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Mathematics I

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

Course Unit Code230-0404/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites
PrerequisitiesCourse Unit CodeCourse Unit Title
230-0400Basics of Mathematics
Name of Lecturer(s)Personal IDName
DLO44Mgr. Dagmar Dlouhá, Ph.D.
JAR71Mgr. Marcela Jarošová, Ph.D.
VOL06RNDr. Petr Volný, Ph.D.
The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three basic parts of mathematics, according to which the learning material is structured. In Differential Calculus, the main motive is the preparation to general use of derivatives of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Analytic geometry, there are, based on vector calculus, described basic linear formations of three-dimensional Euclidean space and some tools to evaluate their mutual position from qualitative and also quantitative point of view.
Learning Outcomes of the Course Unit
Mathematics is essential part of education on technical universities.
It should be considered rather the method in the study of technical
courses than a goal. Thus the goal of mathematics is train logical
reasoning than mere list of mathematical notions, algorithms and
methods.Students should learn how toanalyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.
Course Contents
1. Real function of one real variable. Operations with functions. (Basic) elementary functions.
2. Properties of functions - intersections with axes, sign of function, boundary, monotonicity, extremes, convexity, concavity, parity, simplicity, invertibility, periodicity.
3. Limit of a function, limit theorems, asmyptotes to a function graph.
4. Continuity and discontinuity of function.
5. Derivative of function - geometric and physical meaning. Derivative of basic elementary functions. Differentiation rules. Derivatives of higher orders.
6. Use of derivatives - L'Hospital rule, basic theorems of differential calculus, analysis of the course of a function.
7. Function differential, Taylor polynomial.
8. Arithmetic vector space. Linear independence vectors.
9. Matrices - types, special matrices, operations.
10. Determinant. Inverse matrix. Rank.
11. Systems of linear equations. Frobenius theorem. Gaussian elimination method. Cramer rule.
12. Line and plane in Euclidean space. Scalar, vector and mixed product of vectors.
13. Line and plane equations in E3 and their relative positions.
14. Distances and deviations of basic objects in E3.
Recommended or Required Reading
Required Reading:
Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3.
Bartsch, Hans Jochen: Handbook of Mathematical Formulas.
Burdette, A.C.:An Introduction to Analytic Geometry and Calculus,Academic Press,1973.
Burda, P., Havelek, R., Hradecká, R., Kreml.P: Matematika I, Učební texty VŠB-TU Ostrava, ISBN 978-80-248-1296-0.
Burda, P., Havelek, R., Hradecká, R.: Algebra a analytická geometrie (Matematika I), učební texty VŠB – TU Ostrava, 1997, ISBN 80-7078-479-2.
Leon, S. J.: Linear Algebra with Applications. MACMILLAN New York, 1980, ISBN 0-02-369810.
Recommended Reading:
Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1.
Leon, S., J.: Linear Algebra with Aplications, Macmillan Publishing Company, New York, 1986, ISBN 0-02-369810-1.
Jain, P.K.:A Textbook of Analytical Geometry of Three Dimensions,New Age International Publisher,1996.
Moore,C: Math quations and inequalities, Science & Nature, 2014.
Škrášek, J. a kol.: Základy aplikované matematiky I. a II. SNTL, Praha 1989, IISBN 04-0544-89.
Burda, P., Kreml, P.: Diferenciální počet funkcí jedné proměnné. Matematika IIa. Učební texty VŠB - TUO, 2004, ISBN 80-248--0634-7.
Bouchala J.: Matematická analýza 1. Učební texty VŠB – TUO, Ostrava, 1998, ISBN 80-
Bartsch, Hans Jochen: Handbook of Mathematical Formulas.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials
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
                Písemná zkouškaWritten test60 25
                Ústní zkouškaOral examination20 5