SubjectsSubjects(version: 950)
Course, academic year 2023/2024
Mathematics I - N431022
Title: Matematika I
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
Actual: from 2008
Semester: both
Points: 9
E-Credits: 9
Examination process:
Hours per week, examination: 3/4, C+Ex [HT]
Capacity: winter:unknown / unknown (1500)
summer:unknown / unknown (1500)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
For type:  
Old code: M1
Note: you can enroll for the course repeatedly
you can enroll for the course in winter and in summer semester
Guarantor: Klíč Alois prof. RNDr. CSc.
Janovská Drahoslava prof. RNDr. CSc.
Simerská Carmen doc. RNDr. CSc.
Interchangeability : Z413002
Examination dates   Schedule   
Annotation -
Last update: SMIDOVAL (23.05.2008)
Course is designed to enable a student to appreciate mathematics and its application to numerous disciplines. It develops and strengthens the concepts and skills of elementary mathematics, particularly skills related to various disciplines of the curriculum. It covers various topics of mathematics that are both conceptual and practical.
Literature - Czech
Last update: SMIDOVAL (23.05.2008)

Klíč, Hapalová: Úvod do studia matematiky na VŠCHT, skripta, VŠCHT Praha, 1997

Klíč a kol.: Matematika I ve strukturovaném studiu, skripta, VŠCHT Praha, 2004

Petáková: Matematika - příprava k maturitě a k přijímacím zkouškám na vysoké školy, Prométheus, 2005

Heřmánek a kol.: Sbírka příkladů k Matematice I ve strukturovaném studiu, skripta, VŠCHT Praha, 2005

Míčka a kol.: Sbírka příkladů z matematiky, skripta, VŠCHT Praha, 2002

Krajňáková, Míčka, Machačová: Zbierka úloh z matematiky, Alfa a SNTL, 1988

Porubský: Fundamental Mathematics for Engineers, Vol.I, VŠCHT, 2001

Syllabus -
Last update: SMIDOVAL (23.05.2008)

1. Elements of Mathematical Logic. Introduction to calculus

2. Continuity and limits of the functions of one and two variables.

3. Derivatives, Mean value theorem, L’ Hospital’s rule. Partial derivatives.

4. Monotone functions, extreme values of a function, asymptotes of the graph.

5. Newton’s methods. Taylor’s formula with remainder. Differential.

6. Curves in plane, tangent vector. Polar coordinates.

7. Antiderivative. Definite integral. Geometric and physical applications.

8. Techniques of integration.

9. Improper integrals. Numerical integration. The mean value theorem for integrals.

10.Ordinary differential equations of the first order. Separable equations. Euler’s method.

11.Linear differential equations of the first order and their applications.

12.The space R^n , geometry in R^3, vectors, dot and cross products.

13.Matrices and Determinants. Inverse matrix.

14.The systems of linear algebraic equations. Gauss-Jordan method. Cramer’s rule.