Syllabus and homework problems for Math 421
| Date | Section | Topics | Homework problems | |
|---|---|---|---|---|
| 9/2 | 4.1 | Definition of the Laplace transform | 1, 3, 5, 7, 13, 24, 31, 35, 37 | |
| 9/8 | 4.2 | The Inverse Transform and Transform of Derivatives | 5, 7, 11, 15, 17, 18, 23, 33, 34, 35, 38 | |
| 9/9 | 4.3 | Translation Theorems | 3, 7, 11, 16, 19, 24, 40, 45, 55, 56 | |
| 9/14 | 4.4 | Additional Operational Properties | 3, 8, 11, 13, 14, 22, 27, 33, 37, 42, 51, 52 | |
| 9/16 | 4.5 | Dirac Delta Function | 1, 3, 8, 10 | |
| 4.6 | Systems of Linear Differential Equations | 1, 3, 5, 7 | ||
| 9/21 | 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 | ||
| 9/23 | 8.3 | Rank of a Matrix | 4, 7, 9, 13, 15, 17 | |
| 8.4 | Determinants | 15, 19, 21, 24, 27 | ||
| 9/28 | 8.5 | Properties of Determinants | 25, 26, 29 | |
| 8.6 | Inverse of a Matrix | 7, 15, 21, 27, 31, 47, 53 | ||
| 9/30 | 8.7 | Cramer's Rule | 1, 8 | |
| 8.8 | The Eigenvalue Problem | 3, 5, 13, 14, 21 | ||
| 10/5 | 8.10 | Orthogonal Matrices | 1, 5, 7, 13, 15, 16 | |
| 8.12 | Diagonalization | 3, 5, 13, 21, 27 | ||
| 10/7 | Catch up and review | |||
| 10/12 | First midterm exam | |||
| 10/14 | 12.1 | Orthogonal Functions | 1, 3, 5, 9, 11 | |
| 12.2 | Fourier Series | 1, 5, 9, 15, 17 | ||
| 10/19 | 12.3 | Fourier Sine and Cosine Series | 3, 5, 8, 13, 20, 23, 29, 36 | |
| 12.4 | Complex Fourier Series | 1, 3, 5, 6 | ||
| 10/21 | 3.9 | Linear Models: Boundary-Value Problems | 11, 16 | |
| 12.5 | Sturm-Liouville Problem | 1, 5 | ||
| 10/26 | 13.1 | Separable Partial Differential Equations | 3, 9, 15, 17, 21, 23 | |
| 10/28 | 13.2 | Classical PDEs and Boundary-Value Problems | 1, 3, 5, 7, 8, 11 | |
| 11/2 | 13.3 | Heat Equation | 1, 2, 3, 4 | |
| 13.4 | Wave Equation | 1, 3, 5, 8 | ||
| 11/4 | 13.5 | Laplace's Equation | 3, 4, 5, 15 | |
| 13.6 | Nonhomogeneous BVPs | |||
| 11/9 | 13.6 | Nonhomogeneous BVPs | 1, 3, 5, 9, 10, 11 | |
| 11/11 | Catch up and review | |||
| 11/16 | Second midterm exam | |||
| 11/18 | 13.7 | Orthogonal Series Expansions | 1, 2, 3, 5, 7 | |
| 13.8 | Fourier Series in Two Variables | 1, 3, 5 | ||
| 11/23 | 14.1 | Laplace's Equation in Polar Coordinates | 1, 3, 7, 10 | |
| 11/30 | 15.3 | Fourier Integral | 1, 3, 7, 9 | |
| 12/2 | 15.4 | Fourier Transforms | 1, 3, 5, 7, 15 | |
| 12/7 | Applications of the Fourier Transform | |||
| 12/9 | Review | |||
| 12/18 | Final Exam | |||