Calendar
This course is divided into four main sections, as shown below. The lecture topics for each section are also provided.
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LEC # |
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SECTIONS |
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TOPICS |
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1-11 |
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Integration of Systems of Ordinary Differential Equations |
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Multi-step (Explicit and Implicit) and Multi-stage (i.e. Runge-Kutta) Integration for Scalar and Systems of ODE's
Analysis of Stability and Accuracy
Solution of Nonlinear Equations |
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12-20 |
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Finite Difference Methods for Partial Differential Equations |
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Finite Difference Approximations of Derivatives
Stability and Accuracy of Finite Difference Schemes
Explicit vs. Implicit Time Discretizations
Thomas Algorithm for Solution of Tri-diagonal Matrices |
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21-29 |
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Finite Element Methods for Partial Differential Equations |
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Galerkin Finite Element Methods
Essential and Natural Boundary Conditions
Accuracy
Gaussian Quadrature |
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30-37 |
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Probabilistic Simulation Techniques |
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Monte Carlo Methods
Response Surface Methods
Moment Methods |
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