714-0366/01 – Mathematics I (MI)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorRNDr. Jan Kotůlek, Ph.D.Subject version guarantordoc. RNDr. Jarmila Doležalová, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction1999/2000Year of cancellation2011/2012
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BEL10 Mgr. Jana Bělohlávková
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DOL10 RNDr. Milan Doležal, CSc.
DOS14 Mgr. Marie Dostálová
DUD88 Mgr. Krista Dudková
KOT31 RNDr. Jan Kotůlek, Ph.D.
LUN44 Mgr. Milena Luňáčková, Ph.D.
MAR20 RNDr. Radmila Murcková
NIK01 Ing. Marek Nikodým, Ph.D.
OTI73 Mgr. Petr Otipka
SKN002 Ing. Petra Schreiberová, Ph.D.
SKA74 Mgr. Sylvie Skalníková
SVO19 Mgr. Ivona Tomečková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 12+4

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

The subject is divided into four chapters. In the first chapter we study real functions of one real variable and their properties, in the second chapter we introduce the notion of derivative and study its properties and applications. In the third chapter we study linear algebra. We introduce Gauss elimination method for solution of systems of linear algebraic equations. In the last chapter we apply it to the geometric problems in three-dimensional Euclidean space.

Compulsory literature:

[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003. [2] DOLEŽALOVÁ, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 [3] NEUSTUPA, J.: Mathematics I., ČVUT, Praha 2004

Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington 1990, 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 excused, -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

Další požadavky na studenta

more requierements are not

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0365 ZM Basics of Mathematics Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Syllabus of lectures 1 Linear algebra. Vector spaces, bases, dimension. 2 Matrices, rank of a matrix. 3 Determinant. Matrix inversion. 4 Systems of linear equations, Gaussian elimination 5 Analytic geometry in Euclidean space. Dot product and cross product 6 Line and plane in 3D-Euclidean space. 7 Functions of one real variable (definitions and basic properties). Inverse functions 8 Elementary functions. Parametric and implicit functions 9 Limit of the function, continuous functions 10 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives 11 Applications of the derivatives, l'Hospital rule. 12 Applications of the derivatives on the construction of the graph. Syllabus of tutorials 1 Linear algebra. Vector spaces, bases, dimension. 2 Matrices, rank of a matrix. 3 Determinant. Matrix inversion. 4 Systems of linear equations, Gaussian elimination 5 Analytic geometry in Euclidean space. Dot product and cross product 6 Line and plane in 3D-Euclidean space. 7 Functions of one real variable (definitions and basic properties). Inverse functions 8 Elementary functions. Parametric and implicit functions 9 Limit of the function, continuous functions 10 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, highes-order derivatives 11 Applications of the derivatives, l'Hospital rule. 12 Applications of the derivatives on the construction of the graph.

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
2010/2011 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2010/2011 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2010/2011 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2010/2011 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2009/2010 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering P Czech Šumperk 1 Compulsory study plan
2009/2010 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2008/2009 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (60) P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (70) P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (50) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (50) P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2002/2003 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2002/2003 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2002/2003 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2001/2002 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner