Solving the 1D Heat Equation

[@ChristopherLum]

In case it is helpful, here are all my PDE videos in a single playlist kzbin.info/aero/PLxdnSsBqCrrFvek-n1MKhFaDARSdKWPnx. Please let me know what you think in the comments. Thanks for watching!

[@timproby7624]

[AE501] 18:35 It is always helpful when you "recall" certain theorems or assumptions, even if you have reviewed them before. It enables the lecture to continue without having to go back, rewind or pull up other videos.

[@ethanngo3203]

AE501: The Mathematica example walk-through really helps with the homework professor. Thanks!

[@fn5002]

AE501: very thorough and clear explanation of the 1D Heat Equation solution. I like how it ties well with the experimentation you previously did on another video. Farouk Nejah

[@KarlaPkva]

AE501 - This was a great walk through on how to solve a 1D heat equation. The visuals were very helpful!

[@GiovanniRiggi-j2q]

AE501: Johnny Riggi. This was an excellent recap, I vaguely remember this concept from undergrad. This helped me understand the solution process through the examples shown. Thanks!

[@hshams28]

AE501: Really good walk through of things we learned previously with the 1d wave equation

[@matthew-bennett13]

AE 501: I appreciate the fact that starting example we work on in this video works with fixed end points like we saw in the wave equation last week. Seeing a similar problem really helped focus on what made the heat equation distinct from the wave equation. In particular it's interesting to see how this builds on the wave equation by seeing the effects of the initial heat distribution causing a change in our resulting behavior. I think this is a cool thing to compare to the guitar string picking we saw last week. Kudos.

[@alexsteahr8458]

This is a great refresher on what I used to know a long time ago.

[@JonathanRiosRoman90]

AE501: Appreciate the Mathematica walkthrough, great explanation!

[@jasondorn3514]

The similarity to the 1D wave equation made it easy to follow along. I was anticipating the next step as the video went along.

[@KennethWright-k2h]

AE501: This solution process was unsurprisingly similar to that of the 1D wave equation. Thank you for including Mathematica demonstration.

[@jacobgivens2000]

AE501: This video was great lecture! I remember the 1d heat equation from last years heat transfer class!

[@paxtonschipper1926]

AE501: Great video that brings it all together

[@matthewbajamundi8774]

This video is a great transition from the 1D wave equation and provides more insight to real world applications.

[@EfremNickel]

AE501: Great helpful video! Your explanations make it much easier to follow along with the textbook as well. Slowly remembering all of this from my undergrad degree haha

[@gigispence6011]

You are truly a gift from GOD when it comes to teaching

[@ChristopherLum]

Thanks for the kind words. There are other videos like this on the channel. Please feel free to check them out. Thanks for watching!

[@robertdelossantos1936]

It's good to have multiple examples of different PDEs. Practice makes perfect, and it's neat to see the nuances between different PDEs.

[@kylekearsley800]

Another good example of separation of variables. Thanks!

[@elijahleonen198]

AE501: The Mathematica plots at the end were very helpful to understanding the 1D heat equation!

[@karlbalitaan]

Thank you for another helpful video on how to solve this type of PDE

[@ryoonoue1076]

AE501. Great video on how to solve the 1D heat equation. Step by step is very helpful when learning new material.

[@mitchellnakaki7900]

great follow on to the PDE video from before. I feel very comfortable solving PDEs now

[@minaanderberg884]

Great video, really solidifies the process of solving partial differential equations.

[@ryancazin5930]

Great explanation! Ties well with the previous derivations and is easy to follow.

[@selamhendrix5252]

thanks for making it easy to follow and reviewing prior concepts throughout.

[@Tamanaaaa1]

AE 501: Great video thank you!

[@michaelrudolf9988]

Good walk through of one of the famous PDEs

[@sethwhittington28]

AE501: In the first part of the video, around the 4:00 minute mark you wrote that u is a function of (x, y, z, t). This makes sense. However, then when you took the laplacian of u, you only took the derivative of u with respect to x, y, and z, but not with respect to t. I dont understand why the laplacian of u didnt result in taking the derivative of u with respect to each of the independent variables (x, y, z, t).

[@daniellerogers5959]

Cool to see concepts from previous weeks for ODEs be utilized to solve this PDE. Nice video

[@Richard_Le]

AE501 35:24 Will the n = 1 Bn term always be undefined for the 1D heat equation or is that due to the choice of IC?

[@HIEPNGUYEN-wb7yg]

Very well explanation and helpful example! Thanks.

[@perperyuno8563]

Thank you so much Sir😭😭 You literally saved my life

[@ChristopherLum]

I'm glad it was helpful. There are several related videos on the channel. Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!

[@thomasireson1427]

Seeing the plot at the end helped to visualize what we're solving.

[@charlesharmon9065]

Interesting to see the similarities and differences between this and the wave equation... and very useful/helpful for the homework.

[@alisoncaprioli4861]

Helpful lecture for the homework!

[@keyshawnb4845]

AE 501: This was a great video on the 1-D heat equation. I'm curious to know what the 2-D or 3-d heat equations look like.

[@marcosszmania5874]

AE 501: Hi professor Lum, at 39:00 you say that from inspection B1 = 100, why not 100 = B1 + B2 + B3 ... ? Thanks.

[@jesusespinoza2349]

Thank you for the thorough solution discussion

[@sajeew]

This is really helpful for us to do the homework. Thank you for showing us.

[@KylePetittEdu]

[AE501] at 20:05 we note that k=-p^2 and p=nPi/L where n is an integer. If k, L, Pi, and n are all given, isn't p over-constrained? I feel like I'm missing something here because surely thermal conductivity values are not limited to a specific set of values dictated by k = -(nPi/L)^2

[@KylePetittEdu]

I now realize that we are using two different "k"s, one for thermal conductivity and one for the separation constant, so never mind

[@atruon17uw]

[AE501] The Mathematica animation was a great addition to simulate the solution

[@Gholdoian]

AE 501 - Pretty amazing again how this concept encompasses the previous knowledge of using 2nd order ODEs and Fourier analysis to solve these complex problems.Seems like this approach/method could work for finding stress in a beam using the appropriate PDEs?

[@ChristopherLum]

Yes, we'd have to see what type of stress calculation we have but many of these are PDEs as well.

[@garrettdavis4665]

Really helpful and informative!

[@mrassbandit23]

Thanks for going through the solution. Can this separation of variables technique work for any PDE?

[@ChristopherLum]

No, unfortunately the separation of variables technique only works for certain types of PDEs (mostly linear, homogeneous).

[@RajChhabraUW]

AE501: Great video!

[@helentat121]

Should it be ODE 2 instead of 1 at 17:11?

[@ChristopherLum]

Good catch, luckily this minor typo on the board should not affect any of the other content. Please let me know if you catch any other typos, thanks!

[@anthonyz2719]

Thank you professor! Appreciate this

[@carlydunford2546]

AE 501: For the applying ICs step, if Bn did not go to zero over zero, I am not sure I understand how you would solve for Bn. How many Bn terms do you take to equal the ICs? or would each Bn change depending on how many terms you sum?

[@mylesdeluca8789]

Thanks professor!

[@kartiniganesha6741]

hello professor, your video is very interesting, I have a question. How about solving 1d with BC on both sides are Robin's?

[@ChristopherLum]

Hi Kartani, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on KZbin 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

[@masontelander3847]

Great video

[@Firefox7755]

Hi Mr Lum, I have a question regarding the Heat Equation, 1D only. I watched your video on solving it but I wanted to know how you would go about solving it, if your boundary conditions are given in the form u_x(0, t) and u_x(pi, t) instead of the usual u(x, t)? Thanks in advance

[@sachdevtruballer]

hi Chris! could you do a series on Reservoir Simulation for Petroleum Engineering? it has alot to do with PDEs and discretization of the analytical solution to a numerical one. Would really appreciate it!

[@ThienNguyen-vx1td]

AE 501: What if it is not a sin equation, Would you just do the summation?

[@KarolOrtizSolar]

AE501: very helpful!

[@TriMartz-f4x]

[AE501] this is great!

[@christophersanchez2256]

Thanks, Professor!

[@jonathonlaird6279]

thanks for the video

[@lienchang8391]

Thank you Professor!

[@BTEEEOmkarYerawar]

If ut = (-1)uxx Then is it 1D Heat equation or not ?

[@LilanieAlfredaAbdur-Rahman]

AE501: So doable but still looking forward to the numerical approach.

[@jakegalleryn6200]

Quite helpful

[@bryanmasserang5190]

Good video

[@SScook206]

Thank you!

[@kingsleyifeanyi3924]

Thank you sir

[@trevorubrown]

Great vid

[@joewalker5753]

very interesting

[@LorraineB_0911]

Thanks for another great video #AE501

[@nopeopleplace]

Thanks! great vid. but your Bn equation is incorrect and that's why you get 0/0 when b=1. If you solve the integral for every n, you'll see that it gets 0 for every value of n except for n=1 than it gets 100.

[@malachimorris1649]

AE501 - Malachi Morris

[@CodySmith]

AE501

[@marissalamadrid8190]

Interesting Bn = 0/0 case ...

[@MrThegonz1]

great video, This is Martin Gonzalez, credit plz

[@MarcoIacoviello-r3w]

AE 501

[@janosinski5617]

Mupppp Ireland!!!

[@NikiThomas]

wave equation? more like hand wave through the actual math T_T