 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Mathematics III

Code Completion Credits Range
2011009 Z,ZK 5 2P+2C
Lecturer:
Radka Keslerová, Leopold Herrmann (guarantor), Luděk Beneš, Tomáš Bodnár, Marta Čertíková, Jiří Fürst, Jan Halama, Stanislav Kračmar, Olga Majlingová, František Mráz, Tomáš Neustupa, Vladimír Prokop, Hynek Řezníček, Petr Sváček, Jan Valášek
Tutor:
Radka Keslerová, Leopold Herrmann (guarantor), Luděk Beneš, Tomáš Bodnár, Marta Čertíková, Gejza Dohnal, Jiří Fürst, Jan Halama, Jiří Holman, Jan Karel, Milana Kittlerová, Stanislav Kračmar, Olga Majlingová, František Mráz, Tomáš Neustupa, Vladimír Prokop, Hynek Řezníček, Petr Sváček, 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 2019/2020:
 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-309Beneš L.10:45–12:15(lecture parallel4)Karlovo nám.Posluchárna KA309 roomKN:A-214Beneš L.10:45–12:15(lecture parallel1)Karlovo nám.Posluchárna KA214roomKN:A-311Holman J.14:15–15:45(parallel nr.8)Karlovo nám.Posluchárna KA311roomKN:A-311Čertíková M.16:00–17:30(parallel nr.14)Karlovo nám.Posluchárna KA311 roomKN:A-311Keslerová R.10:45–12:15(parallel nr.7)Karlovo nám.Posluchárna KA311roomKN:A-311Řezníček H.12:30–14:00(parallel nr.15)Karlovo nám.Posluchárna KA311 roomKN:A-313Kittlerová M.09:00–10:30(parallel nr.1)Karlovo nám.Učebna KA313roomKN:A-313Valášek J.14:15–15:45(parallel nr.11)Karlovo nám.Učebna KA313roomKN:A-310Beneš L.17:45–19:15(parallel nr.5)Karlovo nám.Posluchárna KA310 roomKN:A-313Holman J.10:45–12:15(parallel nr.4)Karlovo nám.Učebna KA313roomKN:A-311Beneš L.16:00–17:30(parallel nr.6)Karlovo nám.Posluchárna KA311 roomKN:A-214Neustupa T.10:45–12:15(lecture parallel3)Karlovo nám.Posluchárna KA214roomKN:A-313Majlingová O.12:30–14:00(parallel nr.12)Karlovo nám.Učebna KA313 roomKN:A-311Bodnár T.09:00–10:30(parallel nr.9)Karlovo nám.Posluchárna KA311roomKN:A-311Řezníček H.10:45–12:15(parallel nr.10)Karlovo nám.Posluchárna KA311roomKN:A-311Kračmar S.12:30–14:00(parallel nr.13)Karlovo nám.Posluchárna KA311
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-06-05
For updated information see http://bilakniha.cvut.cz/en/predmet10343102.html