Professor MathTheBeautiful, thank you for explaining the Solution of Poisson Equation on the Unit Disk in Partial Differential Equations. This is an error free video/lecture on TH-cam TV.
Hi, at 13:28, why there is -1/25 r^5 inside the Fourier series( or inside the sum)? I think there are a 1/25 r^5 which is the particular solution at the outside of the Fourier series, so we don't need to write -1/25 r^5 inside the Fourier series, right?
10:44 You intrigued me :q Now I wanna know how this tensor calculus trick works. Can you link to that video in the description? I was already wondering about these different "compact forms" of differential operators that have those coefficients that look awful lot like corrections for different measures in different directions, or change of coordinates, but I couldn't put my finger on it how it really works. And the usual derivation of the laplacian in spherical coordinates is simply DISGUSTING: it took me 6 A4 paper sheets and several hours to do it myself, and it made me wonder if there could be some better way to do it, because the coefficients that appear in the derivation looked awful lot like some elements in a transformation matrix for rotations and scaling.
exactly.... i felt the same thing...now, I want to learn tensor calculus.. and i found the course in your channel... i will start it today.. thank you for wonderful lectures
Glad I found this channel. I took my pdes course last year but I still like to watch these to refresh my knowledge.
Thanks professor!
Professor MathTheBeautiful, thank you for explaining the Solution of Poisson Equation on the Unit Disk in Partial Differential Equations. This is an error free video/lecture on TH-cam TV.
Glad it was helpful!
Hi, at 13:28, why there is -1/25 r^5 inside the Fourier series( or inside the sum)? I think there are a 1/25 r^5 which is the particular solution at the outside of the Fourier series, so we don't need to write -1/25 r^5 inside the Fourier series, right?
He didn't write out the Fourier series. He wrote "=" after the summation sign.
10:44 You intrigued me :q Now I wanna know how this tensor calculus trick works. Can you link to that video in the description? I was already wondering about these different "compact forms" of differential operators that have those coefficients that look awful lot like corrections for different measures in different directions, or change of coordinates, but I couldn't put my finger on it how it really works. And the usual derivation of the laplacian in spherical coordinates is simply DISGUSTING: it took me 6 A4 paper sheets and several hours to do it myself, and it made me wonder if there could be some better way to do it, because the coefficients that appear in the derivation looked awful lot like some elements in a transformation matrix for rotations and scaling.
The formula is discussed here: th-cam.com/video/BD2AiFk651E/w-d-xo.html, but I'm not sure where to find its application to the Laplacian.
exactly.... i felt the same thing...now, I want to learn tensor calculus.. and i found the course in your channel... i will start it today.. thank you for wonderful lectures