Math 314 Lecture 25: Friday, November 5th 1999.
D'Alembert's Method of solving the 1-dimensional wave equation was
discussed in detail. It turns out that the solution for a finite
string can be constructed from the odd periodic extension of the
initial displacement and the even periodic extension of the
initial velocity, thus avoiding a Fourier series!
D'Alembert's method was then applied to the wave equation on a
semi-infinite string. In this case, the solution can be constructed
from the odd extension of the initial displacement and the
even extension of the initial velocity, but in this case the
extensions are non-periodic.
A simple example was then animated in
Maple.
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Revised 11 November 1999 by
John Hebron.