| Session Date |
Section | Topics (Quiz on previous two lectures) |
Homework problems (* = hand in for grading) |
Date due |
|---|---|---|---|---|
| #1
9/03 |
4.1 | Definition of the Laplace transform | 1, 3, 5, 7*, 13, 23*, 25, 29, 31, 35, 37, 39, 41 | 9/14 |
| #2
9/07 |
4.2.1 | Inverse Laplace Transform | 7, 8*, 11, 15, 17, 18*, 23 | 9/14 |
| 4.2.2 | Laplace Transform of Derivatives
Linear Differential Equations |
31, 32*, 35, 38* | 9/14 | |
| #3
9/10 |
4.3 | Translation Theorems
Unit Step Function (Heaviside Function) (Quiz) |
3, 7, 9, 11, 15, 19*, 24*, 40*, 41, 45, 47, 49-54, 55, 63*, 67 | 9/14 |
| #4
9/14 |
4.4.1 | Derivatives of Transforms | 3, 7, 8*, 11*, 13, 14* | 9/21 |
| 4.4.2 | Transforms of Integrals; Convolution
Volterra Integral Equation |
19, 22, 25, 27*, 33, 37*, 39* | 9/21 | |
| #5
9/17 |
4.4.3 | Transforms of a Periodic Function | 49*, 51*, 52 | 9/21 |
| 4.5 | Dirac Delta Function
Impulse Response Function (Quiz) |
1, 2*, 3, 5, 9* | 9/21 | |
| #6
9/21 |
4.6 | Systems of Linear Differential Equations | 1, 2*, 7, 9*, 11* | 9/28 |
| #7
9/24 |
7.6 | Vector Spaces | 11, 13, 17, 27*, 28* | 9/28 |
| 8.1 | Matrix Algebra | 15, 17, 19*, 23*, 29, 35, 37, 39 | 9/28 | |
| 8.2 | Systems of Linear Algebraic Equations (Quiz) | 5, 9*, 11, 15*, 17* | 9/28 | |
| #8
9/28 |
8.3 | Rank of a Matrix | 1, 5, 7*, 13*, 15, 17 | 10/05 |
| 8.4 | Determinants | 15, 19, 21, 25*, 27, 29 | 10/05 | |
| 8.5 | Properties of Determinants | 1, 3, 5, 7, 9, 11, 13*, 15, 21, 23*, 31, 33* | 10/05 | |
| #9
10/01 |
8.6 | Inverse of a Matrix | 5, 7*, 19, 23*, 27, 31, 43, 51*, 53 | 10/05 |
| 8.7 | Cramer's Rule (Quiz) | 1, 9, 11* | 10/05 | |
| #10
10/05 |
8.8 | Eigenvalue Problem | 3, 5, 13*, 15*, 21* | 10/12 |
| #11
10/08 |
8.10 | Orthogonal Matrices | 1*, 5, 7, 13, 15* | 10/12 |
| 8.12 | Diagonalization of Matrices (Quiz) | 3*, 5*, 13*, 21, 25, 27, 37*, 38, 39* | 10/12 | |
| #12
10/12 |
Catch up and review | |||
| #13
10/15 |
First midterm exam on Chapter 4 and Chapter 8 (sections 1-8, 10, and 12)
(closed book - Laplace transform formula page provided) |
|||
| #14
10/19 |
12.1 | Orthogonal Sets of Functions | 1, 3*, 5*, 7, 8*, 9, 12, 15, 16, 17, 18*, 21 | 10/26 |
| 12.2 | Fourier Series | 1*, 2, 3*, 5*, 7, 9* | 10/26 | |
| #15
10/22 |
12.2 | Convergence of Fourier Series (Quiz) | 11, 13, 17*, 19, 20*, 21 | 10/26 |
| #16
10/26 |
12.3 | Fourier Sine and Cosine Series
Half range expansions |
1, 3, 5, 7, 13*, 14*, 19, 25*, 27, 29*, 41* | 11/02 |
| 12.4 | Complex Fourier Series | 1*, 3*, 5*, 11, 12 | 11/02 | |
| #17
10/29 |
3.9 | Example 2: Boundary Value Problems (BVP) | 9, 11* | 11/02 |
| 12.5 | Regular Sturm-Liouville Problems (Quiz) | 1*, 5 | 11/02 | |
| #18
11/02 |
13.1 | Separable Partial Differential Equations | 1*, 3*, 9* | 11/09 |
| #19
11/05 | 13.2 | Heat Equation and BVP | 1, 3*, 5*, 9* | 11/09 |
| 13.3 | Solution to BVP for Heat Equation (Quiz) | 1*, 2*, 3*, 4* | 11/09 | |
| #20
11/09 |
13.2 | Wave Equation and BVP | 7, 8 | |
| 13.4 | Solution to BVP for Wave Equation | 1*, 2*, 5*, 8*, 11* | 11/16 | |
| #21
11/12 |
13.2 | Laplace Equation and BVP | 11 | |
| 13.5 | Solution to Laplace's Equation in a Rectangle (Quiz) | 1*, 3, 4* | 11/16 | |
| #22
11/16 |
13.5 | Dirichlet problem for Laplace's Equation in a Rectangle | 5*, 7*, 15* | 11/30 |
| #23
11/19 |
Second midterm exam on Chapter 12 (sections 1-5)
and Chapter 13 (sections 1-5)
(closed book - formula page provided) |
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| #24
11/23 |
13.6 | Nonhomogeneous BVP | 1*, 5* | 11/30 |
| #25
11/30 |
13.7 | Orthogonal Series Expansions for BVP | 1*, 5* | 12/07 |
| #26
12/03 |
13.8 | Fourier Series in Two Variables (Quiz) | 1*, 3*, 5* | 12/07 |
| #27
12/07 |
14.1 | Laplace's Equation in Polar Coordinates
Steady Temperatures in Circular Plates |
1*, 3*, 7* | 12/10 |
| #28
12/10 |
Catch up and review | |||
| 12/16 | 12:00 - 3:00 pm (room TBA) Final exam (closed book - formula page provided) | |||
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