SubjectsSubjects(version: 945)
Course, academic year 2023/2024
   Login via CAS
Mathematical analysis for teachers - OKBM4M044A
Title: Matematická analýza pro učitele
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2022
Semester: summer
E-Credits: 5
Examination process: summer s.:
Hours per week, examination: summer s.:0/0, Ex [HT]
Extent per academic year: 14 [hours]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: 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: prof. RNDr. Ladislav Kvasz, DSc., Dr.
Teacher(s): RNDr. František Mošna, Ph.D.
Is pre-requisite for: OKBM4M061A
Annotation -
Last update: RNDr. František Mošna, Ph.D. (30.01.2023)
Basics of integral calculus, differential equations, infinite series and sequences, and series of functions.
Aim of the course -
Last update: RNDr. František Mošna, Ph.D. (30.01.2023)

The primary goal of the course is to make students acquainted with the basics of integral calculus, with methods of solving and applications of differential equations, as well as with basic concepts, knowledge and contexts related to series and functional sequences and series. A secondary goal is to review, review and consolidate knowledge from previous courses in mathematical analysis.

Descriptors -
Last update: RNDr. František Mošna, Ph.D. (31.01.2023)

lecture 2 hours per week, 24 hours in total

seminars 1 hour per week, 12 hours in total

preparation for seminars 1 hour per week, 12 hours in total

reading mathematical literature 24 h

homework - 8 h

expected total time load of students - 80 h

Literature -
Last update: RNDr. František Mošna, Ph.D. (30.01.2023)

basic: 

Veselý, Jiří: Matematická analýza pro učitele I, II. Matfyzpress, Praha 1997

Mošna, František: Obyčejné diferenciální rovnice, PedFUK Praha 2019

Došlá, Zuzana, Novák, Vítězslav: Nekonečné řady, MU Brno 2002

others:

Jarník, V.: Integrální počet I, II. Academia, Praha 1984

Děmidovič, B. P.: Sbírka úloh a cvičení z matematické analýzy. Fragment, Praha 2004

Kalas, Josef, Ráb, Miloš: Obyčejné diferenciální rovnice, MU Brno 2001

Kalas, Josef, Pospíšil, Zdeněk: Spojité modely v biologii, MU Brno 2001

Ráb, Miloš: Metody řešení obyčejných diferenciálních rovnic, MU Brno 2012

Plch, Roman: Příklady z matematické analýzy, Diferenciální rovnice, MU Brno 2002

Barták, Jaroslav: Diferenciální rovnice, Praha 1984

Pelikán, Štěpán, Zdráhal, Tomáš: Matematická analýza, Číselné řady, posloupnosti a řady funkcí, UJEP Ústí n. L. 1994

Requirements to the exam -
Last update: RNDr. František Mošna, Ph.D. (13.02.2023)
The exam consists of written and oral parts. The written part will focus on students' numerical knowledge and will include examples for calculating integrals, solving differential equations, deciding on convergence, uniform convergence and using the theory to calculate sums of series and limits. It will be possible for students to complete the written part already during the semester in the form of tests. 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. (30.01.2023)

Integral calculus - antiderivative, indefinite integral, calculation methods, Newton's and Riemann's definite integral, basic theorem of integral calculus Newton - Leibniz formula.

Differential equation - existence, unicity of solution of differential equations, methods of solving (separation of variables, linear differential equations, variation of a constant), use of differetial equations.

Series - convergence criteria (comparative, integral, quotient, square root, Leibniz), absolute convergence, sums of series.

Sequences and series of functions - uniform convergence of sequences and series, Weierstrass criterion, power series, expansion of basic functions in power series, using for calculating limits.

Learning resources - Czech
Last update: doc. RNDr. Antonín Jančařík, Ph.D. (28.09.2019)

https://dl1.cuni.cz/course/view.php?id=8039

 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html