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Lecturer(s)
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Pech Ondřej, Ing. Ph.D.
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Breitfelder Ondřej, Mgr.
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Caletka Tomáš, RNDr. CSc.
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Valentová Ivana, doc. Ing. Ph.D.
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Zouvalová Katarína, Ing. Ph.D.
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Course content
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Week 1-2: ODEs of the 1st order, nonlinear, linear. General and particular solutions, singular solutions. Formulation of the initial value problem. Methods of solving ODEs of the 1st order: direct integration, separation of variables, variation of parameters. Week 3-6: Linear ODEs of higher orders - homogeneous, nonhomogeneous, with constant coefficients. Method of characteristic equation. Variation of parameters. Week 7: Systems of ODEs of the 1st order. Week 8 : Laplace transform. Inverse Laplace transform. Application to initial value problems for ODEs. Week 10-11: Function series, point convergence, uniform convergence. Power series. Taylor series. Fourier series. Week 12: Power and Fourier methods of solving boundary value problems. Week 13: Recapitulation.
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Learning activities and teaching methods
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Seminar classes, Seminar, Practicum
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Contact hours
- 26 hours per semester
- Preparation for comprehensive test (10-40)
- 18 hours per semester
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| prerequisite |
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| Knowledge |
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| There is no prerequisite for this course. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M1E. |
| learning outcomes |
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| By the end of the course, a successful student should be able to: 1. Classify ordinary differential equations; 2. Formulate the basic initial and boundary value problems for ODEs; 3. Solve ODEs of the first order; 4. Solve linear ODEs of the n-th order with constant coefficients; 5. Solve systems of linear ODEs of the first order; 6. Deal with function sequences and function series. 7. Expend a function into Fourier series. |
| teaching methods |
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| Seminar |
| Practicum |
| Seminar classes |
| assessment methods |
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| Test |
| Skills demonstration during practicum |
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Recommended literature
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Jirásek, František; Kriegelstein, Eduard; Tichý, Zdeněk. Sbírka řešených příkladů z matematiky : logika a množiny, lineární a vektorová algebra, analytická geometrie, posloupnosti a řady, diferenciální a integrální počet funkcí jedné proměnn. Praha : SNTL, 1981.
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Jirásek, František; Vacek, Ivan; Čipera, Stanislav. Sbírka řešených příkladů z matematiky II. 1. vyd. Praha : SNTL, 1989.
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Mašek, Josef. Základy matematiky II : cvičení. 1. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-507-3.
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