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Course, academic year 2020/2021
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Calculus III - OKB2310209
Title: Matematická analýza III
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2019 to 2021
Semester: winter
E-Credits: 4
Examination process: winter s.:
Hours per week, examination: winter s.:0/0, C+Ex [HS]
Extent per academic year: 12 [hours]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: combined
Is provided by: OKBM1M130A
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: RNDr. František Mošna, Ph.D.
prof. RNDr. Ladislav Kvasz, DSc., Dr.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Pre-requisite : OKB2310004
Is co-requisite for: OKB1310201
Is interchangeable with: OKB2310N05
Annotation -
Last update: RNDr. František Mošna, Ph.D. (24.05.2018)
Differential equations, methods of solution, linear differential equations of 1st and 2nd order, series and its convergence, sequences and series of functions, uniform convergence, power series.
Aim of the course -
Last update: RNDr. František Mošna, Ph.D. (13.09.2017)

Primary purpose of the course is to make students acquainted with basic mathods of differemtial equations solutions and applications and with basic ideas, knowledges and correlations concerning series and function sequences and series. Secondary aim is to prove, repetite and fix knowledges of previous mathematical analysis courses.

Literature -
Last update: RNDr. František Mošna, Ph.D. (24.05.2018)
  • Knopp, Konrad: Theory and Application of Infinite Series, Blackie London 1957
  • Hyslop, James M.: Infinite Series, Oliver and Boyd Edinburgh 1965
  • Singal, M. K., Singal, A. R.: A first cours in Real Analysis, R.Chand New Delhi 1999
  • Ross, K.A.:Elementary Analysis: The Tudory of Calculus. Undergraduate texts in Mathematics, Springer New York-Heidelberg-Berlin 1980
  • Fischer, E.: Intermediate Real Analisis. Undergraduate Texts in Mathematics, Springer NewYork-Heidelberg-Berlin 1983
Teaching methods -
Last update: RNDr. František Mošna, Ph.D. (13.09.2017)

Lecture and seminar.

Requirements to the exam -
Last update: RNDr. František Mošna, Ph.D. (13.09.2017)
  • credit requirements: active participation at seminars, two control tests (the first on differential equations, the second on series, sequences and series of fiunctions), control tests consists from examples presented at materials on Moodle,  (for both tests there will be two terms during the examination period for possible correction)
  • exam requirements: writing exam - examples, oral exam - understanding of given concepts, relationships in three questions (the first question examines certain concept, its definition, theorem, connections, introduction..., the second question asks the student to decide on validity of submitted state and justify his decision or support it by a counterexample, the third question relates to some process, proof, problem solving etc, )
Syllabus -
Last update: RNDr. František Mošna, Ph.D. (24.05.2018)
  • Differential equations - existence and uniquity, methods of solutions of first order differential equations (separation of variables method and variation of constant method for linear ones) and second order equations (undetermined coefficients method), thair applications.
  • Series - tests for convergence (comparison, ratio, root, Leibniz, Abel, Dirichlet tests), absolut convergence, sums of series.
  • Sequences and series of functions - uniform convergence of sequences and series, tests (Weierstrass, Abel, Dirichlet tests), power series, power series expansion of basic functions, application for calculation of limits.
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