# 714-0660/01 – Basic Mathematics (ZM)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 7 Subject guarantor Mgr. Jiří Vrbický, Ph.D. Subject version guarantor Mgr. Jiří Vrbický, Ph.D. Study level undergraduate or graduate Study language Czech Year of introduction 1999/2000 Year of cancellation 2013/2014 Intended for the faculties FMT Intended for study types Bachelor
Instruction secured by
OND10 Mgr. Ivana Onderková, Ph.D.
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

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 to analyze 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
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:

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X

### Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1 James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 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/

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

Conditions for completion are defined only for particular subject version and form of study

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2013/2014 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2109) Metallurgical Engineering (2109R031) Art Foundry Engineering P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2113) Materiálové technologie (2109R031) Artistic Foundry P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2113) Materiálové technologie (2109R031) Artistic Foundry P Czech Ostrava 1 Compulsory study plan
2002/2003 (B2113) Materiálové technologie (2109R031) Artistic Foundry P Czech Ostrava 1 Compulsory study plan
2001/2002 (B2113) Materiálové technologie (2109R031) Artistic Foundry P Czech Ostrava 1 Compulsory study plan
2000/2001 (B2113) Materiálové technologie (2109R031) Artistic Foundry P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner