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Mathematical Models: Analysis and Simulation
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Lecturer:
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Prof. M. Hanke,
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Extent:
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2 SWS, 3 ECTS
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Intended Audience:
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Students of the Bavarian Graduate School in Computational Engineering
If space is available also other (phd)students from related fields are welcome.
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Annotation:
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The number of participants is limited. Register now via email to
harald.koestler@informatik.uni-erlangen.de !
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Place and time:
Room:
Lectures : 0.111, Cauerstrasse 6.
Tutorials: 0.139, Cauerstrasse 6.
Date: 27.07.09-31.07.09
Time: 9:00-12:00,14:00-17:00
Overview:
The overall goal of the course is to give basic knowledge of applied and
numerical mathematics useful for scientific and engineering modeling. Especially, the
close connection between the properties of mathematical models and their
successful numerical can compare different methods and select suitable algorithms for given
problems.
Lecture Topics:
- Modelling by ordinary differential equations: Qualitative methods,
stability, phase space, bifurcations, limit cycles, chaos, numerical aspects
- Introduction to singular perturbations: Asymptotic expansions, applications
- Differential-algebraic equations: Examples in network modelling, constraint
mechanical multibody systems; analytic theory, well-posedness, numerical
stability (Lax theorem); numerical methods for DAE's, asymptotic stability;
index reduction
- Spectral methods
Material
Singular Perturbations
DAE
Mofied Nodal Analysis
MNA for electrical curcuits
DFT
Literature
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