SubjectsSubjects(version: 949)
Course, academic year 2019/2020
Elementary Mathematics - B413008
Title: Základy matematiky
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
Actual: from 2019 to 2020
Semester: summer
Points: summer s.:5
E-Credits: summer s.:5
Examination process: summer s.:
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited / unlimited (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
For type: Bachelor's
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Pavlíková Pavla RNDr. Ph.D.
Interchangeability : N413019, Z413019
Examination dates   Schedule   
Annotation -
Last update: Kubová Petra Ing. (15.01.2018)
This course is designed for undergraduate students to acquire solid background in elementary mathematics. The studied topics are: properties of functions, limits, derivatives of functions of one variable, primitive functions and definite integrals. Students will become familiar with a number of applications in the field of physics and chemistry. Evaluation is based on the final written exam.
Aim of the course -
Last update: Kubová Petra Ing. (15.01.2018)

Students will be able to:

use the basic mathematical concepts to solve simple equations and inequalities,

to handle basic computations of limits, derivatives, primitive functions and definite integrals.

Literature -
Last update: Kubová Petra Ing. (15.01.2018)

R: Pavlíková P., Schmidt O.: Základy matematiky. Skripta VŠCHT Praha. ISBN 80-7080-615-X

A: Heřmánek L. a kol.: Sbírka příkladů k Matematice I ve strukturovaném studiu. Skripta VŠCHT Praha. ISBN 80-7080-688-3

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

Learning resources -
Last update: Kubová Petra Ing. (15.01.2018)

Teaching methods -
Last update: Kubová Petra Ing. (15.01.2018)

Lectures and exercise classes.

Requirements to the exam - Czech
Last update: Pavlíková Pavla RNDr. Ph.D. (30.09.2020)

Předmět je zakončen písemnou zkouškou (zkouškový test). Zápočet student získá na základě výsledků průběžných testů.

Syllabus -
Last update: Kubová Petra Ing. (15.01.2018)

1. Numeric fields. Working with fractions, percentages. Powers and roots. Polynomials, finding roots of polynomials. Absolute value of real numbers, its geometric meaning. Algebraic expressions.

2. The concept of functions of one variable, its domain, range, graph. Basic properties of functions. Elementary functions, their properties and graphs.

3. Right-angled triangle - Pythagoras, Euclid's theorems and their applications. Trigonometric functions.

4. Equations and Inequalities - equivalent and non-equivalent transformations, results verification. Linear and quadratic (without complex roots) equations and inequalities - numerical/graphical solution. Absolute value equations and inequalities. Cross-multiplication.

5. Simple exponential, logarithmic and trigonometric equations. Simple trigonometric, polynomi,al and rational inequalities.

6. Arithmetic and geometric sequences, sum of geometric series. Conversion between fractions and decimal expansions. Basics of Financial Mathematics - simple and cumulative interest.

7. Analytic geometry in plane and space: coordinates of points, the notion of vectors, vector coordinates. Description of line in R2 and of plane in R3. Algebraic, slope-intercept form and parametric description of line. Relative positions of two lines, of line and plane.

8. Limit and continuity - intuitive approach. Simple limit calculations.

9. Derivative and its practical significance. Derivatives of elementary functions.

10. Rules for finding the derivative - sum, product, and quotient rule. Applications: tangents, velocity, rates of chemical processes.

11. Properties of functions (without general asymptotes).

12. Applications of derivatives: local extremes, properties of functions.

13. Primitive functions and definite integrals, simple examples. Applications: free fall, area of a two-dimensional shape in a plane.

14. Linear algebra: systems of linear equations (without parameters), the geometric meaning.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (06.05.2019)

No requirements.

Course completion requirements - Czech
Last update: Kubová Petra Ing. (08.03.2018)

Předmět je zakončen písemnou zkouškou (zkouškový test). Zápočet student získá na základě výsledků průběžných testů.

Teaching methods
Activity Credits Hours
Konzultace s vyučujícími 0.3 7
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 0.7 20
Příprava na zkoušku a její absolvování 2 57
Účast na seminářích 1 28
5 / 5 140 / 140
Coursework assessment
Form Significance
Regular attendance 5
Examination test 70
Continuous assessment of study performance and course -credit tests 25