Simple PDE

Simple Examples of Partial Differential Equations

In this video, I give a couple of simple examples of PDEs, which you can solve directly just by integrating.
This is to give you confidence that you can solve PDEs and to show you that they are not as hard as you think! Enjoy!

[sweetea__]

I'm crying!!! Thank you soooo much for explaining the very basics. Every book and video expects you to already know this.

[Peter_]

I believe that partial differential equations are the first type of math that is considered "advanced" math at university.

[frozenmoon]

Hidden, but beautiful video on the PDE series!

[AriosJentu]

Looks absolutely awesome, interesting. When I have solving this equations, I use just something I call "partial integral" - just basic integral, but with arbitrary constant as function, independent on integration variable :D

[ramaronin]

i absolutely love his energy towards any topic, its uplifting!

[historybuff]

2:12 The most interesting mathematician in the world, lol

[azhar]

We get many of these in fluid dynamics.

[OtherTheDave]

Let u, ux, uxx, and uxy all equal 0. Done.

[Salmanul_]

Thanks, this gave me enough confidence to learn about PDEs more deeply

[lexinwonderland]

Dr. Peyam, your smile is infectious. Great lecture, thank you for your content!!

[dyer]

Dr.Peyam you should totally make videos on energy/max principles for PDEs!!!

[dr.merlot]

Yes, I can solve all 7 because I work as a telemarketer.

[stephencowart]

ODEs were fun but I cant wait to learn PDEs! Thank you Dr. Peyam!

[jamesbra]

Next can you please do Cauchy's Integral Formula but using matrices instead of scalars to determine the resolvent.

[Phi]

The general solution to the first PDE is actually f(y) + c, because it could also include a constant that doesn't depend on either x or y.

[theultimatereductionist]

I love PDEs and FPDEs = functional partial differential equations. That means the dependent variable, in this case, U, and its partial derivatives, evaluated not just at x and y, but at arbitrary functions of x and y!

[michalbotor]

dr peyam, could I ask you to make a video about the derivation and explanation of the 'triple product rule' for the partial derivatives of three interdependent variables? namely, why is this product equal to -1 and what does it mean?

[youkaihenge]

"Pulls out change of coordinates, " "Aw shit here we go again."

[devinhansa]

4:57 Uxy means first differentiate from x and then from y or in other way?

[zerocoll]

PDE is extremely harder than that. Some PDE you can got solve via fourier transforms, fourier series. To prove somethings related to PDE you need a good knowledge in functional analysis.