understand the 1D wave equation concept.
AE501: Very thorough derivation of the solution to the 1D Wave Equation
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!
I keep referring to this video for later HW problems. Very informative lecture. Thank you. #AE501
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.
AE 501: I really like the manipulate command in Mathematica, makes things really easy to visualize
A lot of content, but clearly presented. Really helpful!
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 video professor Lum.!
Amazing series of lectures! Thank you!
Good examples that help explain the topic! thanks!
Found this very helpful, thank you!
[AE501] Very thorough treatment of the topic!
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
Systematic & comprehendible. Thumbs up!
AE 501 This lecture is great! Thanks for breaking every step down so it is easy to understand.
@ 51:09 you mention a textbook you are using. What textbook? I'm using Boyce & DiPrima, which uses somewhat different notation. Also B&D skip steps like mad, especially in Laplace's equation. Another book would be helpful.
Hi John,
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. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching!
-Chris
@Christopher Lum So basically you won't tell me the textbook you were referring to unless I buy the product. Fair enough
Hi John, I usually cannot keep up with the amount of comments I receive via UA-cam. As such, I like to encourage people to interact via Patreon as I'm able to interact more closely with them and answer questions on that platform. If it helps, the textbook I recommend to students is Advanced Engineering Mathematics by Kreyszig.
Very much enjoy these videos, keep up the great work
Thank you very very much, I start understanding wave eq!!
Glad it was helpful, thanks for watching!
Thanks for these, videos, they're excellent.
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
Great video, a really good explanation of the wave Equation.
Helped a lot. Thank you sir !!!
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
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!
AE501: Thank you for simplifying the 1D wave equation. I learned this in the context of "particle in a box" which always confused me.
AE501: Great video, really helped me bring it all together.
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!
Best explanation, I wish you were my tutor
Very thorough solution discussion
AE 501: Great video thank you!
Great explanation! Will help quite a bit with the homework!
Thanks for the great videos!
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:
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.
Many Thanks
I'm glad it was helpful, thanks for watching!
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.
You are awesome! Thanks!
Thanks for the great video!
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.
Thank you professor!
Thank you , very helpful
which text book you have used?
Good video, thanks!
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
AE 501: Thanks Professor
AE501: Great video, super useful
15:05 I initially thought he toppled the whiteboard during wiping🤣
Great video
Thank you sir!
from were can i get the code
DIVINE TEACHING
Manipulate in mathematica is a really cool feature.
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.
Good explanations
thanks for the video
Well done ... But I was hoping you would explain why lambda_n are called eigenvalues ....