# Schedule

This schedule is not final but this is the anticipated curriculum of TMA4212.

JCS = John C. Strikwerda's book on finite differences

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 N Subject
2 10.01, 12.01 Appendix A ch. 1-2 Introduction to PDEs, examples of PDEs and principles of finite difference discretizations, matrix- and vector- norms. Orthogonal diagonalization of symmetric matrices. Jordan canonical form, Schur factorization. Spectral radius and norms of matrices. Linear algebra exercises. Difference operators. Difference formulae.
3 17.01, 19.01 ch. 1,2,3. Linear algebra. Boundary value problems.
4 24.01, 26.01 4.1-4.5 Parabolic problems.
5 31.01, 02.02 5.1–5.4, 5.6. Parabolic problems.
6 07.02, 09.02 5.8–5.9, 6 Parabolic problems. Elliptic equations.
7 14.02, 16.02 Elliptic equations.
8 21.02, 23.02 7.1–7.4. Advection equations and hyperbolic systems.
9 28.02, 01.03 Project work. No lectures.
10 06.03, 08.03 7.4–7.7 Advection equations and hyperbolic systems. Dissipation and dispersion.
11 13.03, 15.03 Numerical solution of linear systems.
12 20.03, 22.03 Project work. No lectures
13 27.03, 29.04 Finite element method: Rayleigh–Ritz and Galerkin principles and methods.
14 03.04, 05.04 Easter holiday.
15 10.04, 12.04 Finite elements.
16 17.04, 19.04 Finite elements.
17 24.04, Project presentation