Derivation and Solution of Laplace’s Equation

In this video we show how the heat equation can be simplified to obtain Laplace’s equation. We investigate how to solve Laplace’s equation using separation of variables.

Additional videos in this series:

Associated videos on software tools relevant to PDEs include:

[anthonyz]

Laplace's equation is everywhere! Thank you for showing how these concepts connect!

[glopez]

Great video, and excitement. Interesting how the hyperbolic function of sin comes in and how it relates to the Fourier constants, (AE501).

[TuanTran-fsll]

AE501-Tuan Tran: I was wondering why u(x, y) has An coefficient instead of An star, but it was corrected toward the end. Thanks professor for very thorough derivation.

[charlesharmon]

Very helpful to see the step-by-step processes by which this and other PDEs are derived and solved!

[connorbaldwin]

AE 501 Your explanations as always make complicated derivations make sense. I wish this was taught with the same structure during my undergrad. Thank you

[alisoncaprioli]

Another helpful lecture for the homework! Being thorough in these videos is so helpful. Thanks!

[enigma]

AE501: Jesse Perez - I always find your videos easy to follow. The derivations are straightforward and make lecture notes much more understandable. In this case, at 3:00, the 2D heat problem was simplified nicely with the listing of most terms and with the elimination of redundant components such as the thermal diffusivity due to the steady state solution. Thanks!

[lienchang]

Thank you professor, the overview of deriving and solving PDE's is getting more clear to me. It seems like there's a general step in solving each case...

[HIEPNGUYEN-wbyg]

Thanks for the very well explanation video! Yes, lecture notes and a summary slide would be helpful.

[iremerkan]

AE501: The last example on the rectangular plate for the calculation of An was really helpful and easy to follow.

[jenniferjohnson]

[AE 501 JENNIFER JOHNSON] This video was really helpful for understanding deriving Laplace's Equation and for my homework.

[daniellerogers]

Always helpful walking through these derivations of equations.

[thomasireson]

Always glad to see the derivation of the equations we use.

[aimeepak]

AE 501: The derivation for the solution of a Dirichlet problem was very easy to follow. Thanks!

[elijahleonen]

AE501: Wonderful lecture and helped me understand the concepts for Laplace's equation.

[sunnysarkar]

AE 501: the construction of relating Fourier to the equation was very clear and easy to follow.

[LorraineB_]

Thanks! Armed and ready to tackle the HW! Great video.

[NataliaErmolaeva-iq]

AE501: Thank you Professor for the example with the rectangular plate, the video of pdf was helpful for Problem 2. -Natalia Ermolaeva

[jasondorn]

Thanks for the video. The reference to the wave equation here 17:34 was great to help differentiate the material

[mitchellhubbard]

Great video, lecture notes would help me follow along much better than writing it out myself.