phy501 - Numerical Methods (Complete module description)

180h (attendance: 56h; self-study: 124h)

phy540 Mathematical Methods for Physics and Engineering I & phy541 Mathematical Methods for Physics and Engineering II

Students acquire theoretical knowledge of basic numerical methods and practical skills to apply these methods to physical problems within all areas of experimental, theoretical and applied physics.

Basic concepts of numerical Mathematics are introduced and applied to Physics problems. Topics include: Finite number representation and numerical errors, linear and nonlinear systems of equations, numerical differentiation and integration, function minimization and model fitting, discrete Fourier analysis, ordinary and partial differential equations. The learned numerical methods will be partly implemented (programmed) and applied to basic problems from mechanics, electrodynamics, etc. in the exercises. The problems are chosen so that analytical solutions are available in most cases. In this way, the quality of the numerical methods can be assessed by comparing numerical and analytical solutions. Programming will be done in C or, preferably, in Matlab, which is a powerful package for numerical computing. Matlab offers easy, portable programming, comfortable visualization tools and already implements most of the numerical methods introduced in this course. These built-in functions can be compared to own implementations or used in the exercises in some cases when own implementations are too costly. The tutorials provide basic programming support.