PDE 5 | Method of characteristics

An introduction to partial differential equations.

Part 5 topics:

-- the method of characteristics
-- applying the method to the transport equation (6:40)
-- non-homogeneous transport (12:04)

[jeremybinagia]

Usually I don't like these types of videos since I prefer reading from a textbook, but this video was super clear. Every source I tried to read online for characteristic curves was just needlessly complicated and assumed too much prior knowledge. Well done!

[AinNoNey]

I hate the fact that understanding it in my second language is lot easier than in my native one. Believe me or not, math in English seems much more acquirable. At least I don't fall asleep after 30 seconds. Cheers from Poland. You've just gone international ;)

[guitarofwar]

Absolutely loved this. The exercise at the end was so helpful for using the method of characteristics. No-one learns just by watching.

[lejakke]

just discovered this and i did not expected this video to be already 9 years old, beautiful graphics and way of presentation

[bartoszdrzygaa]

Just want to say, you are awesome. This is the best series on PDEs I've seen on YT. I love the way you use examples, like with a moving cart, to visualize what's behind the equations.

[elliemokhtari]

Your videos are awesome, I am graduate student and I use your videos for my PDE cours and I learn each and every of your videos, Thank you so much

[kenmcc]

This is magic - thank-you for making it so much easier to understand than textbooks make it

[imagedezach]

Thank you for these videos on method of characteristics. Yours are the only ones I've found that explain this topic clearly and concisely.

[DANISHKHAN-cvox]

this is the only explanation which solved all my doubts. Finally understood the meaning of the phrase "solution propagates along characteristics"

[damgnj]

I love when someone explain something in math easy, like in this video. Thanks!

[bjar]

Great videos; well explained, easy to understand and good progress pace. Thank you! :-)

[ammarshaikh]

Thank you! Your illustrations in the video about observer and the wave are helpful. Before, I was not able to understand what phenomena this PDE was describing

[haniehsoleimani]

helped me a lot, thanks. It is much clear than any text book explanation.

[smath]

This was helpful and also wonderful, really really well done. Thanks a million.

[SaiPraneeth]

Excellent video, the it was smooth as butter to understand
Thanks a lot.

[cristianegrossiferrarezzi]

Thanks a lot for the video. I was trying to understand this method for a long time and your explanation solved all of my doubts. I would be so thankful if you could make a video about Duhamel's Theorem. Thank you! ;)

[harryliu]

This is a very enlightening method! Thanks for posting this question!

[hadadvitor]

Extremely helpful, commutant! You have the best PDE videos in Youtube! Thanks!

[superphilschneider]

Hi commutant, thanks for a very good video. Doing what you did in this video is not easy, so nice going. I'm trying to learn my engineering mathematics again, but this time properly, so videos like yours are very helpful. What happens in the original PDE when the wave propagation speed, c, is not a constant? If c depends only on time, t, then I think it's not so bad, but what about when c depends on x. Do you have a video for that?

[ZappelFly]

du/dt + u du/dt=0 is the so-called burgers equation and it's well studied in every pde-textbook. For example Lawrence C. Evans - Partial Differential Equations