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Lecturer(s)
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Course content
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Lecture topics after weeks of semester 1. Functions of complex variable 2. Derivative of a complex variable function, singular points 3. Laurent series, integral of a complex variable function, Cauchy theorem 4. Residual of function, residual theorem 5. Calculation of the roots of a complex variable polynomial 6. Solving systems of linear equations 7. LU matrix decomposition and its applications 8. QR decomposition of matrix 9. Calculation of eigenvalues of a matrix 10. Discrete Fourier transform 11. Fast Fourier transform 12. Advanced optimization methods 13. Advanced methods for ODE, stiff problems In case of extraordinary measures, the teaching will take place remotely using the MS Teams program at the time according to the schedule. Attending group meetings at MS Teams is equivalent to attending lectures and seminars.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Skills training
- Contact teaching
- 150 hours per semester
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Learning outcomes
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The aim of the course is to provice mathematical basis for the most important theoretical courses in Process Control. In particular, the basic knowledge of complex analysis and selected parts of numerical mathematics.
Student after completing the course - demonstrates knowledge of complex analysis - is able to use basic methods of numerical mathematics - is able to solve mathematical problems using a computer
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Prerequisites
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Knowledge of mathematics from bachelor study program is expected. It is the knowledge of the subjects Mathematics 1, Mathematics 2, Mathematics 3.
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Assessment methods and criteria
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unspecified
Students are required to actively participate in seminars and the elaboration of individual works, which are part of the evaluation of the course. Active participation in seminars can be replaced by the elaboration of a semester work. The course ends with an oral exam.
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Recommended literature
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Francis Scheid. Numerical Analysis. New York: McGraw-Hill, 1989. ISBN 0070552215.
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FUKS,B.A., ŠABAT,B.V. Funkce komplexní proměnné. Praha: ŠCAV, 1961.
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JEVGRAFOV,M.A. Funkce komplexní proměnné. Praha: STNL, 1981.
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Přikryl, Petr. Numerické metody matematické analýzy. Praha: Státní nakladatelství technické literatury, 1985.
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Vitásek, Emil. Numerické metody. Praha: Státní nakladatelství technické literatury, 1987.
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