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Unformatted text preview: APPM 4350/5350: Fourier Series and Boundary Value Problems Homework #1 Aug. 23, 2010 Due: Friday, September 3, 2010. Usually HW are due on Monday’s, but this one is due on Friday because of late Labor day holiday. 1. Solve: dy dt + k y = b, where y ( t = 0) = a, k,a,b constant. Explain when lim t →∞ y ( t ) exists and find this limit. 2. Solve : dy dt + p ( t ) y = 0 , where p ( t ) is a continuous function and y ( t = 0) = a,a consant. Put a condition on the integral of p ( t ) so that lim t →∞ y ( t ) exists and then find this limit. 3. Solve : d 2 y dt 2 + ω 2 y = β, with y ( t = 0) = A, dy dt ( t = 0) = B where ω > ,A,B,β are constants. Explain when lim t →∞ y ( t ) exists and find this limit. 4. (a) Solve : d 2 y dt 2- α 2 y = β with y ( t = 0) = A, dy dt ( t = 0) = B where α > ,A,B,β are constants. (b) Put the solution in terms of both exponentials as well as hyperbolic functions....
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This note was uploaded on 10/24/2010 for the course APPM 4350 taught by Professor Ablowitz during the Fall '08 term at Colorado.
- Fall '08