01, Jan. 06. |
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First class (CANCELLED)
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02, Jan. 13. |
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Newtons' method for system of nonlinear equations |
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Secant method and unconstrained minimization
HW1 |
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03, Jan. 20. |
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ODE background, Euler method
HW2 |
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TR, midpoint, and theta method. |
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04, Jan. 27. |
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Taylor method and numerical integration
HW3
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Explicit Runge-Kutta method |
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05, Feb. 03. |
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Explicit, Implicit Runge-Kutta, collocation method
HW4
Quiz 1 |
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Collocation method, Multistep method, accuracy |
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06, Feb. 10. |
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Multistep method, convergence and BDF method
HW5 |
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Stability and linear stability domain |
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07, Feb. 17. |
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A-stability, and stability of RK method
HW6 |
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Stability of RK, multi-step methods
Programming assignment 1 |
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08, Feb. 24. |
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No Class |
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No Class |
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09, Mar. 03. |
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Stability of multi-step method
Quiz 2
HW7 |
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PDE and finite difference operator |
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10, Mar. 10. |
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Finite different methods for 1D Poisson equation
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Midterm |
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11, Mar. 17. |
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Finite difference methods for 2D Poisson equation
HW8 |
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Finite element methods for the Poisson equation |
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12, Mar. 24. |
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Spring break |
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Spring break |
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13, Mar. 31. |
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Finite element methods for the Poisson equation: weak formulation
HW9 |
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Finite element methods for the Poisson equation: space,
finite difference methods for the heat equation: A simple example |
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14, Apr. 07. |
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Finite difference methods for the heat equation: method of line, stability
HW10
Solution to problem 3 |
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Finite difference methods for the heat equation: stability
Programming assignment 2 |
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15, Apr. 14. |
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Finite difference methods for the heat equation: multi-dimensional case
HW11 Quiz 3 |
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Finite difference methods for the advection equation: method of line and some examples
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16, Apr. 21. |
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Finite difference methods for the advection equation: stability
HW12 |
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Last class
Finite difference methods for the advection equation: CFL condition, system
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17, Apr. 28. |
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18, May. 05. |
Final exam
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