springps10

# springps10 - 18.03 Problem Set 10 Spring 2009 Due in Room...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

## 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.

### Page1 / 2

springps10 - 18.03 Problem Set 10 Spring 2009 Due in Room...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online