CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

# Mathematics III

Code Completion Credits Range Language
2011009 Z,ZK 5 2P+2C Czech
Garant předmětu:
Stanislav Kračmar
Lecturer:
Luděk Beneš, Tomáš Bodnár, Marta Čertíková, Jiří Fürst, Jan Halama, Radka Keslerová, Stanislav Kračmar, Olga Majlingová, Tomáš Neustupa, Vladimír Prokop, Hynek Řezníček, Petr Sváček, Jan Valášek
Tutor:
Luděk Beneš, Tomáš Bodnár, Marta Čertíková, Gejza Dohnal, Jiří Fürst, Jan Halama, Jiří Holman, Vladimír Hric, Jan Karel, Radka Keslerová, Milana Kittlerová, Stanislav Kračmar, Olga Majlingová, Tomáš Neustupa, Vladimír Prokop, Hynek Řezníček, Petr Sváček, David Trdlička, Jan Valášek
Supervisor:
Department of Technical Mathematics
Synopsis:

An introductory course in ordinary differential equation and infinite series.

Requirements:
Syllabus of lectures:

Ordinary differential equations. Basic notions. First-order equations. Second-order linear equations. Systems of equations in normal form. Autonomous systems. Linear systems. Linear systems with constant coefficients. Infinite series. Function series. Power series, Fourier series.

Syllabus of tutorials:

Ordinary differential equations. Basic notions. First-order equations. Second-order linear equations. Systems of equations in normal form. Autonomous systems. Linear systems. Linear systems with constant coefficients. Infinite series. Function series. Power series, Fourier series.

Study Objective:

1. Ordinary differential equations of first order. Basic concepts. Maximal solution. Existence and uniqueness of maximal solution of the initial value problem., 2. Separable differential equations. Homogeneous differential equations of first order. Exact equation. Linear differential equation of first order. Bernoulli equation., 3. Systems of differential equations in normal form. Fundamental set of solutions of homogeneous linear systems. The Wronskian., 4. Linear differential equations of 2-nd order. Method of undetermined coefficients., 5. Autonomous systems. Dynamic interpretation in the phase space., 6. Homogeneous linear autonomous systems. The Euler method for the general solution., 7. Phase diagram of the homogeneous linear autonomous system in the plane. Various types of equilibrium points. Nonhomogeneous linear autonomous systems., 8. Nonlinear autonomous systems. Properties of phase trajectories. First integral., 9. Infinite series of numbers. Tests of convergence for the series with positive terms., 10. Series with arbitrary real terms. Absolute and conditional convergence. The Leibnitz test., 11. Power series. Structure of the domain of convergence and determination of the domain., 12. Operations on power series (multiplication, differentiation, and integration of power series)., 13. The expansion of a function into the Taylor/MacLaurin series., 14. Application of power series to the solution of the initial value problem for the linear differential equation of 2-nd order with variable coefficients.

Study materials:

1. Burda, P.: Mathematics III, Ordinary Differential Equations and Infinite Series, CTU Publishing House, Prague, 1998.

Note:
Time-table for winter semester 2022/2023:
 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 roomKN:A-420Čertíková M.09:00–10:30(parallel nr.11)Karlovo nám.Učebna KA420roomT4:C2-136Neustupa T.12:30–14:00(lecture parallel1)DejvicePosluchárna 136 roomKN:A-420Kittlerová M.10:45–12:15(parallel nr.9)Karlovo nám.Učebna KA420roomKN:A-420Kittlerová M.12:30–14:00(parallel nr.12)Karlovo nám.Učebna KA420 roomKN:A-309Beneš L.10:45–12:15(lecture parallel3)Karlovo nám.Posluchárna KA309 roomKN:A-420Majlingová O.09:00–10:30(parallel nr.4)Karlovo nám.Učebna KA420roomKN:A-420Holman J.12:30–14:00(parallel nr.3)Karlovo nám.Učebna KA420roomKN:A-404Keslerová R.17:45–19:15(parallel nr.6)Karlovo nám.Posluchárna KA404 roomKN:A-420Holman J.10:45–12:15(parallel nr.5)Karlovo nám.Učebna KA420roomKN:A-420Beneš L.14:15–15:45(parallel nr.7)Karlovo nám.Učebna KA420roomKN:A-420Keslerová R.16:00–17:30(parallel nr.8)Karlovo nám.Učebna KA420 roomT4:C2-136Beneš L.10:45–12:15(lecture parallel2)DejvicePosluchárna 136 roomKN:A-420Řezníček H.07:15–08:45(parallel nr.1)Karlovo nám.Učebna KA420roomKN:A-420Bodnár T.09:00–10:30(parallel nr.2)Karlovo nám.Učebna KA420roomKN:A-420Kračmar S.10:45–12:15(parallel nr.10)Karlovo nám.Učebna KA420
Time-table for summer semester 2022/2023:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-06-02
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet10343102.html