SubjectsSubjects(version: 877)
Course, academic year 2020/2021
  
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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
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
K//Is co-requisite for: NMAX056, NMAI056
XP//In complex pre-requisite: MC260P01M, MZ370P19
XK//Is complex co-requisite for: MC260P112, MC260P28
Annotation -
Last update: Mgr. Jan Kynčl, Ph.D. (03.05.2019)
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
Course completion requirements -
Last update: Irena Penev, Dr. (02.03.2020)

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).

For tutorials by I. Penev the requirements for obtaining tutorial credit are as follows: (1) score at least 40% combined on weekly/biweekly homework and quizzes (homework and quizzes are worth 50% each); and (2) score at least 70% on the test that will be given at the end of the semester.

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

Literature -
Last update: doc. RNDr. Martin Klazar, Dr. (26.11.2012)

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.

Requirements to the exam -
Last update: Irena Penev, Dr. (02.03.2020)

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.

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

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).

 
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