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Basic Mathematics

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-2210/01
Number of ECTS Credits Allocated7 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
KRC76Mgr. Jiří Krček
Summary
Linear Algebra: An algebraic vector, basic terms. A matrix, the rank of a
matrix, elementary treatments of a matrix. Systems of linear equations. A determinant, determinant properties. Foundations of the matrix calculus.
The Real-Valued Function of a Real Variable: Definition, the domain of definition, the range of values, the graph of a function. Properties of functions. Inverse, composite functions. Basic elementary functions.
The sequence of real numbers and the limit of the sequence. The limit of a function at a point. The continuity of a function.
The Derivation of a Function: Derivation definition and the geometric significance of the derivation. The derivation of basic elementary functions.
Derivation Applications: A tangent and a normal. Monotony. Local and absolute
extreme values of a function. Convexity, concavity, inflection points. Asymptotes. The behaviour of a function.
The Indefinite Integral: An indefinite integral and a primitive function. Basic formulas. Integration by parts. The method of substitution.


Learning Outcomes of the Course Unit
The goal of the cource is to introduce grounding of linear algebra, differential and integral calculus.
Course Contents
1 Linear algebra: Vectors, matrice (basic properties).
2 Determinants (basic properties, calculation, evaluation).
3 Matrix inversion.
4 Systems of linear equations, Cramer’s rule, Gaussian elimination.
5 Functions of one real variable (definitions and basic properties).
6 Elementary functions.
7 Limit of the function, continuity of the functions , basic rules.
8 Differential calculus functions of one real variable. The derivative of function (basic rules for differentiation).
9 Derivatives of selected functions.
10 Differential of the function, parametric differentiation, highes-order derivative.
11 Applications of the derivatives.
12 Monotonic functions and extremes of function, convexity and concavity of a function.
13 Integral calculus: antiderivative and indefinite integral for functions of one variable.


Recommended or Required Reading
Required Reading:
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456
Vrbenská, H., Němčíková, J.: Základy matematiky pro bakaláře I. Skriptum VŠB-TUO, Ostrava 1999. ISBN 80-7078-351-6
Vrbenská, H., Bělohlávková, J.: Základy matematiky pro bakaláře II. Skriptum VŠB-TUO, Ostrava 1998. ISBN 80-7078-545-4
Recommended Reading:
[1] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6
Burda, P.-Kreml, P.: Diferenciální počet funkcí jedné proměnné. Skriptum VŠB, Ostrava 2004. ISBN 80-248-0634-7
Burda,P.: Algebra a analytická geometrie. Skripta VŠB-TU, Ostrava 1997. ISBN 80-7078-479-2
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit20 5
        ExaminationExamination80 (80)30
                písemkaWritten test60 25
                teorieOral examination20 5