PDE 7 | Wave equation: intuition

An introduction to partial differential equations.

Part 7 topics:
-- intuition for one dimensional wave equation

[james]

You are quite possibly the clearest (in terms of voice, handwriting, AND presentation), most logical, and most helpful teacher I have ever had by far! With your videos I hope to survive at least a portion of my PDE class, because let's face it, everyone's curriculum is too varied for one person to cater to. But this video alone has made a huge difference so please, feel free to add ANYTHING at all in the near future, I'm positive it will be helpful in one way or another!

[joseortiz]

Intuition is just awesome, and it is so undervalued. Its what separates the "geniuses" from the "stragglers", and it only requires some discipline or a helping hand to achieve.

[Rowan-lf]

The way your teaching and your voice just have magic. Thank you.

[samblake]

Very intuitive justification with a beautiful marriage between physics 1 and pre calculus. Really warms my heart seeing a tough subject tackled like this!

[adisoneverettunsworth]

This is the most confident I have felt about PDE's yet.

[AndrewJames]

Amazingly clear explanation that connects the dots that are not always plainly apparent on first look.

[pauluk]

This is very clear 'hand-wavy' explanation. With no prior experience of the subject of PDEs I like it. See the lecture from Yale: "Maxwell's Equations and Electromagnetic Waves" - it goes the same informal way.

[johnholme]

Thanks for producing this video, it’s helped me make more sense of the wave equation. I like to visualise everything, not just understand the maths.

[MrJking]

My intuition is comparing the wave equation to the heat equation. The heat concavity profile is fixed with respect to x and simply diffuses in time. The wave concavity profile is moving with respect to x and so you have two separate concavity profiles, one in time and one in distance.

[sjsawyer]

Wow nice derivation I've never seen that one. Yes a little quick and simplified but makes a very good way of remembering the wave equation anyhow, or at least "justifying" it without a full derivation one would probably not understand fully on the first go anyhow.

[sculptedmercedes]

Thanks, this brings together physics and math in an "aha!" way!

[sunilalimbu]

Came here after reading malalasekera book on "intro to cfd". If anyone has understood the book chaper two's equilibrium and marching problems, please make video to explain it. Thanks.

Your video is helpful to some extent commuter

[airmikec]

WOW! Dude you simplified the crap out of the wave equation. I wish my PDE teacher was that good. Unfortunately, she knows how to do the math and she knows the science behind it, but she doesn't explain crap for any equation she gives us. Now, if you can do a heat equation sometime, start your own website and charge $2 / video, you would make your self some money. Almost no one tutors PDEs, I believe because PDEs are pretty brutal.

[elyepes]

Hi there, great video, thanks for it. However, there is a mistake in the interpretation of the sign of the constant of proportionality 'k', you say that bc the force vectors are directed towards the x, then k must be positive; it's actually the contrary, if you think of the x axis like "a mass attracting points of the rope", analogous to gravity fields, attraction forces are negative by convention, that's why you square k, to guarantee that it will be positive

[james]

Oh and by the way, if you have another website or something with additional teaching materials I would be extremely grateful to hear about it! Or for that manner ANY other help with PDEs that you can recommend would be fantastic! Hell, I'll even buy another textbook if you think it presents the material well because the one that I'm using in class just can't get the topics across to me, and we've only had it for a week...

[Chausies]

These are wonderful, wonderful videos, and your explanations of PDE's is just great. The intuition you give for what they mean and how to solve them really is delicious. I eagerly await more videos in the series (here's hoping that more are coming T~T)

[gsgp]

Excellent explanation!!
I understood the wave equation by this video.
Very good.

[james]

We are using "A First Course In Partial Differential Equations with Complex Variables and Transform Methods" by H. F. Weinberger

[Pasuishero]

Well you just solved all my doubts of differential equtions hope it works for my GATE paper ..
:) Thanks a lot ..

[ankurc]

you help me become a better student and a better teacher thank you