NMAC04	Numerical methods, a second course, ECTS-points /NUMERISKA METODER, fördjupning/ Advancement level: C
	Aim: The course treats four different main subjects: numerical linear algebra, numerical methods of unconstrained optimization, ordinary and partial differential equations. Its aim is to give an overview of numerical methods for the solution of problems in these different areas and to prevent the theory needed to analyse the methods. In order to illustrate the methods, computer experiments using MATLAB and FORTRAN (Pascal) are made. Prerequisites: Knowledge of mathematics and numerical analysis as taught in the first two years of the mathematics program. Course organization: The course consists of lectures, lessons and computer exercises. Course content: Linear algebra: Norms. Partitioning and block matrices. Givens transformation. Householder transformation. QR-factorization. The singular value decomposition. Symmetric, positive definite matrices. Iterative methods for the solution of systems of linear equations. Linear least squares problems. The matrix eigenvalue problem. Nonlinear unconstrained optimization: Newton-like methods. Conjugate gradient methods. Trustregion methods. Non-linear least squares problems. Ordinary differential equations: Linear multistep methods: stability, consistency, convergence. Stiff differential equations. Runge-Kutta-methods. Error estimation and stepsize control. Partial differential equations: Classification. Wellposedness. Characteristics. Consistency. Convergence. Stability analysis. Explicit and implicit difference methods for parabolic equations. Iterative methods for elliptic problems. Orientation about the finite element method. Application of the methods in computer exercises. Course literature: Dahlquist-Björck: Numerical methods, manuscript. Ch. 6, 7, 10-14. G. D. Smith: Numerical solution of partial differential equations: Finite difference methods. Oxford Applied Mathematics and Computing Science Series, 1985. R. Fletcher: Practical methods of optimization. Chichester Wiley, 1987 (complementary). J. D. Lambert: Numerical methods for ordinary differential equations. John Wiley & Sons, 1991 (complementary). Exercises and examples of earlier written examinations.
NMLI	A written examination in linear algebra and optimization. 4 points.
NMOD	A written examination in ordinary and partial differential equations. 4 points.
LAB1	Computer exercises in linear algebra and optimization. 1 point.
LAB2	Computer exercises in ordinary and partial differential equations. 1 point.

Course language is Swedish.