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:

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 2023/2024:

	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 parallel2) Karlovo nám. Posluchárna KA309
Tue	roomKN:A-214 Neustupa T. 12:30–14:00 (lecture parallel1) Karlovo nám. Posluchárna KA214roomKN:A-311 Čertíková M. 16:00–17:30 (parallel nr.7) Karlovo nám. Posluchárna KA311roomKN:A-311 Bodnár T. 17:45–19:15 (parallel nr.8) Karlovo nám. Posluchárna KA311
Wed
Thu	roomKN:A-311 Keslerová R. 12:30–14:00 (parallel nr.1) Karlovo nám. Posluchárna KA311roomKN:A-311 Beneš L. 14:15–15:45 (parallel nr.2) Karlovo nám. Posluchárna KA311roomKN:A-311 Majlingová O. 16:00–17:30 (parallel nr.3) Karlovo nám. Posluchárna KA311
Fri	roomKN:A-311 Hric V. 09:00–10:30 (parallel nr.4) Karlovo nám. Posluchárna KA311roomKN:A-311 Kittlerová M. 10:45–12:15 (parallel nr.5) Karlovo nám. Posluchárna KA311roomKN:A-311 Kittlerová M. 12:30–14:00 (parallel nr.6) Karlovo nám. Posluchárna KA311

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

10 62 67 00 BTZI 2012 P základ (compulsory course in the program)
11 68 73 00 BTZI 2012 K základ (compulsory course in the program)
02 26 31 34 BSTR EPT 2012 P základ (compulsory course in the program)
03 26 31 36 BSTR IAT 2012 P základ (compulsory course in the program)
04 26 31 38 BSTR KPP 2012 P základ (compulsory course in the program)
06 40 45 48 BSTR EPT 2012 K základ (compulsory course in the program)
07 40 45 50 BSTR IAT 2012 K základ (compulsory course in the program)
08 40 45 52 BSTR KPP 2012 K základ (compulsory course in the program)
05 40 45 46 BSTR TZP 2012 K základ (compulsory course in the program)
16 80 85 00 BVES TVA 2012 P základ (compulsory course in the program)
14 80 85 00 BVES MAT 2012 P základ (compulsory course in the program)
15 80 85 00 BVES OBR 2012 P základ (compulsory course in the program)
13 80 85 00 BVES EKO 2012 P základ (compulsory course in the program)
18 86 90 00 BVES MAT 2012 K základ (compulsory course in the program)
20 86 90 00 BVES TVA 2012 K základ (compulsory course in the program)
19 86 90 00 BVES OBR 2012 K základ (compulsory course in the program)
17 86 90 00 BVES EKO 2012 K základ (compulsory course in the program)
05 40 45 46 DSTR TZP 2012 K základ (compulsory course in the program)
06 40 45 48 DSTR EPT 2012 K základ (compulsory course in the program)
07 40 45 50 DSTR IAT 2012 K základ (compulsory course in the program)
08 40 45 52 DSTR KPP 2012 K základ (compulsory course in the program)
10 62 67 00 DTZI 2012 P základ (compulsory course in the program)
11 68 73 00 DTZI 2012 K základ (compulsory course in the program)
13 80 85 00 DVES 2012 P úvodní studijní plán (compulsory course in the program)
13 80 85 00 DVES EKO 2012 P (compulsory course in the program)
14 80 85 00 DVES MAT 2012 P (compulsory course in the program)
15 80 85 00 DVES OBR 2012 P (compulsory course in the program)
16 80 85 00 DVES TVA 2012 P (compulsory course in the program)
17 86 90 00 DVES 2012 K úvodní studijní plán (compulsory course in the program)
B TZSI 2021 - prezenční (compulsory course in the program)