310-2210/01 – Basic Mathematics (ZM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits7
Subject guarantorMgr. Jiří Vrbický, Ph.D.Subject version guarantorMgr. Jiří Vrbický, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC76 Mgr. Jiří Krček
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+3

Subject aims expressed by acquired skills and competences

The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems,suggest a method of solution, analyze correctness of achieved results with respect to given conditions.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

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 Differential Calculus of Functions of Several Variables: The definition of functions of two and several variables, the domain of definition. The partial derivations of the first and higher orders. The Indefinite Integral: An indefinite integral and a primitive function. Basic formulas. Integration by parts. The method of substitution.

Compulsory literature:

James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

Recommended literature:

[1] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

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 programs, -pass the written tests, Point 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 obtains at 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/M/

Other requirements

No special requirements.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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. 14 Integration methods - substitution, integration by parts.

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
                písemka Written test 60  25
                teorie Oral examination 20  5
Mandatory attendence parzicipation: 80%

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (B0214A270001) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0214A270001) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0214A270001) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner