Learning Maple: Partial Differential Equation Topic - Heat Equation in 2D

Topics:
* Solve the heat equation symbolically for a 2-dimensional system - for one that fails.
* Solve correctly
* Create the following:
- 12-term solution
- N-term solution
- animation

Authorship:
(C) Scot Gould, Scripps, Pitzer, Claremont McKenna - Members of The Claremont Colleges
Claremont, California, USA

Maple is a trademark of Maplesoft, Waterloo, ON, Canada.
I do not work for Maplesoft. Maplesoft did not compensate me for this video.

[thomasolson]

Hi, sorry, I'm not a math or physics guy. I'm talking nonsense. Just kind of here because I am on welfare and have nothing better to do with my time. I'm a time waster, everyone hates me. I finished G12 though.
Squares in complex exponentials seem to show up when derivatives are involved. And look at that, the imaginary part got squared, making it a hyperbolic function. When I see sin functions like that, I think they are there to accept or deny terms on integer values. They are often better represented with roots of polynomials. That way you can get the fractional values of time.
This is one of two functions of the hyperbolic version of Kepler's elliptic eccentricity. I'm guessing this is regular probability of some sort, a statistics function. And all that made the 3d oscillating surface? That's weird. I think I seen those waves when I played with Pell Numbers. I made an error when I did that. The fractional values of time on these kinds of functions are complex numbers, making it 4d. I don't believe I did the Laplacian derivative thing on that.
So, Pell Numbers are hyperbolic. I'm guessing the sum of an exponential without the imaginary part is either probability or energy. And with the sum of the imaginary part, it is an oscillating path of a massless object in space.