| Lectures | Sections in Text | Brief Description |
|---|---|---|
| Day 1: | 1.3, 1.1, 1.2 |
Introduction; Classification of differential equations; Direction fields; |
| Day 2: | 2.2, 2.6 | Separable and Exact DEs |
| Day 3: | 2.1, 2.4 | Linear Equations; comparison to non-linear |
| Day 4: | 2.3 | Modeling with 1st order DEs |
| Day 5: | 3.1, 3.4, (3.5) | Homogeneous equations with constant coefficients; Complex and repeated roots |
| Day 6: | 3.2, 3.3 | Fundamental Solutions: Linear independence and Wronskian |
| Day 7: | 3.5 | Reduction of order |
| Day 8: | 3.6, 3.7 | Nonhomogeneous equations, Undetermined coefficients; Variation of parameters |
| Day 9: | 3.8, 3.9 | Mechanical vibrations; Forced vibrations |
| Day 10: | 7.1 | Systems of DEs |
| Day 11: | 7.2, 7.3, 7.4 | Matrices, eigenvalues, eigenvectors etc. |
| Day 12: | 7.5, 7.6 | Systems of DEs: real distinct and complex eigenvalues |
| Day 13: | 7.6, 7.8 | Systems of DEs: complex and repeated real eigenvalues |
| Day 14: | 2.5, 9.1 |
Critical points of autonomous 1st order DEs; Phase portraits of linear systems |
| Day 15: | 9.2 | Autonomous systems and stability |
| Day 16: | 9.3 | Almost linear systems |
| Day 17: | 5.1 | Review of series |
| Day 18: | 5.2 | Series solutions, I |
| Day 19: | 5.3 | Series solutions, II |
| Day 20: | 10.2 | Fourier series |
| Day 21: | 10.3 | Fourier convergence theorem |
| Day 22: | 10.4 | Fourier series: even and odd extensions |
| Day 23: | 10.5 | Heat equation; Separation of variables |
| Day 24: | 10.6 | Other heat equations: nonhomogeneous + insulated ends |
| Day 25: | 10.7 | Wave equation |
| Day 26: | 10.7, 10.8 | Wave equation; Laplace equation |
| Day 27: | 10.8 | Laplace equation |
| Day 28: | :o) | Review |