Mathematics I - N413022
Title: Matematika I
Guaranteed by: Department of Mathematics (413)
Actual: from 2020
Semester: both
Points: 9
E-Credits: 9
Examination process:
Hours per week, examination: 3/4 C+Ex [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Is provided by: B413001
For type:  
Old code: M1
Note: you can enroll for the course in winter and in summer semester
Guarantor: Janovská Drahoslava prof. RNDr. CSc.
Turzík Daniel doc. RNDr. CSc.
Simerská Carmen doc. RNDr. CSc.
Class: Předměty pro matematiku
Z//Is interchangeable with: AB413001, B413001
XP//In complex pre-requisite: AB413003, B413003
Examination dates   Schedule   
This subject contains the following additional online materials
Annotation -
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)
Basic course in Calculus for students in bachelor program. It provides mathematical skills necessary for other subjects (physics, physical chemistry,...) in bachelor program. Success in Mathematics I is a prerequisite for Mathematics II.
Aim of the course -
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

General skills:

1. basic mathematical terms

2. knowledge and understanding of basic algorithms

3. individual problem solving

4. basic mathematical background for formulation and solving of natural and engineering problems

5. numerical algorithms (algebraic equations, integration).

Literature -
Last update: KNOBLOCL (17.12.2015)

A: Porubský: Fundamental Mathematics for Engineers, Vol.I, VŠCHT, 2001, ISBN: 80-7080-418-1

Learning resources -
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

Teaching methods -
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

Lectures and seminars

Requirements to the exam - Czech
Last update: Turzík Daniel doc. RNDr. CSc. (13.06.2017)

K udělení zápočtu je nutné splnit dva kontrolní testy v průběhu semestru nebo úspěšně absolvovat souhrnný test. Další podmínkou k udělení zápočtu je i vyplnění vstupního testu. Zkouška je kombinovaná - písemná a ústní. Bližší informace viz

Syllabus -
Last update: Dubcová Miroslava RNDr. Ph.D. (04.11.2014)

1. Functions of one real variable. Domain and range, graphs and basic properties of real functions of one variable.

2. Inverse function, composition of functions. Elementary functions, exponential, logarithmic, trigonometric and inverse trigonometric functions.

3. Continuity of functions. Basic theorems on continuous functions. Limit of functions and sequences.

4. Definition of derivative. Geometrical and physical meaning of the derivative. Basic rules for derivatives. Derivatives of elementary functions. Differential of a function.

5. Mean value theorem and its applications, L' Hospital's rule. Taylor's formula.

6. Monotone functions, extreme values of a function, asymptotes of the graph. Newton's method for the solution of the equation f(x)=0.

7. Parametric curves, vector tangent to curve, application in Physics.

8. Antiderivative and its property. Newton's definite integral, its properties and geometrical meaning. Numerical integration - trapezoidal rule

9. Techniques of integration. Integration by parts, substitution.Integration of rational functions. Improper integrals.

10. Definition of Riemann definite integral. The mean value theorem for integrals.

11. Differential equations, basic notions, method of separation and variation of constant. Euler's method.

12. Vectors and matrices. Linear independence of the system of vectors, rank of the matrix. Determinants. Systems of linear algebraic equations. Cramer's rule.

13. Linear differential equations of the first and second order with constant coefficients and a particular right hand side and their solution.

14. Functions of two real variables, domain, graph, partial derivative, tangent plane, total differential

Registration requirements -
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

No requirements

Teaching methods
Activity Credits Hours
Konzultace s vyučujícími 0,5 14
Účast na přednáškách 1,5 42
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 3 84
Příprava na zkoušku a její absolvování 2 56
Účast na seminářích 2 56
9 / 9 252 / 252
Coursework assessment
Form Significance
Regular attendance 10
Examination test 35
Continuous assessment of study performance and course -credit tests 20
Oral examination 35