Course number:	M-CE-1.06
Course:	Advanced Mathematics
Type:	Integrierte Lehrveranstaltung
SPPW:	3
ECTS-Credits:	4
Instructor:	Professor Dipl.-Ing. Dr. Peter Bachhiesl
Course ID:	AMAT
Semester:	WS 2011
Semester of degree program	1
Number of groups	1
Language of instruction:
Curriculum version:	2011

Description:
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 emphasize on the implementation of numerical concepts, numerical experiments and the interpretation of accordingly achieved results.

Contents:
1. Partial Differential Equations
• Separation of variables – Fourier approaches (Wave- and Poisson equation)
• Remarks on Laplace approach
• Finite differences and finite elements

2. Advanced Statistics
• Probability, Random variables and distributions
• Random numbers and Monte Carlo methods
• Data analysis: estimation on the basis of samples, testing hypotheses

3. Modelling and Simulation
• Modelling traffic
• Remarks on chaos (structure and chaos, attractors, self-similarity and fractals)


Aims:

Previous knowledge:
Fundamentals according to Mathematik-Grundlagen (NETbb-1.02), Softwaregestützte Mathematik (NETbb-2.02) and Mathematische Simulation (NETbb-3.03).

Method of instruction:
Integrated course (theory with subsequent analytical and numerical exercise). For demonstration purpose (numerical methods) CAS MATLAB is used.

Assessment:
Written or oral examination.

Literature:
E. Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 9-th ed., 2006
A. Quateroni, et. al., Numerical Mathematics, Springer, 2009
P.I. Kattan, MATLAB guide to finite elements: an interactive approach, Springer, 2008
J. Fish, et. al., A first course in finite elements, John Wiley & Sons, 2007
S. Brandt, Data Analysis, Springer, 3-rd ed., 1998
H.J. Bungartz, et. al., Modellbildung und Simulation, Springer, 2009

Remarks: