| LEC # | TOPICS | READINGS |
|---|---|---|
| 1 | Introduction, definitions and modeling | (BR) 1.1-1.2 (SN) 0-3 |
| 2 | First-order linear equations, separable equations | (BR) 1.3-1.4 |
| 3 | First-order equations, Solution by quadrature | (BR) 1.5-1.7 (Notes) QD (PDF) |
| 4 | The initial value problem, uniqueness; the algebra of complex numbers | (BR) 1.9-1.10 (SN) 5 |
| 5 | Second-order linear equations | (BR) 2.1-2.2 |
| 6 | Undetermined coefficients | (SN) 11 |
| 7 | Stability criteria, the uniqueness theorem | (BR) 2.3-2.4 |
| 8 | The Wronskian, sturm separation and comparison theorems | (BR) 2.5-2.6 |
| 9 | Green's function I: Initial value problem | (BR) 2.9 |
| 10 | Green's function II: Boundary value problem | (BR) 2.10-2.11 |
| 11 | nth-order linear DEs with constant coefficients | (BR) 3.1-3.3 |
| 12 | Basis of solutions, the uniqueness theorem | (BR) 3.1-3.3 |
| 13 | Inhomogeneous equations, stability criteria | (BR) 3.5-3.6 |
| 14 | Laplace transform: Basic properties | (Notes) LT1 (PDF) |
| 15 | Laplace transform techniques; step functions | (SN) 20 (Notes) LT1 (PDF) |
| 16 | The Dirac delta and impulse functions, convolution | (SN) 17-19 (Notes) LT2 (PDF) |
| 17 | Generalized functions, the pole diagram | (SN) 21-23 (Notes) LT2 (PDF) |
| 18 | Plane autonomous systems | (BR) 5.1-5.4 (Notes) AS (PDF) |
| 19 | Linear autonomous systems | (BR) 5.4-5.5 |
| 20 | Wellposedness I | (BR) 6.1-2 and 6.5 |
| 21 | Wellposedness II: Picard's iteration method | (BR) 6.2 and 6.7-6.8 |
| 22 | Wellposedness III: Local theorems, Peano's existence theorem | (BR) 5.3, 5.9, and 5.10 |
| 23 | Wellposedness IV: Strong continuity, bifurcation; exponential matrix | (BR) 5.4 (BR) Appendix A (Notes) EX (PDF) |
| 24 | Phase portraits I | (BR) 2.7, 3.3, and 5.5 (SN) 24-25 |
| 25 | Phase portraits II | (BR) 2.7, 3.3, and 5.5 (SN) 24-25 |
| 26 | Stability | (BR) 5.7 |
| 27 | Methods of Lyapunov | (BR) 5.8 (Notes) LY (PDF) |
| 28 | Damped and undamped pendulum | (BR) 5.9 and 5.11 |
| 29 | Limit cycles | (BR) 5.12 (Notes) LC (PDF) |
| 30 | Fourier series | (BR) 11.1 (Notes) FS (PDF) |
| 31 | The heat equation | (Notes) BV (PDF) |
| 32 | The wave equation, the Laplace equation | (Notes) BV (PDF) |
| 33 | Sturm-Liouville systems | (BR) 10.1-10.2 and 10.5-10.8 |
| 34-37 | Reviews | Handouts |
Table of Contents
Study Materials
Readings
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Key to reading assignments:
(BR) are section numbers of Birkhoff, Garret, and Gian-Carlo Rota. Ordinary Differential Equations. 4th ed. New York, NY: Wiley, 1989. ISBN: 9780471860037.
(SN) are chapter numbers of 18.03 Supplementary Notes by Prof. Haynes Miller.
(Notes) refers to the PDFs in the lecture notes section.