714-0566/04 – Bachelor Mathematics I (BM I)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorMgr. Dagmar Dlouhá, Ph.D.Subject version guarantorMgr. Dagmar Dlouhá, Ph.D.
Study levelundergraduate or graduate
Study languageEnglish
Year of introduction2016/2017Year of cancellation
Intended for the facultiesHGFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DRO03 Mgr. Jaroslav Drobek, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Credit and Examination 18+0

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

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 at least on 8 of 18 hours condition satisfying for 5 points, more participation for 0 - 15 points. Summary course classification: 5-20 points. Exam Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtainsat least 5 points. Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0 ECTS grade A B C D E F Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0 National grading scheme excellent very good satisfactory failed

E-learning

http://www.studopory.vsb.cz http://mdg.vsb.cz http://mdg.vsb.cz/wiki/public/ZM_MI_listy.pdf

Další požadavky na studenta

No more requirements.

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0565 ZM Basics of Mathematics Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Functions of one real variable (definitions and basic properties). Elementary functions. Limit of the function, continuity of the functions, basic rules. 2. Differential calculus of functions of one real variable: The derivative of a function (basic rules for differentiation). Derivatives of selected functions. Differential of the function. Taylor polynom. Parametric differentiation. Highes-order derivative. Applications of the derivatives. Monotonic functions and extremes of function, convexity and concavity of a function. 3. Linear algebra: Vectors, linear independence. Matrices (basic properties), determinants (basic properties, calculation, evaluation). Matrix inversion. Systems of linear equations, Cramer’s rule. Gaussian elimination 4. Analytical geometry in E3: Product of vectors (basic properties).

Conditions for subject completion

Combined form (validity from: 2016/2017 Summer 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
                Written examination Written examination 60  25
                Verbal examination Oral examination 20  5
Mandatory attendence parzicipation: presence on lectures

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