| LEC # | TOPICS | LECTURE NOTES |
|---|---|---|
1 | Review of Linear Algebra | Week 1 Lecture (PDF) |
2 | Review of Linear Algebra (cont.) | |
3 | Review of Linear Algebra (cont.) | |
4 | Differences, Derivatives, and Boundary Conditions | Week 2 Lecture (PDF) |
5 | Inverses and Delta Functions | |
6 | Eigenvalues and Eigenvectors | |
7 | Positive Definite Matrices and Least Squares | Week 3 Lecture (PDF) |
8 | Numerical Linear Algebra: LU, QR, SVD | |
9 | Equilibrium and the Stiffness Matrix | |
10 | Oscillation by Newton’s Law I | Week 4 Lecture (PDF) |
11 | Oscillation by Newton’s Law II | |
12 | Graph Models and Kirchhoff’s Laws | |
13 | Damped Harmonic Oscillators and the Laplace Transform I | Week 5 Lecture (PDF) |
14 | Damped Harmonic Oscillators and the Laplace Transform II | |
15 | Review of Vector Calculus I | |
16 | Review of Vector Calculus II; Fourier Series | Week 6 Lecture (PDF) |
17 | Fourier Series (cont.) | |
18 | Polar Coordinates and Laplace’s Equation | |
19 | Laplace’s Equation and Separation of Variables | Week 7 Lecture (PDF) |
20 | Laplace’s Equation and Finite Difference | |
21 | The Finite Element Method I | |
22 | The Finite Element Method II | Week 8 Lecture (PDF) |
23 | The Discrete Fourier Transform and the FFT I | |
24 | The Discrete Fourier Transform and the FFT II | |
25 | Convolution and Signal Processing | Week 9 Lecture (PDF) |
26 | Fourier Integrals | |
27 | Course Review | |
28 | Guest Lectures:
| Signal Processing and FT Application (PDF - 4.3MB) (Used with permission.) Signal Processing and FT Application (PPTX - 12.5MB) (Used with permission.) Numerical Differentiation and Thunderstorm Research (PDF - 1.4MB) (Used with permission.) Solving Linear Equation Ax = b: Techniques and Examples (PDF) (Used with permission.) Dynamical Systems and Traffic Control (PDF) (Used with permission.) Dynamical Systems and Traffic Control (PPTX - 1.8MB) (Used with permission.) Finite Element Modeling of the Detachment of Soft Adhesives (PDF - 1.4MB) (Used with permission.) Wave Energy Generation (PDF - 2.3MB) (Used with permission.) Wave Energy Generation (PPSX - 3.2MB) (Used with permission.) [For image credit, see Wave Energy Generation (PDF - 2.3MB).] |
29 | Special Topic: Deep Learning/Double Descent by Prof. Gilbert Strang |  Deep Learning/Double Descent (PDF) (Used with permission.) |