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Lecturer(s)
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Šimůnková Martina, RNDr. Ph.D.
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Hozman Jiří, RNDr. Ph.D.
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Course content
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The subject covers the fundamentals of metric spaces, the theory of series of functions, and the differential calculus of functions of several real variables. Lectures: 1. Metric spaces: metric, norm, examples of metric spaces. Inner product, Euclidean space. 2. Metric spaces: other notions (distance of sets, open and close sets, neighborhood of a point, interior points, boundary etc.). 3. Convergence in metric spaces. Mappings between metric spaces, limits and continuity. 4. Completeness, separability, compactness. 5. Sequences of functions, pointwise and uniform convergence. 6. Theorem on the continuity of the limit of a uniformly convergent sequence. 7. Power series, radius and disk of convergence. 8. Term-by-term differentiation and integration of power series. Application to series summation. 9. Functions of several variables, domain, graph, contour lines, level surfaces. 10. Directional and partial derivatives, total differential. Curve, surface, tangent line, normal line, tangent plane. 11. Partial derivatives of the composite function. Implicit function. 12. Local extrema of functions of several variables. 13. Absolut extrema and constrained extrema. 14. Reserve.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 56 hours per semester
- Preparation for credit
- 28 hours per semester
- Preparation for exam
- 28 hours per semester
- Home preparation for classes
- 68 hours per semester
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Learning outcomes
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The content of the subject is mastering the basics of the differential calculus of functions of several real variables and the theory of functional series in a complex domain.
Metric spaces, sequences and series of functions, functions of several variables.
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Prerequisites
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Mathematical Analysis 1, Mathematical analysis 2, Algebra and geometry 1, Algebra and geometry 2
KMA/PAN1M and KMA/PAN2M
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Assessment methods and criteria
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Oral exam, Written exam
Credit: Active participation in the lecture. Exam: writtten and oral
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Recommended literature
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Brabec, J., Hrůza, B.:. Matematická analýza II. Praha, SNTL 1986..
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Černý, I:. Matematická analýza, 2. část. Liberec, TUL 1996..
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Černý, I:. Matematická analýza, 3. část. Liberec, TUL 1996..
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Dont, M. - Opic, B.:. Matematická analýza III - úlohy. Praha, ČVUT 1982..
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Jarník, V.:. Diferenciální počet I. Praha, 1963.
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Jirásek, F. - Čipera, S. - Vacek, M.:. Sbírka řešených příkladů z matematiky II. Praha, SNTL 1989..
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Nekvinda M.:. Matematika II. Liberec, TUL 2000..
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Sikorski, R.:. Diferenciální a integrální počet, Praha, Academia 1973..
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Veselý, J.:. Matematická analýza pro učitele, I, II. Matfyzpress, Praha, 1997..
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