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# hw6 - CAAM 336 DIFFERENTIAL EQUATIONS Problem Set 6 Posted...

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CAAM 336 · DIFFERENTIAL EQUATIONS Problem Set 6 Posted Wednesday 29 September 2010. Due Wednesday 6 October 2010, 5pm. General advice: You may compute any integrals you encounter using symbolic mathematics tools such as WolframAlpha, Mathematica, or the Symbolic Math Toolbox in MATLAB. 1. [60 points] Solve the following boundary value problems using the spectral method. For each problem, (i) write down the expansions of the right hand side functions as linear combinations of the eigenfunctions; (ii) write down the sum for the solution u obtained from the spectral method; and (iii) produce a plot showing the sum of the ﬁrst twenty terms in the series for u . For parts (c)–(e) you may use the eigenvalues and eigenfunctions computed in Problem 1(d) of Problem Set 5, and the results of Section 5.2.3 of the text. (a) - d 2 u dx 2 ( x ) = e x , u (0) = 1, u (1) = 0. (b) - d 2 u dx 2 ( x ) - 10 u ( x ) = e x , u (0) = 0, u (1) = 0. (c)

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hw6 - CAAM 336 DIFFERENTIAL EQUATIONS Problem Set 6 Posted...

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