Communication Engineering part time

Area of studies
Civil Engineering

Level of qualification
2. Cycle (Master)

Qualification awarded
DiplomingenieurIn (DI)

Mode of study
Part-time

Duration of study
4 Semesters

ECTS-Credits awarded
120 ECTS

Language
English

FH site
Klagenfurt

Tuition fees
€ 363.36

ÖH contribution
€ 18,50

 

Details - Advanced Mathematics


Course number: M-CE-1.06
Course: Advanced Mathematics
Type: Integrierte Lehrveranstaltung (Integrated Course)
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

learning outcomes of the course unit:
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 rucial competence for recent topics (chaos, self-similarity etc.).


mode of delivery: Presencecourse

prerequisits and co-requisits: Fundamentals according to Mathematik-Grundlagen (NETbb-1.02), Softwaregestützte Mathematik (NETbb-2.02) and Mathematische Simulation (NETbb-3.03).

recommended optional programme components:

course contents:
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.




Contents:


* 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

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)

recommended or required reading:
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

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

planned learning activities and teaching methods:
Integrated course (theory with subsequent analytical and numerical exercise). For demonstration purpose (numerical methods) CAS MATLAB is used.

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

assessment methods and criteria: Written or oral examination.

work placement(s):

of note:
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