Advanced Mathematics (ILV)Back
|Semester of degree program||Semester 1|
|Mode of delivery||Presencecourse|
|Language of instruction||English|
The mathematical principles of linear and non-linear dynamics will be provided. Hence the students shall be in the position to discuss the quantitative and qualitative behaviour of dynamics, which represents a crucial competence for recent topics (chaos, self-similarity etc.).
Fundamentals according to Mathematik-Grundlagen (NET-1.02), Softwaregestützte Mathematik (NET-2.02) and Mathematische Simulation (NET-3.03).
We focus on mathematical topics which play an important role in communication engineering. The topics will be discussed under the analytical and numerical point of view. We put emphasis on the implementation of numerical concepts, numerical experiments and the interpretation of accordingly achieved results.
* Systems of ordinary differential equations
- Basics from Linear Algebra
- Linear systems
- Popular non-linear systems
- Numerical approaches for ODE systems
- Stability of ODE-systems
* Partial differential equations
- Wave equation
- Finite differences
* Control and optimization of dynamics
- Parameter identification
- Control theory for systems
J. Baillieul, Mathematical Control Theory, Springer, 1999
E. Kreyszig, Advanced Engineering Mathematics, 9th ed. , John Wiley & Sons
S. Larson, et. al., Partial differential equations with numerical methods; 1st ed., Springer, 2003
A. Quateroni, et. al., Numerical Mathematics, 2nd. edition, Texts in Applied Mathematics, Springer, 2007
W. Walter, Ordinary Differential equations, 1st. ed, Springer, 1998
Integrated course (theory with subsequent analytical and numerical exercise). For demonstration purpose (numerical methods) CAS MATLAB is used.
Written or oral examination.