# 714-0866/01 – Mathematics 1 (Math 1)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor RNDr. Jan Kotůlek, Ph.D. Subject version guarantor RNDr. Jan Kotůlek, Ph.D. Study level undergraduate or graduate Study language English Year of introduction 2009/2010 Year of cancellation 2019/2020 Intended for the faculties USP, FBI, FS, FEI, FMT, HGF, FAST Intended for study types Bachelor
Instruction secured by
BEL10 Mgr. Jana Bělohlávková
KOT31 RNDr. Jan Kotůlek, Ph.D.
ZID76 Mgr. Arnošt Žídek, 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

Goals After completing this course, students should have the following skills: * Use rules of differentiation to differentiate functions. * Sketch the graph of a function using asymptotes, critical points. * Apply differentiation to solve problems. * Solve a system of linear algebraic equations. * Work with basic objects in three dimensional Euclidean space.

### Teaching methods

Lectures
Individual consultations
Tutorials

### Summary

Course description I. Calculus. Function of one variable (basic notions, inverse function, elementary functions); Limits and Continuity of a function; Differentiation of a function (differentiation rules, application, L'Hospital's rule). II. Linear algebra. Vector spaces; Matrices and determinants; Systems of linear algebraic equations (Gaussian elimination, Frobeniu theorem). III. Introduction to analytic geometry (lines and planes in E3, intersection, distance, angle).

### Compulsory literature:

Neustupa J.: Mathematics I. ČVUT, Praha 2004. Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0. Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.

### Recommended literature:

Neustupa J.: Mathematics I. ČVUT, Praha 2004. Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0 Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.

### Way of continuous check of knowledge in the course of semester

Passing the course, requirements 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 (in Czech)

### Other requirements

There is no further requirements.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Program of lectures -------------------------------------------------- 1 Linear algebra. Operations with matrices. Determinants. Properties of determinants. 2 Rank of a matrix. Inverse matrix. 3 Solution of linear equations. Frobenius theorem. Cramer's rule. 4 Gaussian elimination algorithm. 5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous, even, odd, periodic. One-to-one function, inverse and composite functions. 6 Elementary functions. 7 Limit of a function. Continuous and discontinuous functions. 8 Differential calculus of one variable. Derivative of a function, its geometrical and physical applications. Rules of differentiation. 9 Derivatives of elementary functions. 10 Differential functions. Derivative of a function defined parametrically. Derivatives of higher orders. L'Hospital's rule. 11 Use of derivatives to detect monotonicity, convexity and concavity features. 12 Extrema of functions. Asymptotes. Graph of a function. 13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties. 14 Equation of a line. Equation of a plane. Relative positions problems. Metric or distance problems. Program of exercises and seminars: -------------------------------------------------- 1 Basic operations with matrices. Determinants. Calculation of determinant developing the elements of any series. 2 Rank of matrix, inverse matrix. 3 Solution of linear equations. 4 Solution of systems of linear equations. 5 1. test (calculate determinant, rank of matrix, solution of the system, the inverse matrix). 6 Functions of a simple, inverse, compound. Elementary functions. Trigonometric functions. 7 2.test (domain, inverse function). Limits of functions. 8 Differentiation of functions. 9 Derivations and differential, equations of tangents and normals point functions. 10 Calculation of the limit L'Hospital rule functions. Extremes of function. 11 Convex and concave function, inflection point. 12 3.test (derivative of the function, use). Asymptotes of the curve. A function. 13 Analytic geometry. 14 Reserve and credits.

### 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.ZaměřeníFormStudy language Tut. centreYearWSType of duty

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS - MechEng - Bachelor Studies 2019/2020 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Bachelor Studies 2018/2019 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FBI_ECTS 2018/2019 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
FMMI 2018/2019 Full-time English Compulsory 601 - Study Office stu. block
ECTS FCE Bc-Mgr 2018/2019 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
ECTS FMG-VSB 2018/2019 Full-time English Optional 501 - Study Office stu. block
ECTS - MechEng - Bachelor Studies 2017/2018 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FBI_ECTS 2017/2018 Full-time English Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
USP 2017/2018 Full-time English Optional USP - University Study Programmes stu. block
FBI_ECTS 2017/2018 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
ECTS FCE Bc-Mgr 2017/2018 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
FMMI 2017/2018 Full-time English Compulsory 601 - Study Office stu. block
ECTS FMG-VSB 2017/2018 Full-time English Optional 501 - Study Office stu. block
ECTS - MechEng - Bachelor Studies 2016/2017 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FMMI 2016/2017 Full-time English Compulsory 601 - Study Office stu. block
ECTS FCE Bc-Mgr 2016/2017 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
FBI_ECTS 2016/2017 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
USP 2016/2017 Full-time English Optional USP - University Study Programmes stu. block
ECTS FMG-VSB 2016/2017 Full-time English Optional 501 - Study Office stu. block
USP 2015/2016 Full-time English Optional USP - University Study Programmes stu. block
V - ECTS - VSB 2015/2016 Full-time English Optional 401 - Study Office stu. block
FMMI 2015/2016 Full-time English Compulsory 601 - Study Office stu. block
ECTS - MechEng - Bachelor Studies 2015/2016 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FBI_ECTS 2015/2016 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
ECTS FMG - VSB 2015/2016 Full-time Czech Optional 501 - Study Office stu. block
V - ECTS - VSB 2014/2015 Full-time Czech Optional 401 - Study Office stu. block
FBI_ECTS 2014/2015 Full-time Czech Optional 010 - Faculty of Safety Engineering - Dean's Office stu. block
FMMI_N 2014/2015 Full-time Czech Compulsory 601 - Study Office stu. block
USP 2014/2015 Full-time Czech Optional USP - University Study Programmes stu. block
O - ECTS FMG - Bc. 2014/2015 Full-time Czech Optional 501 - Study Office stu. block
ECTS - MechEng 2014/2015 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block
V - ECTS - VSB 2013/2014 Full-time Czech Optional 401 - Study Office stu. block
O - ECTS FMG - Bc. 2013/2014 Full-time Czech Optional 501 - Study Office stu. block
USP 2013/2014 Full-time Czech Optional USP - University Study Programmes stu. block
FMMI 2013/2014 Full-time Czech Compulsory 601 - Study Office stu. block
ECTS - MechEng 2013/2014 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng 2012/2013 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block
O - ECTS FMG - Bc. 2012/2013 Full-time Czech Optional 501 - Study Office stu. block
FMMI 2012/2013 Full-time Czech Compulsory 601 - Study Office stu. block
USP 2012/2013 Full-time Czech Optional USP - University Study Programmes stu. block
V - ECTS - bc. 2011/2012 Full-time Czech Optional 401 - Study Office stu. block

### Assessment of instruction

Předmět neobsahuje žádné hodnocení.