Engineering Applications - BE1M15IAP

Credits 5
Semesters Winter
Completion Assessment + Examination
Language of teaching English
Extent of teaching 2P+2C
The aim of the course is to get an overview of solving basic mathematical problems occurring in engineering practice using computer algebra systems
Course outlines
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.
Exercises outlines
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
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.
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.