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Activity
| Week | Dates | Theme | Süli and Mayers | Extra Material | Recommended exercises. |
|---|---|---|---|---|---|
| 2 | 07.01 10.01 | Introduction to the course, principles of computational mathematics, learning outcome of the course. Floating point numbers, roundoff error, stability of problems and algorithms. Bisection method and Newton method. Convergence of fixed point iterations. Brouwer's Theorem. Contraction mapping Theorem. | 1 | Slides | exercise 4.7 in SM (for a solution see Problems lecture 3). |
| 3 | 14.01 17.01 | Convergence of Newton method. Newton for systems. Introduction to Python. Supervision of the first assignment. | 1, 4 | Python program from class Note on Newton methods for systems. Slides. | |
| 4 | 21.01 24.01 | Solution of systems of linear equations | 2 | See iterative methods in ch. 13 of Finite difference schemes and partial differential equations, John C. Strikwerda, SIAM, (second edition). See also Linear algebra note part 1.Problems lecture 3 with solutions. | |
| 5 | 28.01 31.01 | Least squares, condition numbers stability of linear systems, SVD | 2.7, 2.9 | Problems lecture 4 with solutions. | |
| 6 | 04.02 | Gaussian Elimination (no exercise lectures on February the 7th) | 2 | ||
| 7 | 11.02 14.02 | Polynomial interpolation | 6 | Problems lecture 6 | |
| 8 | 18.02 21.02 | Polynomial interpolation | 8 | Problems lecture 7 | |
| 9 | 25.02 28.02 | Project second part | |||
| 10 | 04.03 07.03 | Numerical integration and differentiation | 7 | ||
| 11 | 11.03 14.03 | Numerical Integration | 10 | ||
| 12 | 18.03 21.03 | Initial value problems for ODEs | 12 | ||
| 13 | 25.03 28.03 | Initial value problems for ODEs | 12 | ||
| 15 | 01.04 04.04 | Boundary value problems | 13 | ||
| 16 | 08.04 11.04 | Boundary value problems | 13 | ||
| 18 | 29.04 | Questions and answers |