# 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.

Lecture notes files.
LEC # | TOPICS
--- | ---
Unit 1: Numerical Integration of ODEs
1 | Course Introduction and Ordinary Differential Equations (ODEs) (notes not available)
2 | Numerical Integration of ODEs: Approximating Time Derivative (PDF - 1.8MB)
3 | Numerical Integration of ODEs: Accuracy and a Pendulum Problem (PDF - 1.4MB)
4 | Numerical Integration of ODEs: Stability and a Ballistics Problem (PDF)
5 | Numerical Integration of ODEs: Nonlinear Systems (PDF)
6 | Numerical Integration of ODEs: Stiffness, Implicit Methods, Runge-Kutta (PDF - 1.3MB)
Unit 2: Numerical Methods for PDEs
7 | Numerical Methods of Partial Differential Equations: Introduction (PDF - 1.1MB)
8 | Numerical Methods of PDEs: Finite Difference Methods 1 (PDF - 1.3MB)
9 | Numerical Methods of PDEs: Finite Difference Methods 2 (PDF - 1.2MB)
10 | Numerical Methods of PDEs: Finite Volume Methods 1 (PDF - 1.5MB)
11 | Numerical Methods of PDEs: Finite Volume Methods 2 (PDF)
12 | 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 | Fourier Stability Analysis (PDF - 1.3MB)
15 | Numerical Methods of PDEs: Collocation and Weighted Residuals (PDF - 1.1MB)
16-18 | Numerical Methods of PDEs: Finite Element Method (PDF - 1.3MB)
Unit 3: Probabilistic Methods and Optimization
19 | Monte Carlo (PDF - 1.3MB)
20 | Monte Carlo Estimators (PDF - 1.1MB)
21 | 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)