Engineering Applications

Garant předmětu:

Lecturer:

Jan Kyncl, Ladislav Musil

Tutor:

Jan Kyncl, Ladislav Musil

Supervisor:

Department of Electrical Power Engineering

Synopsis:

The aim of the course is to get an overview of solving basic mathematical problems occurring in engineering practice using computer algebra systems

Requirements:

Condition for obtaining assessment is participation in seminars and semester thesis elaboration. Passing the exam is given by the Study and Examination Code for Students of the Czech Technical University in Prague.

Syllabus of lectures:

1. Analytical and numerical solutions of technical problems, examples from electrical engineering.

2. Finite and numerical solutions of linear systems, equations, examples from electrical circuits.

3. Numerical solutions of nonlinear equations and their systems, load flow.

4. Free and bounded extrema of functions of several variables, overview of used methods.

5. Solution of overdetermined systems of equations, linear regression.

6. Nonlinear regression, interpolations of functions.

7. Interpolation, use of interpolation in technical practice and for solving equations.

8. Numerical quadrature, example of determining the energy from the time course of power.

9. Numerical methods of ODE solution.

10. Eigenvalues and vectors of matrices, connection with stability of lines. dynamic systems.

11. Basic problems on PDE in high-current practice (thermal and diffusion equations, electromagnetic field equations), network method and Schmidt method for parabolic equations.

12. Examples of signal processing, determination of Fourier series.

13. Examples of signal processing, determination of frequency and synchrophasors.

14. Reserve.

Syllabus of tutorials:

1.Analytical and numerical solutions of technical problems, electrical engineering examples

2.Eigenvalues and eigenvectors of matrices and the stability of dynamic linear systems

3.Finite and numerical solution of systems lin. equations, examples of electrical circuits, linear transformations

4.Free and constrained extremes of functions, overview of methods

5.Use optimization methods for the design of power devices

6.Overdetermined lin. equations, interpolation, regression

7. Examples of signal processing, Fourier series

8.Numerical quadrature (example of the determination of energy from time dependence of the power, basic numer. Methods for solving ODE)

9.Basic tasks using PDE in heavy power engineering, boundary and initial conditions (heat and diffusion equation, electromagnetic. field equations), Schmidt's method for parabolic equations

10.Weak solutions of PDE, Galerkin method, the use of FEM

11.Statistics and probability in technical tasks

12.Reliability assessment of basic arrangements

13.Correspondence of different task types, frequently used functions for approximation

14.Reserve

Study Objective:

Study materials:

DUBIN, Daniel H. Numerical and analytical methods for scientists and engineers using mathematica. Hoboken, N.J.: Wiley-Interscience, 2003, xvi, 633 p. ISBN 0471266108.

Esfandiari, R.S.: Numerical Methods for Engineers and Scientists Using MATLAB?, Second Edition. CRC Press, NY 2017.

Note:

Further information:

https://moodle.fel.cvut.cz/courses/BE1M15IAP

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed	roomT2:F1-109 Kyncl J. Musil L. 14:30–16:00 (lecture parallel1) Dejvice haly Výpočetní lab.315
Thu	roomT2:F1-109 Musil L. 16:15–17:45 (lecture parallel1 parallel nr.1) Dejvice haly Výpočetní lab.315
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Electrical Engineering, Power Engineering and Management - Electrical Power Engineering (compulsory course in the program)
• Electrical Engineering, Power Engineering and Management - Technological Systems (compulsory course in the program)
• Electrical Engineering, Power Engineering and Management - Management of Power Eng. and Electr. (compulsory course in the program)
• Electrical Engineering, Power Engineering and Management - Electrical Drives (compulsory course in the program)