230-0401/01 – Bachelor Mathematics I (BM I)

Gurantor departmentDepartment of MathematicsCredits5
Subject guarantorMgr. Dagmar Dlouhá, Ph.D.Subject version guarantorMgr. Dagmar Dlouhá, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesHGFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
TUZ006 RNDr. Michaela Bobková, Ph.D.
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
KRC23 Mgr. Jitka Krčková, Ph.D.
STA50 RNDr. Jana Staňková, Ph.D.
URB0186 RNDr. Zbyněk Urban, Ph.D.
VOL18 RNDr. Jana Volná, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Individual consultations
Tutorials

Summary

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.

Compulsory literature:

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 http://mdg.vsb.cz/portal/en/Mathematics1.pdf

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

Course-credit - participation on tutorials is obligatory, 20% of absence can be apologized, - elaborate 2-3 programs, - pass the written 3 tests, conditions satisfying for 5 points, tests for 0 - 15 points.

E-learning

http://www.studopory.vsb.cz http://mdg.vsb.cz

Další požadavky na studenta

Basic knowledges and thematic orientation in:

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1 Functions of one real variable (definitions and basic properties) 2 Elementary functions 3 Limit of the function, continuity of the functions , basic rules 4 Differential calculus functions of one real variable. the derivative of function (basic rules for differentiation). 5 Derivatives of selected functions 6 Differential of the function, Taylor polynom, parametric differentiation, highes-order derivative, L'Hospital rule 7 Applications of the derivatives, convexity and concavity of a function 8 Extremes of function, asmptotes, function graph constructing 9 Linear algebra: Vectors, linear independence. Matrices (basic properties) 10 Determinants (basic properties, calculation, evaluation) 11 Rank of matrix, matrix inversion 12 Systems of linear equations, Frobenius theorem, Gaussian elimination 13 Products of vectors (basic properties) 14 Line and plane equation in E3, mutual positions of lines and planes

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80 (80) 30
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

Show history

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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner