Matlab Applications

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

Synopsis:

Systematic application of Matlab optimization toolbox for the solution of linear, quadratic, binary, integer an nonlinear programming tasks. Simulation of chaotic systems an fractal set generation.

Analysis of trajectories, attractors and fractal sets including estimation of their properties.

Requirements:

Passing 18MTL module.

Syllabus of lectures:

1 Linear programming and related tasks in Matlab

2 Quadratic programming and related tasks in Matlab

3 Binary and integer programming and related tasks in Matlab

4 Nonlinear programming in Matlab

5 Penalization techniques and nonlinear optimization

6 Nonlinear regression and robust identification as optimization tasks

7 Discrete and continuous dynamic systems, simulation approaches and problems

8 Chaotic and turbulent systems in 1D

9 Trajectory and attractor

10 Lyapunov exponent estimation and power spectrum of chaotic trajectory

11 Deterministic fractal and similarity dimension

12 Fractal as result of stochastic modelling

13 Attractor as fractal set

14 Estimation of capacity, information and correlation dimensions

Syllabus of tutorials:

1 Linear programming and related tasks in Matlab

2 Quadratic programming and related tasks in Matlab

3 Binary and integer programming and related tasks in Matlab

4 Nonlinear programming in Matlab

5 Penalization techniques and nonlinear optimization

6 Nonlinear regression and robust identification as optimization tasks

7 Discrete and continuous dynamic systems, simulation approaches and problems

8 Chaotic and turbulent systems in 1D

9 Trajectory and attractor

10 Lyapunov exponent estimation and power spectrum of chaotic trajectory

11 Deterministic fractal and similarity dimension

12 Fractal as result of stochastic modelling

13 Attractor as fractal set

14 Estimation of capacity, information and correlation dimensions

Study Objective:

Knowledge:

Motivate the students for the solution of selected numeric problems in the Matlab environment. Matlab is only a tool for the efficient solution of given tasks.

Abilities:

Orientation in given subject and ability to solve real tasks in Matlab.

Study materials:

Key references:

Sierkisma G.: Linear and Integer Programming, Marcel Dekker, 2002.

Dostal Z.: Optimal Quadratic Programming Algorithms, Springer, 2009.

Recommended references:

Moler C.: Numerical Computing with Matlab, SIAM, 2004.

Baker G.L., Golub J.P.: Chaotic Dynamics, Cambridge University Press, 1998.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikace softwarového inženýrství (elective course)
• Aplikované matematicko-stochastické metody (elective course)
• Aplikace informatiky v přírodních vědách (elective course)
• Radiolgická fyzika (elective course)