Schedule
This schedule is not final but this is the anticipated curriculum of TMA4212.
JCS = John C. Strikwerda's book on finite differences
SM = Suli adn Mayers, An introduction to Numerical Analysis
N = course note This note is still under construction (especially chapter 7). Please let me know of any mistakes you find.
Prerequisites
| Subject | Topics | subtopics |
|---|---|---|
| Linear algebra | Basics | Vector and matrix norms; Symmetric Positive Definite matrices; Inner product spaces; Linear independence; basis of a vector space; orthonormal basis. |
| Matrix factorizations | Diagonalization and orthogonal diagonalization of matrices; LU decomposition (Gaussian elimination, pivoting); Cholesky factorization; QR factorization; SVD; Jordan Canonical form; Schur factorization. | |
| Topics of interest in numerical linear algebra | Spectral radius; Gershgoring's theorem; Condition number; Neumann series. | |
| Iterative methods | Newton method; fixed point iteration; convergence of the basic iterative methods (Jacobi, Gauss-Seidel and SOR) for linear systems. | |
| Calculus | Taylor theorem |
Schedule
| Week | Date | JCS and SM | N | Subject |
|---|---|---|---|---|
| 2 | 06.01, 07.01, 08.01 | ch. 1-2,3 | Introduction to the course. Difference operators and difference formulae. Boundary value problems. | |
| 3 | 13.01, 14.01, 15.01 | 3, 4.1-4.5 | Boundary value problems. Parabolic problems. | |
| 4 | 20.01, 21.01, 22.01 | 5.1–5.4, 5.6, 5.8. | Parabolic problems. 5.5 is not part of the curriculum. | |
| 5 | 27.01, 28.01, 29.01 | 5.8–5.9, 6 | Parabolic problems. Elliptic equations. 5.7 is not part of the curriculum. | |
| 6 | 03.02, 04.02, 05.02 | 6 | Elliptic equations. | |
| 7 | 10.02,11.02, 12.02 | 7.1–7.4. | Advection equations and hyperbolic systems. | |
| 8 | 17.02, 18.02, 19.02 | 7.4–7.5 | Advection equations and hyperbolic systems. | |
| 9 | 24.02, 25.02, 26.02 | 7.6, 7.7 | Dissipation and dispersion. Project work. No lectures. | |
| 10 | 03.03, 04.03, 05.03 | 13 JCS p 339-349 p 354-356 | Numerical solution of linear systems. | |
| 11 | 10.03, 11.03, 12.03 | 14 JCS p 373-387 p 390-391 | Numerical solution of linear systems. Finite element method. | |
| 12 | 17.03, 18.03, 19.03 | 14 SM p 385-399 | Finite element method: Rayleigh–Ritz and Galerkin principles and methods. | |
| 13 | 24.03, 25.03, 26.03 | 14 SM p 385-399 | Finite element method. Project work. | |
| 14 | 31.03, 01.04, 02.04 | Project work. No lectures. Project presentation. | ||
| 15 | 07.04, 09.04 | SM chaper 14 p 385-399. See material in It's learning. | Finite element method. Error estimastes (from Suli and Mayers). 2D Poisson equation. Exam problems. |