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**Unformatted text preview: **Homework List for Math 415.01/415.02 (Spring 2010) Kiam Heong Kwa May 27, 2010 Remark 1. This list will be updated throughout the quarter. Remark 2. A problem with an asterisk (*) is relatively more difficult. Sec 7.8 2, 4, 8, 10, 15** • Problems 2, 4, 8, 10: You may sketch the direction fields and trajectories using the java applet “Pplane” available at http://math.rice.edu/ dfield/dfpp.html. • Problem 15: Use the fact that if r 1 ,r 2 are the eigenvalues of the matrix A = a b c d , then tr A := a + d = r 1 + r 2 and det A := ad- bc = r 1 r 2 . As an application of the conclusion of this problem, note that the current I ( t ) and the voltage V ( t ) in problem 16 can be shown to vanish eventually, i.e., lim t →∞ I ( t ) = 0 and lim t →∞ V ( t ) = 0 , by considering only the coefficient matrix 1 L- 1 C- 1 RC . Sec 7.6 4, 5, 6, 10 • Problems 4, 5, 6, 10: You may sketch the direction fields and trajectories using the java applet “Pplane” available at http://math.rice.edu/ dfield/dfpp.html. Sec 7.5 06/03: 2, 4, 6, 8 • Problems 2, 4, 6, 8: You may sketch the direction fields and trajectories us- ing the java applet “Pplane” available at http://math.rice.edu/ dfield/dfpp.html. Sec 7.3 due 06/03: 6, 7, 17, 18, 19 • Problems 6, 7: The solutions of these problems are in the notes. Do not turn in these problems. Sec 7.2 cancelled : 1, 22, 24, 26 1 Sec 7.1 due 05/27: 3, 4, 10, 11, 16*, 17, 19 • Problems 17, 19: These are instances where systems of differential equa- tions arise from physical phenomena. Do not turn in these problems....

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