Mathematics for telecommuications

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course covers various mathematical topics for radio technique and telecomunication, in particular: Matrix theory (eigenvectors, spectral decomposition), Integral transform (Fourier, Laplace and Z-transform), Special functions.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

1. Laurent series and Fourier series in complex field. Singularity and residua

2. Fourier transform. Inverse Fourier transform

3. Complex Laplace transform, image of periodic function and power series

4. Inverse Laplace transform (ILT). Inverse image of rational function

5. Integral form of ILT. Residua method.

6. Z-transform, basic properties

7. Finding inverse Z-transform by means of residua. Difference equations

8. Gamma and Beta function in the complex field

9. Bessel functions, application to wave equation

10. Eigenvalues and eigenvectors of matrices. Hermitian, positive and unitary matrices

11. Spectral resolution of the matrix

12. Function calculus for matrices. Linear equations with sparse matrix.

13. Numerical solution of the system of nonlinear equations -- Newton method

14. Partial differential equation -- boundary condition

Syllabus of tutorials:

1. Laurent series and Fourier series in complex field. Singularity and residua

2. Fourier transform. Inverse Fourier transform

3. Complex Laplace transform, image of periodic function and power series

4. Inverse Laplace transform (ILT). Inverse image of rational function

5. Integral form of ILT. Residua method.

6. Z-transform, basic properties

7. Finding inverse Z-transform by means of residua. Difference equations

8. Gamma and Beta function in the complex field

9. Bessel functions, application to wave equation

10. Eigenvalues and eigenvectors of matrices. Hermitian, positive and unitary matrices

11. Spectral resolution of the matrix

12. Function calculus for matrices. Linear equations with sparse matrix.

13. Numerical solution of the system of nonlinear equations -- Newton method

14. Partial differential equation -- boundary condition

Study Objective:

Study materials:

1. There is no text-book covering the course completely. The lecturer will hint resources to particular topics.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: