course: Numerical Methods and Scientific Computing

number:
150118
teaching methods:
lecture with integrated tutorials
media:
computer based presentation, black board and chalk
responsible person:
Dr. rer. nat. Mario Lipinski
lecturer:
Dr. rer. nat. Mario Lipinski (Mathematik)
language:
english
HWS:
3
CP:
4
offered in:

Exam

Oral

Date according to prior agreement with lecturer.

Duration: 30min
Exam registration: FlexNow

goals

The students have got an introduction to numerical methods and their implementation in MatLab/Octave

content

The following problems and methods will be discussed in the lecture:

  • systems of linear and non-linear equations (matrix decompositions, iterative solvers, Newton’s method)
  • interpolation (Lagrange, Hermite, cubic splines)
  • numerical integration (composite rules, Romberg’s method, multi-dimensional integration)
  • ordinary differential equations (Runge-Kutta methods, multistep methods)
  • ordinary boundary value problems (difference method, variational method)
  • partial differential equations (difference method, finite element method)
  • eigenvalues and eigenvectors of matrices (power iteration, Rayleigh quotient, QR method)

requirements

none

recommended knowledge

Mathematik für Studierende der Elektrotechnik und der Informationstechnik I-III

literature

  1. Dahmen, Wolfgang, Reusken, Arnold "Numerik für Ingenieure und Naturwissenschaftler", Springer Verlag, 2008
  2. Köckler, Norbert, Schwarz, Hans R. "Numerische Mathematik", Teubner Verlag, 2006