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.) 
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Summer
2020
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