Course detail

Mathematical Analysis 1

FIT-IMA1Acad. year: 2022/2023

Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

doc. RNDr. Dana Hliněná, Ph.D.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

The ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.

Prerequisites

secondary school mathematics

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Written tests during the semester (maximum 20 points).

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The main goal of the course is to explain the basic principles and methods of calculus. The emphasis is put on handling the practical use of these methods for solving specific tasks.

Specification of controlled education, way of implementation and compensation for absences

Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Basic literature

Not applicable.

Recommended reading

Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966. (CS)

Classification of course in study plans

  • Programme BIT Bachelor's 1 year of study, summer semester, compulsory
  • Programme BIT Bachelor's 1 year of study, summer semester, compulsory

  • Programme IT-BC-3 Bachelor's

    branch BIT , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.
doc. RNDr. Dana Hliněná, Ph.D.

Syllabus

  1. The concept of a function of a real variable, properties of functions and basic operations with functions.
  2. Elementary functions of a real variable.
  3. Limit and continuity of a function. Limit of a sequence.
  4. Derivative and a differential of a function.
  5. Higher-order derivatives. Taylor polynomial. Extrema of a function.
  6. Graph properties.
  7. Interpolation and approximation.
  8. Numerical solutions of equations.
  9. Indefinite integral, basic methods of integration.
  10. Definite Riemann integral, its applications.
  11. Improper integral.
  12. Numerical integration.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.
Mgr. Irena Hlavičková, Ph.D.
doc. RNDr. Dana Hliněná, Ph.D.
Ing. Michal Fusek, Ph.D.
Mgr. Martin Tůma, Ph.D.

Syllabus

Problems discussed at numerical classes are chosen so as to complement suitably the lectures.

E-learning texts

Krupková, Fuchs: Matematická analýza pro FIT
Ima.pdf 5.29 MB
Fajmon, Hlavičková, Novák, Vítovec: Numerická matematika a pravděpodobnost
Inm.pdf 2.79 MB
Kolářová: Matematika 1 - Sbírka úloh
Matematika_1_sbirka.pdf 0.45 MB
Novák: Matematika 3 - Sbírka příkladů z numerických metod
Matematika_3_num.pdf 0.28 MB