Lecture Log for Math 285
| Date | Topics covered | Reference | Date | Topics covered | Reference | Date | Topics covered | Reference | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1/19 | NO CLASS | 1/21 | Introduction Solving DE's by integration |
1.1, 1.2 | 1/23 | separable equations | 1.4 | |||||
| 1/26 | First IODE lab | Lab 1 | 1/28 | Vector Fields Existence and Uniqueness Theorem |
1.3 handout |
1/30 | finish separable equations first-order linear equations |
1.4, 1.5 | ||||
| 2/2 | finish linear equations | 1.5 handout |
2/4 | substitution methods | 1.6 | 2/6 | autonomous equations, phaseline qualitative methods |
2.1, 2.2 | ||||
| 2/9 | Second IODE lab | Lab 2 | 2/11 | Euler's method | 2.4 | 2/13 | introduction to higher-order equations | 3.1 | ||||
| 2/16 | constant-coefficient equations (2nd order) | 3.1 | 2/18 | existence/uniqueness for linear equations the Wronskian test |
3.1 | 2/20 | higher order equations | 3.2 handout |
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| 2/23 | constant-coefficient equations (arbitrary order) differential operators |
3.3 | 2/25 | review for exam I | study guide for exam I |
2/27 | Midterm Exam I | |||||
| 3/1 | mechanical oscillations | 3.4 | 3/3 | mechanical oscillations (continued) |
3.4 | 3/5 | forced (nonhomogeneous) equations method of undetermined coefficients |
3.5 | ||||
| 3/8 | forced (nonhomogeneous) equations method of undetermined coefficients (continued) |
3.5 | 3/10 | forced (nonhomogeneous) equations method of variation of parameters mechanical oscillations |
3.5, 3.6 | 3/12 | mechanical oscillations (continued) |
3.6 | ||||
| 3/15 | boundary value problems eigenvalues and eigenfunctions |
3.8 | 3/17 | periodicity of functions | 9.1 | 3/19 | introduction to Fourier series | 9.1 | ||||
| 3/29 | Fourier series for 2 pi -periodic functions | 9.1 study guide for exam II |
3/31 | Fourier series for arbitrary periodic functions | 9.2 | 4/2 | Fourier series (continued) | 9.2 handout | ||||
| 4/5 | sine and cosine Fourier series even and odd extensions solving constant coefficient equations via Fourier series |
9.3 | 4/7 | Midterm Exam II | 4/9 | solving constant coefficient equations via Fourier series | 9.3, 9.4 | |||||
| 4/12 | solving constant coefficient equations via Fourier series
applications to oscillation problems |
9.4 | 4/14 | heat equation | 9.5 | 4/16 | heat equation (continued) | 9.5 | ||||
| 4/19 | heat equation (continued) | 9.5 | 4/21 | wave equation | 9.6 | 4/23 | wave equation (continued) | 9.6 | ||||
| 4/26 | wave equation (continued) | 9.6 | 4/28 | Laplace's equation | 9.7 | 4/30 | Laplace's equation (continued) | 9.7 | ||||
| 5/3 | Laplace's equation (continued) | 9.7 | 5/5 | review for the final exam | study guide for the final exam review problems |
5/7 | NO CLASS |