Lecture Notes

This table compiles all the lecture notes available for the course. These notes correspond to the lecture videos. Notes are not available for lectures 1, 13 and 25, and videos are not available for lectures 9, 13–14, 17–20, and 22.

LEC # TOPICS
Unit 1: Numerical Integration of ODEs
1 Course Introduction and Ordinary Differential Equations (ODEs) (notes not available)
2 This resource may not render correctly in a screen reader.Numerical Integration of ODEs: Approximating Time Derivative (PDF - 1.8MB)
3 This resource may not render correctly in a screen reader.Numerical Integration of ODEs: Accuracy and a Pendulum Problem (PDF - 1.4MB)
4 This resource may not render correctly in a screen reader.Numerical Integration of ODEs: Stability and a Ballistics Problem (PDF)
5 This resource may not render correctly in a screen reader.Numerical Integration of ODEs: Nonlinear Systems (PDF)
6 This resource may not render correctly in a screen reader.Numerical Integration of ODEs: Stiffness, Implicit Methods, Runge-Kutta (PDF - 1.3MB)
Unit 2: Numerical Methods for PDEs
7 This resource may not render correctly in a screen reader.Numerical Methods of Partial Differential Equations: Introduction (PDF - 1.1MB)
8 This resource may not render correctly in a screen reader.Numerical Methods of PDEs: Finite Difference Methods 1 (PDF - 1.3MB)
9 This resource may not render correctly in a screen reader.Numerical Methods of PDEs: Finite Difference Methods 2 (PDF - 1.2MB)
10 This resource may not render correctly in a screen reader.Numerical Methods of PDEs: Finite Volume Methods 1 (PDF - 1.5MB)
11 This resource may not render correctly in a screen reader.Numerical Methods of PDEs: Finite Volume Methods 2 (PDF)
12 This resource may not render correctly in a screen reader.Numerical Methods of PDEs: Finite Volume in 2D and Midterm Review (PDF - 1.8MB)
  Midterm Exam
13 Numerical Methods of PDEs: Matrix Stability Analysis (notes not available)
14 This resource may not render correctly in a screen reader.Fourier Stability Analysis (PDF - 1.3MB)
15 This resource may not render correctly in a screen reader.Numerical Methods of PDEs: Collocation and Weighted Residuals (PDF - 1.1MB)
16-18 This resource may not render correctly in a screen reader.Numerical Methods of PDEs: Finite Element Method (PDF - 1.3MB)
Unit 3: Probabilistic Methods and Optimization
19 This resource may not render correctly in a screen reader.Monte Carlo (PDF - 1.3MB)
20 This resource may not render correctly in a screen reader.Monte Carlo Estimators (PDF - 1.1MB)
21 This resource may not render correctly in a screen reader.Probabilistic Methods & Optimization: Statistical Sampling Methods (PDF - 1.5MB)
22 Probabilistic Methods & Optimization: Design of Experiments (PDF)
23 Probabilistic Methods & Optimization: Intro to Optimization Methods (PDF)
24 Probabilistic Methods & Optimization: Sensitivity Analysis (PDF)
25 Probabilistic Methods & Optimization: Final Exam Review (notes not available)