Úvod FMEPCG 2111001

2111001

Title of the subject: Mathematical tools of automation

Semester_of_study (WT – winter/ST – summer): WT

Learning outcomes: The aim of subject is to teach students to use selected mathematical methods and means for solving tasks of modeling, analysis and simulation of dynamic systems.

Brief content of course: Complex numbers. Operation with them. The absolute value and argument of complex numbers. Goniometric and exponential form of complex numbers. Some concepts of functions of a complex variable. Limit, derivative, integral. Laplace transform and backward Laplace transform. Uses of Laplace transform to solve differential equations and systems of differential equation. Fourier's transformation. Phase and amplitude spectrum .Z-transformation and backward z-transformation. Utilization of Z-transformation in solving of difference equations and systems of difference equations. Partial differential equations. Classification of partial differential equations of the second order. Solving of partial differential equations by difference methods. Stability. The equation of heat conduction. Explicit and implicit scheme. Wave equation. Derivative and integral of fractional order. Numerical calculation. Fractional-order differential equations and its numerical solution. Besides the classical calculation it will put emphasis on the use of modern supporting computer software systems.

Literature: Andreescu, T, Andrica, D.: Complex Numbers from A to ...Z, Birkhäuser; Texas, 2005 McLachlan, N. W.: Laplace Transforms and Their Applications to Differential Equations, Dover Publications, New York, 2014. Kon, B. Z.: University Mathematics Handbook Kindle Edition, Contento Now, Tel Aviv, 2015. Astrom, K. A., Wittenmark, B.: Computer-Controlled Systems: Theory and Design, 3r Ed., Dover Publications; Third Edition edition, 2011. Bequette, B.W.: Process Control: Modeling, Design and Simulation, 1st Ed., Prentice Hall, 2003. Gilat, A.: MATLAB: An Introduction with Applications 5th Ed., Wiley, 2004. Hespanha, J. P.: Linear Systems Theory, Princeton University Press, 2009. Tyagi, A. K.: MATLAB and SIMULINK for Engineers, Oxford University Press, 2012. Hagglund, T., Astrom, K.: PID Controllers: Theory, Design, and Tuning, 2nd Ed., Instrument Society of America, ISA, 1995. Smyth, M. P.: Linear Engineering Systems. Pergamon Press, New York, 1982. Dorf, D.: Modern Control Systems. Academic Press, New York, 1990.