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Course, academic year 2023/2024
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Mathematical analysis I - NMTM101
Title: Matematická analýza I
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: RNDr. Jakub Staněk, Ph.D.
RNDr. Martin Rmoutil, Ph.D.
Incompatibility : NMUM101
Interchangeability : NMUM101
Is incompatible with: NMUM101, NMMA111
Is pre-requisite for: NMTM262
Is interchangeable with: NMMA111, NMUM101
In complex pre-requisite: MC260P01M, MZ370P19, NMFM204, NMFM205, NMMA211, NMMA212, NMMA221, NMNM211, NMSA336
Is complex co-requisite for: MC260P112, MC260P28
Annotation -
Basic course of mathematical analysis for prospective teachers.
Last update: Staněk Jakub, RNDr., Ph.D. (14.06.2019)
Course completion requirements -

To succesfully pass the subject it is necessary to obtain "zapocet" (a necessary condition for signing to an examination) and pass the examination.

The conditions for obtaining "zapocet" consist of passing two short tests (will be announced by the teacher). The tests will consist of computation problems. Precise conditions for obtaining "zapocet" will be specified by the teacher.

Last update: Staněk Jakub, RNDr., Ph.D. (10.10.2020)
Literature -

Veselý, J. Základy matematické analýzy I. Matfyzpress, Praha, 2004.

Veselý, J. Základy matematické analýzy II. Matfyzpress, Praha, 2009.

Kopáček, J. Matematická analýza nejen pro fyziky I. Matfyzpress, Praha, 2005.

Kopáček, J. Příklady z matematiky nejen pro fyziky I. Matfyzpress, Praha, 2004.

Černý, I. Úvod do inteligentního kalkulu. Academia, Praha, 2002.

Brabec, J. a kol. Matematická analýza I. SNTL/Alfa, Praha, 1985.

Jarník, V. Diferenciální počet I. Academia, Praha, 1974.

Trench, W. F. Introduction to Real Analysis. Dostupné z http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

Hairer, E., Wanner, G. Analysis by its History. Springer, 2008.

Last update: Staněk Jakub, RNDr., Ph.D. (14.06.2019)
Requirements to the exam -

The exam consists of written and oral part. If the result is clear already based on the written part, the oral exam need not happen. Precise requirements will be in accordance with the contents of the class and will be specified in detail on the website of the lecturer (there will be a .pdf file detailing the definitions, theorems, proofs etc. that might be in the exam).

Not passing the written test means the exam is not passed as a whole and one should apply for another attempt. Not passing the oral part means the exam is not passed as a whole and one should apply for another attempt (both parts). The exam is finally assigned a mark, taking into account both parts of the exam.

Last update: Rmoutil Martin, RNDr., Ph.D. (29.10.2019)
Syllabus -

Real numbers, supremum. Sequences and their limits. Functions, elementary functions. Continuity, properties of continuous functions. Derivative, mean value theorem and its corollaries, L'Hôpital's rule, Taylor's theorem, maxima and minima. Infinite series, absolute and nonabsolute convergence, criteria of convergence.

Last update: Staněk Jakub, RNDr., Ph.D. (14.06.2019)
 
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