The Wave Equation: Numbers in 3D

I'm sitting in my friend Lewis' dining room on the computer in the corner listening to choral music in the background, and reading about ways to map waves through math and equations. It's pretty crazy watching how some guys can just build one equation after another, and just use all sorts of crazy methods and formulas and incorporate them in order to model some pretty technical natural phenomena. It's crazy to think that our world is so complex that in order to just solve one formula, you have to use all sorts of techniques developed by mathematicians and theorists. Props to Mr. Broten for the link.


And so I read about "the wave equation":


Now, just so you know, the wave equation is "the important partial differential equation that describes propagation of waves with speed v".

Here's a one-dimensional wave equation:


It seems simple enough (at least for a math genius), but don't forget that as with all partial differential equations, "suitable initial and/or boundary conditions must be given to obtain solutions to the equation for particular geometries and starting conditions."

And there's a wave equation video link here from harvard.

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