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Lecturer(s)
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Šimůnková Martina, RNDr. Ph.D.
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Course content
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Course program (syllabus): 1. Gaussian plane C, mapping of complex numbers in the Gaussian plane, convergence in C. Series of complex numbers, Bolzano-Cauchy criterion of convergence, absolute and relative convergence. Criteria of convergence for series. 2. Power series in C. Radius and circle of convergence. Properties of power series. 3. Term-by-term differentiating and integration of power series. 4. Taylor series. Definitions of trigonometric and exponential functions by power series. 5. Metric spaces: metric, norm, examples of metric spaces. 6. Metric spaces: other terms (distance of sets, open and closed sets, neighbourhoods of points, interior of a set, boundary etc.). 7. Metric spaces - convergence, continuity, limit. Complete and compact space. 8. Functions of more real variables. Definition, basic terms, contour lines, domains. 9. Differential and derivative (gradient) of functions of more real variables. Applications. 10. Directional derivatives, partial derivatives. Curves, surfaces, tangent, normal, tangent plane. 11. Partial derivatives of composite functions. Implicit functions. Solving equations. 12. Extremes of functions of more real variables. 13. Constrained and global extremes. 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
- 38 hours per semester
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Learning outcomes
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Elementary concepts of metric spaces, compact and complete spaces. Differential calculus of a real fuction of several real variables.
Functions of several real variables.
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Prerequisites
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Analytic thinking. AN2E.
KMA/AN2
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Assessment methods and criteria
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Oral exam, Written exam
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Recommended literature
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Brabec, J. - Hrůza, B. Matematická analýza II. Praha 1986..
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Bruthans, V. - Nekvinda, M. - Vild, J. Matematika II - cvičení. [Skripta VŠST.].
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Budinský, B. - Charvát, J. Matematika II. Praha 1990..
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Černý, I. Matematická analýza - 1. část. [Skripta TU v Liberci.] Liberec 1996.. &, &.
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Černý, I. Matematická analýza - 2. část. [Skripta TU v Liberci.] Liberec 1996..
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Černý, I. Matematická analýza - 3. část. [Skripta TU v Liberci.] Liberec 1996..
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Černý, I. Rokyta, M.: Differential and Integral Calculus of One Real Variable..
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Kluvánek, I. - Mišík, L. - Švec, M. Matematika II. Bratislava 1961..
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Tumajer, F. - Fabiánová, H. Matematika II. [Skripta VŠST.] VŠST, Liberec 1991..
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Veselý, J. Matematická analýza pro učitele I, II. Matfyzpress, Praha 1997..
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