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Unformatted text preview: 18.03 Problem Set 10 Spring 2009 Due in Room 2-106 at 12:55 pm, Friday, May 8 Part A (10 points) 1. (Lec 34 Fri May 1) Complex eigenvalues and repeated eigenvalues. Read: LS.3, LS.4, rest of EP 5.4, 5.6 to middle of p. 398. Work: 4D-1, 2, 3. 2. (Lec 35, Mon May 4) Exponential matrix Read: LS 6; EP 5.7; Work: 4G-1, 2b; 4H-2, 7 3. (Lec 36, Wed May 6) Inhomogeneous equations; variation of parameters Read: LS 5–6; EP 5.8 Work: 4F-1; 4I-2a Carry out 4I-2a as follows: i) Given a matrix fundamental solution F = F ( t ) satisfying F = AF for the con- stant coefficient matrix A , derive the equation satisfied by v = v ( t ) if x = F v satisfies x ( t ) = A x ( t ) + b ( t ), expressed in symbols using F- 1 . (This is the method of variation of parameters.) ii) Use the fundamental solution F = e- 3 t e 2 t- 4 e- 3 t e 2 t to find the equation for v in explicit form; solve for v and subsequently for x . 4. (Lecture 37 Fri May 8) Nonlinear systems. Read: EP 7.2, 7.3 5. (Lecture 38 Mon May 11) Examples of nonlinear systems. Read: EP 7.4, 7.5 Part B (38 points) 0. (at due date) Write the names of any person, web site, or materials you consulted....
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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