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Lecturer(s)
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Valentová Ivana, doc. Ing. Ph.D.
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Course content
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Week 1: Point-wise and uniform convergence of function sequences; Week 2: Function series; Week 3: Power series and their convergence; Fourier series; Week 4: Vector functions of one real variable and their properties; curves in Rn; Week 5: Subsets of Rn and their topological properties; Week 6: Functions of n variables, their limits and continuity; Week 7: Directional derivative, total differential, tangent manifolds; chain rule; Week 8: Solvability of functional equations and differentiation of implicit functions; Week 9: Fundamental notions of min/max theory in Rn; Week 10: Mapping from Rn to Rm, its continuity and differentiability; regular mappings and transformations of coordinate systems; Week 11: Double and triple integral, Fubini theorem, basic techniques; Week 12: Application of double and triple integrals in geometry and physics; Week 13: Integrals depending on parameters and their differentiation. Further information and the lecture notes can be found on the web page http://analyza.kma.zcu.cz.
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, Task-based study method
- Contact hours
- 78 hours per semester
- Preparation for comprehensive test (10-40)
- 36 hours per semester
- Preparation for an examination (30-60)
- 60 hours per semester
- Presentation preparation (report) (1-10)
- 10 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/M1 or KMA/ MA1 or KMA/MA1-A. |
| learning outcomes |
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| By the end of the course, a successful student should be able to: 1. Use notions of advanced calculus in English; 2. Demonstrate knowledge of the definitions and fundamental theorems concerning function sequences, function series, vector functions of one real variable and real functions of more variables; 3. Deal with function sequences and function series; 4. Expend a function into a power of Fourier series; 5. Describe curves in Rn and work with them; 6. Determine properties of functions of more variables; 7. Compute directional and partial derivatives of functions of more variables; 8. Formulate basic min/max problems and solve them using differential calculus; 9. Evaluate double and triple integrals; 10.Deal with integrals depending on parameters; 11.Use developed theory in solving problems on physical systems. |
| teaching methods |
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| Lecture supplemented with a discussion |
| Interactive lecture |
| Task-based study method |
| assessment methods |
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| Combined exam |
| Skills demonstration during practicum |
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Recommended literature
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Brabec, Jiří; Hrůza, Bohuslav. Matematická analýza II. Praha : SNTL, 1986.
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Drábek, Pavel; Míka, Stanislav. Matematická analýza II.. 4. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-977-X.
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