PDE 3 | Transport equation: derivation

An introduction to partial differential equations from a practical viewpoint.

Part 3 topics:

-- a derivation of the transport equation
-- characteristic lines

[nathaliarivera]

I know you probably get this a lot, but I just have to say, your videos are supremely excellent. You don't just provide a formula with no context to solve the problem, but you introduce concepts and methods to really understand the math intuitively. Very rare to find an explanation like yours, and for that, I thank you and tremendously admire your approach. You have inspired a fellow math lover!

[김현진-kfo]

You're really really really an awesome teacher!
I give you so much thankful mind!
I am going to listen all of your lectures.
Thank you so much again.

[HarryRunes]

Whoa that description of characteristics at 4:20 is really great. Made me understand them more in 30 seconds than in 2 weeks of class. Great video!

Wow, you do a very thorough clear neat approach that I just love. Plus your voice is just pleasant to listen to.

[alephnull]

Great explanation. My notes were so unclear about this and didn't even derive it, but now I understand the equation intuitively and exactly why it holds :).

[aiyakuchukova]

The way you get the result so naturally is super-fascinating! Thanks a lot. Didn't really get that in class, and now finally got (maybe I deserve some sleep now, finally)

[khandmo]

Let me just say I attend a pretty well-known college and these videos have been instrumental in my understanding 9 years after publication. Bravo to you.

[yousufaero]

How did I miss this channel? I understood this characteristic lines now from a video which is more than a decade old. Its great.

[surfing_youtube]

The best illustrative video teaching the concept of characteristic lines with a transport equation. Thank you very much.

[hooochiecooochieman]

Thanks so much for the great explanation. Very informative videos and a great way to show the physics behind the PDEs.

[jinweiyang]

You are really a genius derive it in this way all the people can understand totally.

[GhostFramez]

Oh my god, this is the only good explanation I found on this topic, I'm so thankful! Helped me lots.

[curtpiazza]

I like you illustrations with the graphs!

[crystalcear]

Fantastic video...I finally understand the meaning behind partial differential equations!!

[nickhodgskin]

Thank you so much for the insight into how the transport equation can be determined through the directional derivative!! We're doing something similar where c is a function, but your explanation was really insightful into the equations derivation (a detail unfortunately skimmed over by our lecturer).
Subbed!

[christosxethalis]

Thank you, best explanation of characteristics I've seen.

[athuljyothis]

thank you for that representation of characteristic curve. i didn't understand this using my last month's lectures.

[benwinstanleymusic]

Thank you so much, easily the best explanation I've seen on this topic

[TheBikerman]

I was about to ask the same question then remembered that is is one of the forms of the multi-variant chain rule. If you have a basic calc book look up the chain rule towards the end. The chain rule is the sum of the partials multiplied by the ordinary derivative. I hope that helps if you are still trying to figure that out.

[junouyang]

thanks you. Even more clear than our lecturer!