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Lecturer(s)
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Obst Alexander, prof. RNDr. DrSc.
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Course content
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Week 1: Antiderivative, indefinite integral, definite integral. Definition, properties. Basic rule for integrals. Week 2: Techniques of integration, substitution, integration by parts. Week 3: Integration of rational functions - integration by parts, integration by substitution. Week 4: Applications of integral calculus. Improper integral. Week 5: Functions of several variables. Elementary functions and their graph, partial derivatives, total differential. Week 6: Directional derivative, gradient. Higher order partial derivatives. Chain rule, differentiation of implicit functions. Week 7: Fundamental notions of min/max theory in Rn; Week 8-9: Differential equations of the 1st order, linear, nonlinear. General and particular solutions, singular solution. Initial-value problem. Methods of solution: separation of variables, variation of parameter. Week 10-11: Linear differential equations of the 2nd order, homogeneous, nonhomogeneous, with constant parameters. Characteristic equation. Week 12:Linear differential equations of the n-th order with constant parameters. Variation of parameters. Week 13: Systems of differential equations.
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Learning activities and teaching methods
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Interactive lecture, Task-based study method, Students' self-study
- Contact hours
- 52 hours per semester
- Preparation for formative assessments (2-20)
- 20 hours per semester
- Preparation for an examination (30-60)
- 32 hours per semester
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| prerequisite |
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| Knowledge |
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| Students should be familiar with basic notions of the course KMA/ZME1. |
| learning outcomes |
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| By the end of the course, a successful student should be able to solve: - basic examples of integral calculus in R1 (integration by parts, integration by substitution) - basic examples of differential calculus in Rn (partial derivative, optimization problems) - elementary differential equations of the 1st and 2nd order |
| teaching methods |
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| Interactive lecture |
| Task-based study method |
| Self-study of literature |
| assessment methods |
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| Combined exam |
| Test |
| Skills demonstration during practicum |
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Recommended literature
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Drábek, Pavel; Míka, Stanislav. Matematická analýza II. 3. nezm. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-528-6.
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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 proměnné. 2. nezměn. vyd. 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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