Textbook: "Ordinary Differential Equations" by M. Tenenbaum and H. Pollard (available at Amazon.com)
Supplementary textbook: "Ordinary Differential Equations and Dynamical Systems" by G. Teschl (available for free from the author's webpage)
Grading: 50% final exam, 2x20% midterm exams, 10% quizzes (given almost every Friday). The textbooks contain many examples, and the exams/quizzes will be based on those examples.
Tentative syllabus:
| Week | Topics |
|---|---|
| Week 1, Jan 13—17 | Separable equations, first order equations with homogeneous coefficients, equations with linear coefficients, exact equations (L6—L9) |
| Week 2, Jan 22—24 | Linear equations of the first order, homogeneous equations of higher order with constant coefficients (L11, L20) |
| Week 3, Jan 27—31 | Nonhomogeneous equations of higher order with constant coefficients (L21) |
| Week 4, Feb 3—7 | Variation of parameters, reduction of order, series solutions of linear equations (L22—L23, L37) |
| Week 5, Feb 10—14 | Singular points, solution about a regular singular point (L40) |
| Week 6, Feb 17—21 | Review and first midterm |
| Week 7, Feb 24—28 | Boundary value problems, Sturm-Liouville problem (T) |
| Week 8, Mar 3—7 | Systems of linear equations (L31), fundamental matrices |
| Week 9, Mar 10—14 | Matrix exponential, T-ordered exponential, Floquet theory (T) |
| Week 10, Mar 17—21 | Linearization of first order systems (L32), fixed points and stability (T) |
| Week 11, Mar 31 — Apr 4 | Review and second midterm |
| Week 12, Apr 7—11 | Nonlinear stability, Liapunov function, conservative fields (T) |
| Week 13, Apr 14—18 | Picard iterations, contraction mappings (L57) |
| Week 14, Apr 21—25 | Existence and uniqueness (L58) |
| Week 15, Apr 28 — May 2 | Overview and preparation for the final exam |