| Date | Section | Topics | Homework problems |
|---|---|---|---|
| 9/1 | 4.1 | Definition of the Laplace transform | 1, 5, 7, 13, 23, 35 |
| 9/6 | 4.2 | The Inverse Transform and Transform of Derivatives | 7, 11, 23, 31, 35, 39 |
| 9/8 | 4.3 | Translation Theorems | 3, 7, 9, 11, 15, 19, 37, 41, 45, 47, 49-54, 67 |
| 9/13 | 4.4 | Additional Operational Properties | 3, 7, 11, 13, 19a, 27, 33, 37, 39 |
| 9/15 | 4.5 | Dirac Delta Function | 1, 3, 9 |
| 9/20 | 4.6 | Solving Systems of Linear Equations | 1, 7, 9, 11 |
| 9/22 | 7.6 | Vector spaces | |
| 8.1 | Matrix Algebra | 17, 23, 29, 35, 37 | |
| 9/27 | 8.2 | Systems of Linear Algebraic Equations | 5, 9, 11, 27 |
| 9/29 | 8.3 | Rank of a Matrix | 9, 13, 15, 17, 19 |
| 10/4 | 8.4 | Determinants | 19, 21, 25, 27 |
| 8.5 | Properties of Determinants | 5, 11, 13, 23, 31, 33 | |
| 10/6 | 8.6 | Inverse of a Matrix | 7, 25, 27, 31, 51, 53 |
| 8.7 | Cramer's Rule | 1, 9 | |
| 10/11 | Catch up and review | ||
| 10/13 | First midterm exam | ||
| 10/18 | 8.8 | The Eigenvalue Problem | 5, 13, 19 |
| 8.10 | Orthogonal Matrices | 7, 13, 15 | |
| 10/20 | 8.12 | Diagonalization | 5, 13, 15, 23 |
| 10/25 | 3.9 | Linear Models: Boundary-Value Problems | 11, 15 |
| 12.1 | Orthogonal Functions | 3, 7, 17 | |
| 10/27 | 12.2 | Fourier Series | 1, 5, 9, 15, 17, 21 Problem 21 is Parseval's Formula |
| 11/1 | 12.3 | Fourier Sine and Cosine Series | 3, 5, 7, 13, 19, 23, 29, 35 |
| 11/3 | 12.4 | Complex Fourier Series and Frequency Spectrum | 5 |
| 12.5 | Sturm-Liouville Problem | 1 | |
| 11/8 | 13.1 | Separable Partial Differential Equations | 3, 11, 15 |
| 11/10 | 13.2 | Classical Equations and Boundary-Value Problems | 1, 3, 5, 9 |
| 11/15 | Catch up and review | ||
| 11/17 | Second midterm exam | ||
| 11/29 | 13.3 | Heat Equation | 1, 3, 4 |
| 13.4 | Wave Equation | 1, 3, 5, 14, 15, 18
Problem 14 gives d'Alembert's solution to the wave equation. |
|
| 12/1 | 13.5 | Laplace's Equation | 5, 7, 15 |
| 13.8 | Fourier Series in Two Variables | 1, 3 | |
| 12/6 | 14.1 | Laplace's Equation in Polar Coordinates | 1, 3, 7 |
| 12/8 | 15.2 | Applications of the Laplace Transform | 5, 9 |
| 12/13 | Review | ||