Hyperbolic, Parabolic, and Elliptic Partial Differential Equations

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Chapter 7 - Numerical Methods for Differential Equations
Section 7.5 - Classification of Second-Order Partial Differential Equations

This video is one of a series based on the book:

"Matrix, Numerical, and Optimization Methods in Science and Engineering," by Kevin W. Cassel

Kevin Cassel

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needs after effects animations ... visualising PDEs makes it much easier to understand the wall of equations

boriscrisp

Eric Weinstein's interview with Lex led me here. He quoted
You know, we have these three kinds of equations that are very important to us. We have elliptic hyperbolic and parabolic. Right. And so the idea is if if I'm chewing gum after eating garlic bread, when I open my mouth and I've got chewing gum between my lips, maybe it's going to form an elliptic object called a minimal surface. Then when I pop that and blow through it, you're going to hear a noise that's going to travel to you by a wave equation, which is going to be hyperbolic.
But then the garlic breath is going to diffuse towards you and you're eventually going to be very upset with me according to a heat equation, which will be parabolic. So those are the three basic paradigms for most of the work that we do. And a lot of the work that we do in mathematics is Elliptic, whereas the physicists are in the hyperbolic case and I don't even know what to do about more than one temporal dimension, because I think almost no one studies that.

kimchi_taco

Explanations to the point. Great lecture :)

Julian-jqej

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