Course detail

Mathematical Analysis 1

FIT-IMA1Acad. year: 2024/2025

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)

Entry knowledge

Secondary school mathematics.

Rules for evaluation and completion of the course

Written tests during the semester (maximum 20 points). Classes are compulsory. Presence at lectures will not be controlled, absence at numerical classes has to be excused.

Aims

The main goal of the course is to explain the basic principles and methods of calculus. The emphasis ismput on handling the practical use of these methods for solving specific tasks and the ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.

Study aids

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

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

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