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Lecturer(s)
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Vodák Rostislav, RNDr. Ph.D.
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Ludvík Pavel, RNDr. Ph.D.
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Bebčáková Iveta, Mgr. Ph.D.
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Course content
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1. Sequences and series of functions: Pointwise and uniform convergence, convergence criteria (esp. the Weierstrass criterion). Properties of the limit function - limit, continuity, derivative and integral. 2. Power series: Radius, interval and domain of convergence. Uniform convergence of power series. Taylor series, Taylor expansion of elementary functions. Approximate computing via series. 3. Metric spaces: Metric on a set, examples of metric spaces. Normed linear space. Classification of points according to a set. Open and closed sets and their properties. Convergent and Cauchy sequences of points. 4. Multivariable functions and mappings in Euclid spaces: Practical aplications. Limit and continuity of a mapping (function). Properties of continuous functions on compact sets.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Attendace
- 52 hours per semester
- Preparation for the Course Credit
- 10 hours per semester
- Preparation for the Exam
- 30 hours per semester
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Learning outcomes
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Understand basic notions concerning function series, metric spaces and multivariable functions.
Comprehension Understand basic notions concerning function series, metric spaces and multivariable functions.
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Prerequisites
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Differential calculus and integration on the real axis.
KAG/MA1 and KAG/MAN2
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Assessment methods and criteria
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Oral exam
Credit: the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test). Attendance at seminars: absence is tolerated at most three times. Exam: the student has to understand the subject and be able to prove the principal results.
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Recommended literature
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Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
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G. B. Thomas. (1998). Calculus and analytic geometry.
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J. Kojecká, I Rachůnková. (1989). Řešené příklady z matematické anylýzy 3. UP Olomouc.
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Novák V. (1985). Nekonečné řady. UJEP Brno.
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V. Jarník. (1976). Diferenciální počet I a II. SPN, Praha.
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