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vpde_lecture25 [2020/03/31 08:55] trinh |
vpde_lecture25 [2020/04/04 21:33] (current) trinh |
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| This lecture will do apply separation of variables and Fourier series in order to solve for the wave equation on a finite interval. | This lecture will do apply separation of variables and Fourier series in order to solve for the wave equation on a finite interval. | ||
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| ===== Definition 16.1 (1D wave equation with homogeneous Dirichlet BCs ===== | ===== Definition 16.1 (1D wave equation with homogeneous Dirichlet BCs ===== | ||
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| \left(\frac{n\pi c}{L}\right)B_n = \frac{2}{L} \int_0^L v_0(x) \sin\left(\frac{n\pi x}{L}\right). | \left(\frac{n\pi c}{L}\right)B_n = \frac{2}{L} \int_0^L v_0(x) \sin\left(\frac{n\pi x}{L}\right). | ||
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| + | //(The video gets very close to the end of this; we managed to get the $A_n$ coefficients and need to address the $B_n$ coefficients in lecture 26)// | ||