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!
AE 501: "When someone finds this mess in the morning, I'll blame it on them". This part cracked me up 😂 Thanks for making these lectures enjoyable and fun to watch!
AE501: Thank you for making these lecture videos fun to watch as much as they are informative. Makes it a much easier watch. And I appreciate that I can come back to any of these lectures right here on youtube!
AE501- the methods are really the gold in these lectures. This does a great job of picking out the importance of assumptions and applicability. It's almost surprising how easily these expand to higher dimensions
AE 501: I'm really glad that you're taking the time to get into depth on the derivation of the equations. I have in the past had professors who tended to skip through equation derivations very quickly or left more up to the student to figure out from text alone. I appreciate you going through this thoroughly.
AE501: Somehow understood the derivation better as soon as the piece of cloth came about, but serious note a very detailed and easy to follow understanding of the derivation of 2D wave equation!
Great. I like the way you made a complex derivation fun to watch. Cleaning up the mess after your video is also a great service to science, something that your wife must be knowing!!
The one thing that I liked the most is that you tell all the assumptions taken at each step. I would just like you to explain how those assumptions don't affect the physical reality of the situation a little bit more.
AE501 - I really enjoyed this video. The props made it easier to understand the 2D wave equation, and gave me a good laugh especially once the dA patch had to come out of the towel.
AE501 - Johnny Riggi. Easy to understand breakdown of a complex topic, especially with the lecture notes. Learned a good bit about double Fourier series as well!
AE501: I really enjoy and appreciate the initial demos with real objects to set the stage for derivations and problem solution it really allows me to tie the two together. It would be very interesting to explore a beam that has resistance to bending and its reaction or different eigenmodes.
Thank you, you did a great job helping me visualize the problem. I was reading the derivation for it in Frank Bowman's Introduction to Bessel functions and I couldn't understand where the partial derivative with respect to x (or y) was coming from. It only had one 2d picture that wasn't particularly helpful.
AE501: Professor Lum, similar to in your one dimensional video, I am confused about the assumptions made regarding small angle approximations when summing vertical forces. REF timestamp 17:30. You noted that since theta was small, we could assume that the Cos(small angle) = 1, and as a result, the horizontal forces cancel out. By that logic it seems to me like a similar argument could be made to the vertical forces such that SIN(small angle) = 0, meaning that the vertical forces would also cancel out and the sum of the forces in the vertical direction = 0. Am I missing something?
Hi Seth, the small angle approximation is that cos(theta) =1 and sin(theta) = theta. You can see why if you plot sin and cos and look at the functions at small values of theta.
@@ChristopherLum I am also confused about how density * area = mass. Typically we see density * volume = mass but in this lecture it looks like we have density * delta x * delta y = mass.
AE501: Your teaching style is appealing in many ways. But if I had to choose only one, I would go with those illustrations that aid in creating mental images.
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: I liked the graphs and visual elements in your lectures. I find it really hard to follow along with theory if there isn't something physical to see in order to understand the material!
AE501: Thank you Chris for the amazing illustration using the towel. Constraining the edges reminds me of drum making as a kid. Could this approach be used to relate the deflection on a hand drum to the notes produced?
AE501: Is there any issue with the fact that when the simplification is made from [u_x (x+deltax,y1),u_x(x,y2)]/deltax to u_x_x that y1 and y2 don't necessarily equal each other? Is it because y1 and y2 are assumed some average or constant value? Similar potential issue for u_y_y?
What are some real world applications of this 2d wave equation? I look online but all I can find is the example of a drum head, are there any less obvious applications? And if so would they all take this exact form but with a different value for c^2 ? Thanks :)
Hi Loriana, 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 or via the 'Thanks' button underneath the video 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: love this video. Examples are great (I hope your wife wasn’t mad about drawing on that towel!) how much more complicated would this get if the membrane was no longer perfectly flexible?
Intuitively this just means that the membrane is secure and won’t slide off. That’s what he means by no horizontal motion. It also means the membrane won’t tear.
For every point on the edge of the boundary (circle) there is a tension that is being balanced (or cancelled) by a point on the opposite side of the boundary. Similar to the 1D version.
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!
These lectures are beautiful sir, thank you for sharing!!!
AE 501: "When someone finds this mess in the morning, I'll blame it on them". This part cracked me up 😂 Thanks for making these lectures enjoyable and fun to watch!
This was not only a helpful video but extremely fun to watch. I loved how you played around with your props.
Cutting out the towel definitely helped visualize how you were going to derive the 2D wave equation.
AE501: I really like how you made again very accessible for someone who hasn’t touch this material in quite sometime. Farouk Nejah
AE501: Thank you for making these lecture videos fun to watch as much as they are informative. Makes it a much easier watch. And I appreciate that I can come back to any of these lectures right here on youtube!
AE 501: I'm excited to Solve the 2-D wave equation! Also the use of props makes this format of video both hilarious and easy to visualize! :)
AE501- the methods are really the gold in these lectures. This does a great job of picking out the importance of assumptions and applicability. It's almost surprising how easily these expand to higher dimensions
AE 501: I'm really glad that you're taking the time to get into depth on the derivation of the equations. I have in the past had professors who tended to skip through equation derivations very quickly or left more up to the student to figure out from text alone. I appreciate you going through this thoroughly.
Great examples. I like that you show a simple model before diving into the derivations.
[AE 501] I really appreciate the demonstration in the beginning, it's hard to visualize surfaces with sketches but this made it very clear!
AE501: Thank you for helping visualize the 2D wave equation with a diagram. Derivation made sense! Thanks!
Helpful extension of the 1D wave equation to another dimension. This also has to be the funniest video you've had this quarter!
Glad it was entertaining!
AE501: Somehow understood the derivation better as soon as the piece of cloth came about, but serious note a very detailed and easy to follow understanding of the derivation of 2D wave equation!
[AE 501] 2:57
You always find simple but effective demos!
AE 501: Normally derivations are harder for me to grasp but I like the way you simplified this one.
Great. I like the way you made a complex derivation fun to watch. Cleaning up the mess after your video is also a great service to science, something that your wife must be knowing!!
I'm glad it was helpful. There are other similar videos on the channel please feel free to check them out. Thanks for watching!
AE501 : Very helpful to have the props and having the diagrams drawn on them. Also found the callbacks to the 1D wave equation helpful
The one thing that I liked the most is that you tell all the assumptions taken at each step. I would just like you to explain how those assumptions don't affect the physical reality of the situation a little bit more.
AE501: Another great demonstration with clever creativity.
My favorite line is “if you look at it long enough, you will…” 😄
AE501 - I really enjoyed this video. The props made it easier to understand the 2D wave equation, and gave me a good laugh especially once the dA patch had to come out of the towel.
Definitely helpful to get a visualization of what the 2D wave equation is solving.
Woah!!!!! the visualization is great, now I'm able to understand it much better.
I'm glad it was helpful thanks for watching!
@@ChristopherLum today at 9:30 I have exam of partial differential equations so it is going to be best for me..... thank you and keep on going...
Thank you for the in depth explanation!
AE 501. This was a very helpful lecture, I did not go into 2D wave equations in my undergrad so this was very informative.
AE501 - Johnny Riggi. Easy to understand breakdown of a complex topic, especially with the lecture notes. Learned a good bit about double Fourier series as well!
AE501: Thanks for the practical demonstrations, they really do help visualize the concepts and help with understanding!
AE501: Once again- I appreciate all the creativity with the visuals , it really helps! -Maggie Shelton
The visualization for the derivation helped a lot!
AE501: thank you for keeping these entertaining!
Enjoyed your towel example. It really helped me visualize this concept.
AE501: Very clear Professor Lum. I just hope this derivation extends as logically to the heat equation.
AE501: I really enjoy and appreciate the initial demos with real objects to set the stage for derivations and problem solution it really allows me to tie the two together. It would be very interesting to explore a beam that has resistance to bending and its reaction or different eigenmodes.
Very cool visual demonstration!
AE501: The derivation helped my understanding of the 2D wave equation. Thank you for the great video!
Great visual of the bounded membrane
Thanks for the derivation and for including the towel visualization.
Thanks for the video! I really liked the example.
This is showed us how to derive the 2D wave equation.Thank you
You are doing so good not only this rather all concept is 😍
AE501: It was very helpful to see and understand what is happening with the physical towel example.
Thank you, you did a great job helping me visualize the problem. I was reading the derivation for it in Frank Bowman's Introduction to Bessel functions and I couldn't understand where the partial derivative with respect to x (or y) was coming from. It only had one 2d picture that wasn't particularly helpful.
Thanks for this and the solution to the 2-D wave equation!
AE501 - Your demonstration really showed the importance that out of plane deflections are small 😂
Another great, easy to follow video. Thanks!
AE501: Great video, I always struggle with derivations and this helped me a lot.
AE 501: Very helpful! Thank you!
The outcome of the derivation was expected but it was great to see the steps to get there.
The 3D graph was very helpful in trying to understand this.
It's very helpful. I have take home exam about this material
"this garbage down here" I'm so happy to learn I'm not the only person who talks about their equations like this
AE501- Easy to understand the derivation with the visual to start out. Makes sense.
Great video. Visualization does help too! Thanks.
AE501: Great demonstration and a mess to clean up.
AE501:
Professor Lum, similar to in your one dimensional video, I am confused about the assumptions made regarding small angle approximations when summing vertical forces. REF timestamp 17:30.
You noted that since theta was small, we could assume that the Cos(small angle) = 1, and as a result, the horizontal forces cancel out. By that logic it seems to me like a similar argument could be made to the vertical forces such that SIN(small angle) = 0, meaning that the vertical forces would also cancel out and the sum of the forces in the vertical direction = 0. Am I missing something?
Hi Seth, the small angle approximation is that cos(theta) =1 and sin(theta) = theta. You can see why if you plot sin and cos and look at the functions at small values of theta.
@@ChristopherLum Okay yes, that makes sense. Thanks.
@@ChristopherLum I am also confused about how density * area = mass. Typically we see density * volume = mass but in this lecture it looks like we have density * delta x * delta y = mass.
@@sethwhittington28 In this case we define density as mass per unit area. You are correct that this is non-standard but is how the problem is setup.
@@ChristopherLum okay yeah I thought you might be doing something along those lines.. thanks for the response.
AE501: Your teaching style is appealing in many ways. But if I had to choose only one, I would go with those illustrations that aid in creating mental images.
interesting how added an additional dimension does not introduce too much more complexity
Best explanation ever
Thank you
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
AE 501: Thanks Professor great video!
AE501: I liked the graphs and visual elements in your lectures. I find it really hard to follow along with theory if there isn't something physical to see in order to understand the material!
Interesting and clear derivation - thanks!
Great video! Helped a lot!
AE 501 very helpful video to understand the derivation of 2d wave equations
Wow youre great ! thank you so much, you made it so simple
I'm glad it was useful, thanks for watching!
AE501: Thank you Chris for the amazing illustration using the towel. Constraining the edges reminds me of drum making as a kid. Could this approach be used to relate the deflection on a hand drum to the notes produced?
Absolutely, it would be even better if we had gotten to the discussion on circular membranes as these more closely resemble drums.
AE501: Is there any issue with the fact that when the simplification is made from [u_x (x+deltax,y1),u_x(x,y2)]/deltax to u_x_x that y1 and y2 don't necessarily equal each other? Is it because y1 and y2 are assumed some average or constant value? Similar potential issue for u_y_y?
[AE501] I wonder what ever happened to the delta x-y patch.
AE501: Really funny video! I don't remember doing this in undergrad so this was interesting
I'm glad it was entertaining and it is good to see you getting a jump on next week's videos!
@@ChristopherLum I've finally got the routine down. Sundays are lecture day. Ready to start the next HW on Tuesday!
What are some real world applications of this 2d wave equation? I look online but all I can find is the example of a drum head, are there any less obvious applications? And if so would they all take this exact form but with a different value for c^2 ? Thanks :)
Hi Loriana,
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 or via the 'Thanks' button underneath the video 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
the demo was helpful. thanks
Great video!
Love the visuals every time. #AE501
[AE501] The cloth was a innovative way to manipulate the shape of the function
Good demonstration
the funny demo actually helped understand the derivation
I wish you were my current teacher(undergraduate) .
I'm glad it was helpful. There are other similar videos on the channel, please let me know what you think, thanks for watching!
Great video
sir could u post a video for three dimensional wave equation
Interesting derivation
Great video.
Great
can you help me for describe a deriviting wave equation from paper Mario ootaviani (1971)-Elastic wave propagation in two evenly-welded quarter-spaces
Thanks Chris!
Very Good!
AE501: Arda Cetken - Digging the shirt!
AE501: love this video. Examples are great (I hope your wife wasn’t mad about drawing on that towel!) how much more complicated would this get if the membrane was no longer perfectly flexible?
This would definitely make things more complicated and the PDE might not be separable but it should hopefully be agreeable to numerical techniques.
Nice 👍
Sir, which book that you preferred
What if density is not uniform for the material?
In writing the Horizontal and Vertical forces (when we start the derivation) why have we not considered the T del x forces?
he didn't derive because he considered x and y are symmetric
Intuitively this just means that the membrane is secure and won’t slide off. That’s what he means by no horizontal motion.
It also means the membrane won’t tear.
Hahahahaha when he says he´d blame his kids and dog for the mess
Very informative
Merci, c'est très clair.
replacement towels from williams-sonoma? :)
Haha, good idea :)
Loved the bead-mess
Great vid
Beautiful❤😍
Hi, Why do we take assumption of tension being constant everywhere ?
Great video though..very nice explanations ..thanks for the hard work.
For every point on the edge of the boundary (circle) there is a tension that is being balanced (or cancelled) by a point on the opposite side of the boundary. Similar to the 1D version.
great video, This is Martin Gonzalez, credit plz