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Unformatted text preview: 18.03 Problem Set 9 Due by 12:45 P.M., Friday, May 9, 2008, in the boxes at 2-106, next to the Undergraduate Mathematics Office. I encourage collaboration on homework in this course. However, if you do your homework in a group, be sure it works to your advantage rather than against you. Good grades for homework you have not thought through will translate to poor grades on exams. You must turn in your own writeups of all problems, and, if you do collaborate, you must write on the front of your solution sheet the names of the students you worked with. Because the solutions will be available immediately after the problem sets are due, no extensions will be possible . IV. First order systems L34 F 2 May Complex or repeated eigenvalues: EP 5.4, Notes LS.3. L35 M 5 May Qualitative behavior of linear systems; phase plane: SN 26. R22 T 6 May Linear phase portraits. L36 W 7 May Normal modes and the matrix exponential: EP 5.7, Notes LS.6. R23 Th 8 May Matrix exponential. L37 F 9 May Nonlinear systems: EP 7.2, 7.3; Notes GS. Part I. 34. (F 2 May) Notes 4D-2. EP 5.6: 1. (Use Linear Phase Portraits: Matrix Entry to construct the phase portrait.) 35. (M 5 May) Notes 5B-4. (This can also be checked using the same applet.) 36. (W 7 May) Notes 4H-1, 4H-2, 4H-3. Part II. 34. (F 2 May) [Complex and repeated eigenvalues] (a) The population of foxes and rabbits on Nantucket Island has been studied by biol- ogists. They measure the populations relative to a baseline, in hundreds of animals. So x (2) = 5 means that there are 500 more foxes than the baseline value, and y (2) =- 5 means that there are 500 fewer rabbits than the baseline value....
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- Spring '09
- Linear Algebra, Complex number, Orthogonal matrix, linear phase, Linear Phase Portraits