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Unformatted text preview: 18.03 Problem Set 6 Spring 2009 Due in Room 2-106 at 12:55 pm, Friday, April 3 Part A (12 points) 1. (Lec 20, Fri Mar 20: Introduction to Fourier series) Read: EP 8.1 Work: 7A-1, 2b, 3, 4 2. (Lec 21, Mon Mar 30: Operations on Fourier series) Read: EP 8.2, 8.3 Work: 7B-1b, 3 (even case only), 4 3. (Lec 22, Wed Apr 1: Fourier series solutions to ODEs) Read: EP 8.3, 8.4 Work: 7B-2a, 7C-1, 3ab Part B (44 points) 0. (at due date) Write the names of any person, web site, or materials you consulted. Write “No C” (no consultation) on your paper if you consulted no outside materials/people. 1. (Lec 15, Mar 9: Euler equations) [10 points: 4 + 4 + 2] We will solve the equation dy dx- (3 /x ) y = x 2 from Exam 1 by a new method. a) Make the change of variables x = e t , and solve for y as a function of t , then return to the variable x to confirm that you have the same general solution as on Exam 1. b) Use the same change of variables to find the general solution to x 2 y 00 + axy + by = 0 for constants a and b . Divide into cases, and express your answer in terms of the roots r 1 and r 2 of the corresponding characteristic equation. c) Knowing the form the solutions to (b) in advance allows us to skip the change of variables. Find the solutions directly by seeking solutions of the formvariables....
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This note was uploaded on 05/06/2010 for the course 18 18.03 taught by Professor Unknown during the Spring '09 term at MIT.
- Spring '09