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Unformatted text preview: 36 Chapter 3 Partial Diﬀerential Equations in Rectangular Coordinates extend x_ : x
2 Floor x 1
periodicf x_ : f extend x
periodicbigg x_ : bigg extend x
Plot periodicf x , periodicbigg x , x, 3, 3 1 0.5 -3 -2 -1 1 2 3 -0.5 -1 Because f ∗ and G are 2-periodic, it follows immediately that f ∗ (x ± ct)
and G(x ± ct) are 2/c-periodic in t. Since c = 1, u is 2-periodic in t.
The following is an array of snapshots of u. You can also illustrate the
motion of the string using Mathematica (see the Mathematica notebooks).
Note that in this array we have graphed the exact solution and not just
an approximation using a Fourier series. This is a big advantage of the
d’Alembert’s solution over the Fourier series solution. ...
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.
- Fall '11