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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Mathematics III

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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, 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
Mon
roomKN:A-309
Beneš L.
10:45–12:15
(lecture parallel4)
Karlovo nám.
Posluchárna KA309
Tue
roomKN:A-214
Beneš L.
10:45–12:15
(lecture parallel1)
Karlovo nám.
Posluchárna KA214
roomKN:A-311
Holman J.
14:15–15:45
(parallel nr.8)
Karlovo nám.
Posluchárna KA311
roomKN:A-311
Čertíková M.
16:00–17:30
(parallel nr.14)
Karlovo nám.
Posluchárna KA311
roomKN:A-311
Keslerová R.
10:45–12:15
(parallel nr.7)
Karlovo nám.
Posluchárna KA311
roomKN:A-311
Řezníček H.
12:30–14:00
(parallel nr.15)
Karlovo nám.
Posluchárna KA311
Fri
roomKN:A-313
Kittlerová M.
09:00–10:30
(parallel nr.1)
Karlovo nám.
Učebna KA313
roomKN:A-313
Valášek J.
14:15–15:45
(parallel nr.11)
Karlovo nám.
Učebna KA313
roomKN:A-310
Beneš L.
17:45–19:15
(parallel nr.5)
Karlovo nám.
Posluchárna KA310
roomKN:A-313
Holman J.
10:45–12:15
(parallel nr.4)
Karlovo nám.
Učebna KA313
roomKN:A-311
Beneš L.
16:00–17:30
(parallel nr.6)
Karlovo nám.
Posluchárna KA311
roomKN:A-311

10:45–12:15
(lecture parallel2)
Karlovo nám.
Posluchárna KA311
roomKN:A-313
Majlingová O.
12:30–14:00
(parallel nr.12)
Karlovo nám.
Učebna KA313
roomKN:A-214
Neustupa T.
10:45–12:15
(lecture parallel3)
Karlovo nám.
Posluchárna KA214
Thu
Fri
roomKN:A-311
Bodnár T.
09:00–10:30
(parallel nr.9)
Karlovo nám.
Posluchárna KA311
roomKN:A-311
Řezníček H.
10:45–12:15
(parallel nr.10)
Karlovo nám.
Posluchárna KA311
roomKN:A-311
Kračmar 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 2019-09-15
For updated information see http://bilakniha.cvut.cz/en/predmet10343102.html