| Date | Section | Topics | Homework problems |
| 1/22 | 4.1 |
Definition of the Laplace transform |
1, 3, 5, 7, 13, 24, 31, 35, 37 |
| 1/27 | 4.2 |
The Inverse Transform and Transform of Derivatives |
5, 7, 11, 15, 17, 18, 23, 33, 34, 35, 38 |
| 1/29 | 4.3 |
Translation Theorems |
3, 7, 11, 16, 19, 24, 40, 45, 55, 56 |
| 2/3 | 4.4 |
Additional Operational Properties |
3, 8, 11, 13, 14, 22, 27, 33, 37, 42, 51, 52 |
| 2/10 | 4.5 |
Dirac Delta Function |
1, 3, 8, 10 |
| 4.6 |
Systems of Linear Differential Equations |
1, 3, 5, 7 |
| 2/12 |
7.6 |
Vector spaces |
11, 13, 17, 27, 28 |
| 8.1 | Matrix Algebra |
13, 17, 42 |
| 8.2 |
Systems of Linear Algebraic Equations |
3, 10, 11, 15 |
| 2/19 |
8.3 |
Rank of a Matrix |
4, 7, 9, 13, 15, 17 |
| 8.4 |
Determinants |
15, 19, 21, 24, 27 |
| 2/24 |
8.5 |
Properties of Determinants |
25, 26, 29 |
| 8.6 |
Inverse of a Matrix |
7, 15, 21, 27, 31, 47, 53 |
| 2/26 |
8.7 |
Cramer's Rule |
1, 8 |
| 8.8 |
The Eigenvalue Problem |
3, 5, 13, 14, 21 |
| 3/2 |
Catch up and review |
| 3/4 |
First midterm exam |
| 3/9 |
8.10 |
Orthogonal Matrices |
1, 5, 7, 13, 15, 16 |
| 8.12 |
Diagonalization |
3, 5, 13, 21, 27 |
| 3/11 |
12.1 |
Orthogonal Functions |
1, 3, 5, 9, 11 |
| 12.2 |
Fourier Series |
1, 5, 9, 15, 17 |
| 3/23 |
12.3 |
Fourier Sine and Cosine Series |
3, 5, 8, 13, 20, 23, 29, 36 |
| 12.4 |
Complex Fourier Series |
1, 3, 5, 6 |
| 3/25 |
3.9 |
Linear Models: Boundary-Value Problems |
11, 16 |
| 12.5 |
Sturm-Liouville Problem |
1, 5 |
| 3/27 | 13.1 |
Separable Partial Differential Equations |
3, 9, 15, 17, 21, 23 |
| 4/1 |
13.2 |
Classical PDEs and Boundary-Value Problems |
1, 3, 5, 7, 8, 11 |
| 4/3 | 13.3 |
Heat Equation |
1, 2, 3, 4 |
| 13.4 |
Wave Equation |
1, 3, 5, 8 |
| 4/8 |
13.5 |
Laplace's Equation |
3, 4, 5, 15 |
| 13.6 |
Nonhomogeneous BVPs |
|
| 4/10 |
Catch up and review |
| 4/15 |
Second midterm exam |
| 4/17 |
13.6 |
Nonhomogeneous BVPs |
1, 3, 5, 9, 10, 11 |
| 4/22 |
13.7 |
Orthogonal Series Expansions |
1, 2, 3, 5, 7 |
| 13.8 |
Fourier Series in Two Variables |
1, 3, 5 |
| 4/24 |
14.1 |
Laplace's Equation in Polar Coordinates |
1, 3, 7, 10 |
| 4/29 |
15.3 |
Fourier Integral |
1, 3, 7, 9 |
| 5/1 |
15.4 |
Fourier Transforms |
1, 3, 5, 7, 15 |
| 5/6 |
Review |
| TBA |
Final Exam |