Calculus III - OPBM1M130A
Title: Matematická analýza III
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2022
Semester: winter
E-Credits: 4
Examination process: winter s.:
Hours per week, examination: winter s.:2/2, Ex [HT]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Is provided by: OPBM2M115A
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.
Pre-requisite : OPBM1M103A
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Annotation -
Last update: RNDr. František Mošna, Ph.D. (09.09.2020)
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. (09.09.2020)

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. (09.09.2020)
  • Veselý, Jiří, 1998. Matematická analýza pro učitele, I, II. Praha: Matfyzpress
  • Mošna, František, 2019. Obyčejné diferenciální rovnice. Praha: PedFUK
  • Kalas, Josef, Ráb, Miloš, 2001. Obyčejné diferenciální rovnice. Brno: MU
  • Kalas, Josef, Pospíšil, Zdeněk, 2001. Spojité modely v biologii. Brno: MU
  • Ráb, Miloš, 2012. Metody řešení obyčejných diferenciálních rovnic. Brno: MU
  • Plch, Roman, 2002. Příklady z matematické analýzy, Diferenciální rovnice. Brno:,MU
  • Barták, Jaroslav, 1984. Diferenciální rovnice. Praha: PedFUK
  • Došlá, Zuzana, Novák, Vítězslav, 2002. Nekonečné řady. Brno: MU
  • Pelikán, Štěpán, Zdráhal, Tomáš, 1994. Matematická analýza, Číselné řady,posloupnosti a řady funkcí. Ústí n. L.: UJEP
  • Trench, William F., 2003. Introduction to Real Analysis. Upper Sadle River: Prentice Hall
  • Knopp, Konrad, 1957. Theory and Application of Infinite Series. London: Blackie
  • Hyslop, James M., 1965. Infinite Series. Edinburgh: Oliver and Boyd
  • Singal, M. K., Singal, A. R., 1999. A first cours in Real Analysis. New Delhi: R.Chand
  • Ross, K.A.,1980. Elementary Analysis: The Theory of Calculus. New York: Springer
  • Fischer, E., 1983. Intermediate Real Analysis. New York: Springer
Teaching methods -
Last update: RNDr. František Mošna, Ph.D. (09.09.2020)

Lecture and seminar.

Requirements to the exam -
Last update: RNDr. František Mošna, Ph.D. (06.10.2022)
    • exam requirements: Students' skills will be checked already during the semester in the form of control tests focused on solving differential equations, deciding on convergence, uniform convergence and using the theory to calculate sums of series and limits (the tests consist of examples published in the materials on Moodle). The oral part of the exam is aimed at understanding the discussed concepts, relationships and contexts and usually consists of three questions (the first question examines a concept, definition, statement, context, introduction..., in the second question the student has to decide on the validity of the presented statement and his justify or support a decision with a counterexample, the third question refers to some kind of inference, proof, problem solving, etc.)
Syllabus -
Last update: RNDr. František Mošna, Ph.D. (09.09.2020)
  • 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.