Math 111.01/02 (Applied Mathematical Analysis I)

Fall 1998

Plan for Week 10

This week we apply our study of matrices and linear algebraic equations to solutions of systems of differential equations.

We write a first-order homogeneous system of linear differential equations in the form X' = AX, where X is a vector of unknown functions, and A is the matrix of coefficients. For now, we assume the entries of A are constants. We saw in Week 9 that the key to finding a fundamental set of solutions is to first find the eigenvalues and eigenvectors for A. Now that we know how to do that, we can complete our study of linear systems of first-order ordinary differential equations. Taking our clues from our study of single second-order equations in Chapter 3, we determine the solutions of systems, first with distinct real eigenvalues, then with complex eigenvalues, and finally with repeated real eigenvalues.

In lab we explore most of the possible trajectories in the phase planes of 2-dimensional systems.

Here is the syllabus for Week 10:

Week 10 Date Topic Reading Activity
M 11/2 Systems of linear DEs 7.4-7.5
W 11/4 Complex roots,
repeated roots		 7.6-7.7
F 11/6 Trajectories Lab: Trajectories of
Linear Systems

Notes

  1. Your next homework papers will be turned in on Monday, November 9. Those papers should include solutions to all problems in the assignment below. The assignment dates are start dates.
  2. In general, no homework problem will be given full credit unless you have written an explanation of why you know it is correct.
  3. You may want to refer to this week's homework problems while working on next week's take-home test. Make a copy of your homework paper before you turn it in on Monday.
  4. Submit your Week 10 lab report (the Maple file) via e-mail by the end of the day Wednesday, November 11.
  5. Remember to submit your e-mail journal entry on Friday, November 6.

Assignments

David A. Smith <das@math.duke.edu>

Last modified: October 27, 1998