D'Alembert Solution to the Wave Equation

Описание: In this video, we derive the D'Alembert Solution to the wave equation. We use the general solution found in the last couple of videos to solve a Wave PDE problem in an infinite domain with two initial conditions (initial displacement and initial velocity). The resulting solution is the D'Alembert Solution/D'Alembert Formula.

We also show earlier on in the video that the Wave Equation consists of the sum of a forward travelling wave (f(x+ct)) and a backward travelling wave (g(x-ct)), because if we're at the same relative location on the wave (e.g. x+ct/x-ct is a constant), then that relative location has to have a decreasing x (backward travelling) for f(x+ct) and an increasing x (forward travelling) for g(x-ct). I hope my explanation here wasn't too confusing because I feel like that was one of the trickier parts of the video. If you have any questions, let me know!

Questions/requests? Ask me in the comments!

Prereqs: This playlist, especially videos 9-12:    • Partial Differential Equations  

Lecture Notes: https://drive.google.com/file/d/0BzC4...
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