| LEC # | TOPICS | KEY DATES |
|---|---|---|
| Unit 1: Numerical Integration of ODEs | ||
| 1 | Course Introduction and Ordinary Differential Equations (ODEs) | Read Unit 1: Numerical Integration of ODEs |
| 2 | Numerical Integration of ODEs: Approximating Time Derivative | |
| 3 | Numerical Integration of ODEs: Accuracy and a Pendulum Problem | |
| 4 | Numerical Integration of ODEs: Stability and a Ballistics Problem | Homework 1 due |
| 5 | Numerical Integration of ODEs: Nonlinear Systems | |
| 6 | Numerical Integration of ODEs: Stiffness, Implicit Methods, Runge-Kutta | Homework 2 due |
| Unit 2: Numerical Methods for PDEs | ||
| 7 | Numerical Methods of Partial Differential Equations: Introduction | Read Unit 2: Numerical Methods for PDEs |
| 8 | Numerical Methods of PDEs: Finite Difference Methods 1 | Homework 3 due |
| 9 | Numerical Methods of PDEs: Finite Difference Methods 2 | Project 1 due |
| 10 | Numerical Methods of PDEs: Finite Volume Methods 1 | Homework 4 due |
| 11 | Numerical Methods of PDEs: Finite Volume Methods 2 | |
| 12 | Numerical Methods of PDEs: Finite Volume in 2D and Midterm Review | Homework 5 due |
| Midterm Exam | Exam | |
| 13 | Numerical Methods of PDEs: Matrix Stability Analysis | |
| 14 | Fourier Stability Analysis | |
| 15 | Numerical Methods of PDEs: Collocation and Weighted Residuals | Homework 6 due |
| 16 | Numerical Methods of PDEs: Finite Element Method 1 | |
| 17 | Numerical Methods of PDEs: Finite Element Method 2 | Homework 7 due |
| 18 | Numerical Methods of PDEs: Finite Element Method 3 | |
| Unit 3: Probabilistic Methods and Optimization | ||
| 19 | Monte Carlo |
Read Unit 3: Probabilistic Methods and Optimization Project 2 due |
| 20 | Monte Carlo Estimators | Homework 8 due |
| 21 | Probabilistic Methods & Optimization: Statistical Sampling Methods | |
| 22 | Probabilistic Methods & Optimization: Design of Experiments | Homework 9 due |
| 23 | Probabilistic Methods & Optimization: Intro to Optimization Methods | Project 3 due |
| 24 | Probabilistic Methods & Optimization: Sensitivity Analysis | |
| 25 | Probabilistic Methods & Optimization: Final Exam Review | |
| Final Exam | Exam | |