Course detail

# Mathematical Analysis 1

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

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.

Recommended optional programme components

Not applicable.

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Written tests during the semester (maximum 30 points).

Exam prerequisites:
At least 10 points from the tests during the semester.

Language of instruction

Czech, English

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.

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Concept of a function of a real variable, properties of functions and basic operations with functions.
2. Elementary functions of a real variable.
3. Complex numbers. Functions of a complex variable.
4. Limit of a sequence. Limit and continuity of a function.
5. Differential calculus of functions of one variable. Derivative at a point, derivative in an interval, differential of a function. Numerical differentiation.
6. Second derivative. Extrema of a function.
7. Graph properties.
8. Taylor theorem. Approximation of functions.
9. Newton and Lagrange interpolation.
10. Numerical solutions of nonlinear equations.
11. Integral calculus of functions of one variable. Indefinite integral, basic methods of integration.
12. Definite Riemann integral, its applications.Numerical integration.
13. Improper integral.

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer

E-learning texts

Krupková, V., Fuchs, P., Matematická analýza pro FIT (cs)
Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J., Numerická matematika a pravděpodobnost (cs)
Kolářová, E., Matematika 1 - sbírka úloh (cs)
Krupková, V., Matematický seminář pro FIT (cs)

eLearning