| Ordinary Differential Equations |
| 1 | Numerical Integration of Ordinary Differential Equations: An Introduction | |
| 2 | Convergence and Accuracy | |
| 3 | Convergence of Multi-Step Methods | |
| 4 | Convergence of Multi-Step Methods (cont.) | Homework 1 due |
| 5 | Convergence of Multi-Step Methods (cont.) | Homework 2 due |
| 6 | Systems of ODE's and Eigenvalue Stability | Homework 3 due |
| 7 | Stiffness and Implicit Methods | |
| 8 | Stiffness and Implicit Methods (cont.) | Homework 4 due |
| 9 | Runge-Kutta Methods | |
| Finite Volume/Difference Methods |
| 10 | Finite Volume Method | Homework 5 due |
| 11 | Finite Volume Method (cont.) | Homework 6 due |
| 12 | Finite Volume Method (cont.) | Homework 7 due |
| 13 | Finite Difference Method | Homework 8 due |
| 14 | Finite Difference Method (cont.) | |
| 15 | Finite Difference Method (cont.) | |
| 16 | Matrix Stability Analysis | Project 1 due |
| 17 | Matrix Stability Analysis (cont.) | |
| 18 | Fourier Stability Analysis | |
| 19 | Fourier Stability Analysis (cont.) | |
| 20 | Fourier Stability Analysis (cont.) | |
| Midterm Oral Exam | |
| Finite Element Methods |
| 21 | Method of Weighted Residuals | |
| 22 | Method of Weighted Residuals (cont.) | Homework 9 due |
| 23 | Finite Element Method for 1-D Diffusion | |
| 24 | Finite Element Method for 1-D Diffusion (cont.) | Homework 10 due |
| 25 | Finite Element Method for 1-D Diffusion (cont.) | Homework 11 due |
| 26 | Finite Element Method for 2-D Diffusion | |
| 27 | Finite Element Method for 2-D Diffusion (cont.) | |
| 28 | Finite Element Method for 2-D Diffusion (cont.) | |
| 29 | Higher-order Finite Element Method | |
| 30 | Higher-order Finite Element Method (cont.) | Project 2 due |
| Probabilistic Simulation Techniques |
| 31 | Introduction to Monte Carlo Method | |
| 32 | Introduction to Monte Carlo Method (cont.) | Homework 12 due |
| 33 | Error Estimates for Monte Carlo Method | |
| 34 | Error Estimates for Monte Carlo Method (cont.) | Homework 13 due |
| 35 | Error Estimates for Monte Carlo Method (cont.) | |
| 36 | Latin Hypercube Sampling | |
| 37 | |
| 38 | Bootstrapping | Project 3 due |
| 39 | Wrap Up | |
| Final Oral Exam | |