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Course, academic year 2023/2024
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Mathematical Analysis 1 - NMAI054
Title: Matematická analýza 1
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
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
Guarantor: doc. RNDr. Martin Klazar, Dr.
doc. Mgr. Robert Šámal, Ph.D.
Class: Informatika Bc.
Classification: Mathematics > Real and Complex Analysis
Is co-requisite for: NMAX056, NMAI056
In complex pre-requisite: MC260P01M, MZ370P19
Is complex co-requisite for: MC260P112, MC260P28
Annotation -
The first part of the mathematical analysis course for students of computer science, an introduction to the continuous world description, especially one-dimensional. Students will learn to compute limits of sequences and functions, to determine and to use continuity of functions, to calculate and to use derivatives and also the basics of integral calculus - all for the functions of one variable. In 2019/20, the course is being taught in both semesters. The winter semester variant is offered to students who started their studies in 2018/19, or earlier. In the summer edition, the
Last update: Kynčl Jan, doc. Mgr., Ph.D. (03.05.2019)
Course completion requirements -

The credit will be given for active participation in tutorials, homeworks and successful completion of tests, the exact weight of each of these criteria is determined by the TA (M. Tyomkyn).

The exam will be written. Obtaining the credit is necessary before the final exam.

Last update: Klazar Martin, doc. RNDr., Dr. (16.02.2022)
Literature -

T. M. Apostol, Mathematical Analysis, Addison-Wesley, 1974 (2nd edition).

Ch. Ch. Pugh, Real Mathematical Analysis, Undergraduate Text in Mathematics, Springer, 2002.

T. Tao, Analysis I, Hindustan Book Agency, 2006.

T. Tao, Analysis II, Hindustan Book Agency, 2006.

V. A. Zorich, Mathematical Analysis I, Universitext, Springer, 2004.

V. A. Zorich, Mathematical Analysis II, Universitext, Springer, 2004.

Last update: Klazar Martin, doc. RNDr., Dr. (26.11.2012)
Requirements to the exam -

For the English section of the course, there will be a written exam. Students must obtain tutorial credit in order to take the exam. The material for the exam corresponds to the syllabus to the extent to which topics were covered during lectures and tutorials. Ability to generalize and apply theoretical knowledge to solving problems will be required.

Last update: Penev Irena, Ph.D. (02.03.2020)
Syllabus -

Real numbers and their relation to rationals, complex numbers.

Sequences of real numbers: Basic properties of limit, bulk points, liminf and limsup. (Bolzano-Weierstrass theorem, limits of monotone sequences, etc.)

Informative series of real numbers.

Basic properties of functions (monotonicity, convexity, ...), definition by a series, basic approximations.

Function limits: methods of calculation.

Continuity of functions: extreme value theorem, intermediate value theorem.

Derivatives of functions: methods of calculation, usage - l'Hospital's rule, mean-value theorem, graphing a function. Taylor's polynomial.

Introduction to integral calculus: Newton integral (and methods of calculation), Riemann integral, applications (areas, volumes, lengths, estimates of sums).

Last update: Töpfer Pavel, doc. RNDr., CSc. (26.01.2018)
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