Title of Course: Numerical Methods in Medicine
Exam number: XM 1420
Length of course: 2 hours per week
Type of course: lecture
Language: English
Lecturer: Prof. Dr. H. Botterweck
Learning outcomes:
The students have to work on numerical methodical problems in the area of medical-technical development (as well in research, simulation, quality check etc) in a systematical way:
1. Realizing the problem and mathematically expressing it (modelling).
2. Choosing an adequate numerical method, applying and checking the results critically.
3. Understanding a possibly existing solution (software, literature, expertises) and adjusting to the given problem.
The most important methods of the operation research for basic numerical exercises are taught and practised.

Course Requirements:
Mathematics on an Engineering-Bachelor´s degree level

Content:
The topics marked with an asterisk are more advanced and will bet treated only short as an outlook/overview.

I) Basic techniques

1 General criteria: condition, stability, convergence, efficiency
2 Linear systems of equations
3 Differentiation and optimization
4 Linear and non-linear regression, interpolation and * splines
5 * Spectral analysis (Fourier-transform, FFT, wavelets)
6 Diagonalization and inversion of linear operators
7 Integration (Quadrature) in few dimensions

II) Application

8 Dimensional analysis, simplification
9 Stationary problems (electrical networks, heat flow, mechanical systems in equilibrium)
10 * Solving (P)Des (types, discretization, diagonalization, overview FEM, examples)
11 * Statistical distributions (momenta, correlations, tests, sampling
12 * Simulation of complex systems (phase-space methods, Monte-Carlo)
13 * Visualization: ray-casting, and –tracing, shading
14 Conventional issues (programming paradigms, intro Matlab(C/C++), parallelization, acceleration by hard- and software)
15 Knowledge about lecturer´s current research projects

Recommended Literature:

• Press. W.: Numerical Recipes, Cambridge University Press, 2007
• Danaila et al.: An Introduction to Scientific Computing, Springer, 2006
  

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