Mathematics I - N413002
Title: Matematika I
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: winter
Points: winter s.:9
E-Credits: winter s.:9
Examination process: winter s.:
Hours per week, examination: winter s.:3/3 C+Ex [hours/week]
Capacity: unknown / unknown (1500)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
Is provided by: B413001
For type:  
Old code: M1
Guarantor: Turzík Daniel doc. RNDr. CSc.
Janovská Drahoslava prof. RNDr. CSc.
Simerská Carmen doc. RNDr. CSc.
Class: Předměty pro matematiku
Interchangeability : N413022, Z413002
Z//Is interchangeable with: B413001, N413022
Examination dates   
Annotation -
Last update: TAJ413 (13.10.2009)
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: TAJ413 (13.09.2011)

Turzík, Dubcová, Pavlíková: Základy matematiky pro bakaláře, skripta, VŠCHT Praha, 2011

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

Pavlíková, Schmidt: Základy matematiky, VŠCHT Praha, 2006

E-sbírka příkladů pro předmět Matematika I, http://www.vscht.cz/mat/sbirka/sbirka1.html

Syllabus -
Last update: TAJ413 (13.09.2011)

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. Drawing of the graph.

7. Newton’s method for the solution of the equation f(x)=0.

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

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

13.The space R^n. Distance in R^n. Dot and cross products. Analytic geometry in R^3.

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