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Unformatted text preview: 18.03 Problem Set 4a Spring 2009 Due with the rest of PS4, 12:55 pm, Friday, March 6 Exam 1 will take place Wed, Feb 25, in Room 10-250 and Walker Memorial (upstairs). This is the first installment of Problem Set 4, called PS 4a. It includes the parts you should do before Exam 1. The whole of PS4, including this part, will be posted after Exam 1. Part A 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 7, Wed Feb 18; Linear response to sinusoidal/exponential input) Read: IR 1-3, 5 (and 6 if you did not already do so) Work: Find the sinusoidal solution to x ′ + 3 x = cos(2 t ) by first finding the complex-valued solution with right side a complex exponential and then taking the real part. Write the solution in the following two forms (finding both directly from the complex solution): a) as a sum of sines and cosines b) in the form A cos( ωt- φ ) 2. (Lec 8, Fri Feb 20: Autonomous equations, phase line, stability) Read: EP 1.7, 7.1 Work: Sketch enough solutions to y ′ = y ( y- 1)(1 + y ) to show all behaviors, including, in particular, all steady state solutions and their stability. (Do not solve!) To the right of yourparticular, all steady state solutions and their stability....
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- Spring '09
- Numerical ordinary differential equations, phase line, Godzillas