Computational Science and Engineering I

Lecture Notes

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: María Cristina Márquez Colás: Signal Processing and FT Application Monika Feldmann: Numerical Differentiation and Thunderstorm Research Sungwoo Jeong: Solving Linear Equation \(Ax=b\): Techniques and Examples Claudio Lombardi: Dynamical Systems and Traffic Control Evelyne Ringoot: Finite Element Modeling of the Detachment of Soft Adhesives Jorge Manuel Marques Silva: Wave Energy Generation	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.)