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Calculus III - OKB2310N05

Title:	Matematická analýza III
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2022
Semester:	winter
E-Credits:	5
Examination process:	winter s.:
Hours per week, examination:	winter s.:0/0, C+Ex [HT]
Extent per academic year:	17 [hours]
Capacity:	unknown / unknown (999)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	combined
Teaching methods:	combined
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 :	OKB2310N04
Interchangeability :	OKB2310209

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: RNDr. František Mošna, Ph.D. (13.09.2017)

Differential equations (especially linear 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. (10.09.2020)

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. (13.09.2017)

Lecture and seminar.

Requirements to the exam -

Last update: RNDr. František Mošna, Ph.D. (10.09.2020)

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.)

In the case of the application of distance learning, the form of teaching can be modified by more extensive homework (assigned using LMS Moodle), elements of self-study and communication by e-mail. Also, the form of completion of the course may undergo changes.

Syllabus -

Last update: RNDr. František Mošna, Ph.D. (13.09.2017)

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.