Differential Equations

Please check the course syllabus each week for any updates.

Please read my list of expectations for the course.

Homework Assignments:

1. "Phase portraits for linear systems". Due Friday, May 22.
2. Equilibria for nonlinear systems. Use the linearization to determine the stability of an equilibrium point and the geometry of nearby solutions. Due Friday, May 29.

Lecture notes:

1. Wed., May 5: finding the JCF and e^tA when eigenvalues are complex, plus a surprise
2. Fri., May 8: phase portraits when eigenvalues are complex
3. Mon., May 11: solutions for mechanical systems
4. Wed., May 13: solutions and phase portraits when an eigenvalue is defective
5. Fri., May 15: when zero is an eigenvalue, solving the system z' = Az + F(t)
6. Mon., May 18: Stability and the phase plane
7. Wed., May 20: geometry and stability for nonlinear systems (didn't get to all of this; will cover it on Tuesday, May 26)
8. Fri., May 22: linearization, eigenvalue game
9. Tues., May 26: stability and geometry in nonlinear systems
10. Fri., May 29: Introduction to Laplace transforms
11. Mon., June 1: section 7.2 of the text
12. Wed., June 3: shifting and step functions
13. Fri., June 5: review of approaches for nonlinear systems