Selected Lectures of Mathematics

Lecturer:

Jan Macháč (gar.)

Tutor:

Jan Macháč (gar.)

Supervisor:

Department of Electromagnetic Field

Synopsis:

The subject extends the students knowledge of mathematics necessary for design of high frequency communication systems. It presents applications of modern branches of mathematics in the design of circuits and systems. Subject is oriented towards partial differential equations, uses of special polynomials and functions. Using of non - traditional possibilities for RF communications systems analysis and components design is presented - e.g. genetic algorithms, fractals, Wavelet transformation, neural networks. The attention is paid to solution of fields in the time domain in applications

for ultra wideband communications.

Requirements:

Basic knowledge of numerical methods. http://www.elmag.org/doku.php/k317

Syllabus of lectures:

1. Introduction to electrodynamics

2. Basic principles of electromagnetic field

3. Green functions

4. Green functions and their applications, method of moments

5. Analytical and numerical solution of partial differential equations

6. Special polynomials and functions, Bessel functions, function approximation

7. Analytical and numerical solution of integral equations

8. Theory of genetic algorithms

9. Applications of genetic algorithms

10. Neuron networks

11. Neuron networks - applications for high frequency systems

12. Fractals

13. Application of fractals

14. Wavelet transformation

Syllabus of tutorials:

1. Introduction into the theory of electromagnetic field

2. Basic principles of electromagnetic field

3. Solution of fields by Green functions

4. Applications of the moment method for the antenna design

5. Numerical and analytic solution of differential equations

6. Special polynomials and functions, Bessel functions, applications in the theory of transmission lines, approximation

7. Neuron networks - circuit application

8. Project submition

9. Project

10. Project

11. Antenna design by fractals

12. Fractals - antenna models

13. Applications of the wavelet transformation

14. Presentation of projects, assesment

Study Objective:

Study materials:

[1] Christodoulou, Ch., Georgiopoulos, M.: Applications of Neural Networks in Electromag. Artech House, London, 01

[2] Angot, A.: Užitá matematika pro elektrotechnické inženýry. SNTL, Praha 1971

[3] Collin R. E.: Field Theory of Guided Waves, IEEE Press, New York 1991

[4] Balanis, C.A.: Advanced Engineering Electromagnetics, J. Wiley, New York, 1989

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Telecommunications and Radio-engineering - High-frequency and Microwave Technology- structured studi (compulsory elective course)
• Telecommunications and Radio-engineering - Opto-electric Systems- structured studies (compulsory elective course)
• Telecommunications and Radio-engineering - Radio Communications, Navigation and Radar Systems- struc (compulsory elective course)
• Telecommunications and Radio-engineering - Multimedia, Sound and Television Technology- structured s (compulsory elective course)
• Telecommunications and Radio-engineering - Telecommunications- structured studies (compulsory elective course)