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