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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