| April 5 |
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Matlab Environment
page. |
| Introduction to Matlab.
See the links in the Resources section below. |
| Euler's method for numerical solutions of
ordinary differential equations. |
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| April 12 |
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| Euler's method. |
| Discussion of Homework 1. |
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| April 19 |
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| Truncation error analysis, order of convergence. |
| Runge-Kutta second order method. |
| Implicit Trapezoidal method. |
| Discussion of Homework 2. |
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| April 26 |
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| Stability, regions of absolute stability. |
| Runge-Kutta fourth order method. |
| Adams-Bashforth and Adams-Moulton methods. |
| Adams predictor-corrector algorithm. |
| Discussion of Homework 3. |
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| May 3 |
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| Runge-Kutta methods for systems. |
| Stability for multistep methods, consistency, convergence. |
| Discussion of Homework 4. |
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Midterm Review. |
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| May 10 |
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| Two points boundary value problems. |
| Finite difference approximation. |
| Midterm Discussion. |
| Discussion of Homework 5. |
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| May 17 |
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| Vector and matrix norms. |
| Iterative methods for the solution of linear systems of
equations. |
| Gauss-Jacobi and Gauss Seidel. |
| Discussion of Homework 6. |
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| May 24 |
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| Error analysis for iterative methods. |
| Convergence results for iterative methods. |
| Condition number. |
| QR Decomposition and Gram-Schmidt process. |
| Discussion of Homework 7. |
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| May 31 |
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| Discrete least squares approximation. |
| Construction of the normal equations. |
| Matrix/vector formulation of the discrete least squares problem. |
| Using the QR decomposition to solve normal equations. |
| Discussion of Homework 8. |
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| June 7 |
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| Fourier Series. |
| Least squares trigonometric polynomials. |
| Discussion of Homework 8. |
| Final Review. |
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| June 8 |
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