The Wave Equation in Higher Dimensions - Partial Differential Equations | Lecture 21

We can derive the wave equation in higher dimensions to describe vibrating membranes, i.e. 2-dimension strings. Here I simply provide the multi-dimensional wave equation and discuss some important features and aspects of it. As with the heat equation, in higher space dimensions we have to pay particular attention to the boundary conditions put on the PDE. We further discuss an important kind of solution to the 3D wave equation: plane waves. Plane waves are solutions that travel and oscillate in a fixed direction, resembling large radio or light waves.
Lectures series on differential equations: • Welcome - Ordinary Dif...
More information on the instructor: hybrid.concord...
Follow @jbramburger7 on Twitter for updates.

[@pauloferraz3042]

this is just great, hopefully KZbin, bring this to more people

[@justinpakarno4346]

I enjoyed this.

[@care3835]

thank you so much for this lecture!

[@drneuropharmacology2496]

Hello Jason, tremendously thankful for your efforts and passion for teaching. After you're finished with this video series, i have some suggestions for some topics that I and others surely would enjoy: (1) A series about weird differential equations, stochastic, fractional, time-delay, and impulse equations with applications to modeling biological phenomena. (2) Expand on your nonlinear dynamic videos with higher dimensional systems or more advamced topics such as ergodic theory perhaps? (3) Combine options one and two; use nonlinear dynamics to analyze systems represented by all sorts of continuous dynamical systems or discrete such as the henon map (4) data-driven dynamical systems theory; the convergence of neural networks and dynamical systems. (5) Theoretical neuroscience and/or systems biology