Lectures | Sections in Text | Brief Description |
---|---|---|
Day 1: | 1.3, 1.1, 1.2, 2.1 |
Classification of differential equations; Direction fields; Linear differential equations |
Day 2: | 2.2 | Separable DEs |
Day 3: | 2.3 | Modeling with 1st order DEs |
Day 4: | 2.4, 2.6 | Linear vs nonlinear equations; Exact equations |
Day 5: | 3.1, 3.2 | Homogeneous equations with constant coefficients: Fundamental solutions |
Day 6: | 3.3, 3.4 | Linear independence and Wronskian; Complex roots |
Day 7: | 3.5 | Repeated roots, 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 |