310-2301/01 – Mathematics 1 (Math 1)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorRNDr. Jan Kotůlek, Ph.D.Subject version guarantorRNDr. Jan Kotůlek, Ph.D.
Study levelundergraduate or graduate
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesHGF, FMT, FS, USP, FEI, FBI, FASTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
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

Individual consultations


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


http://www.studopory.vsb.cz (in Czech)

Další požadavky na studenta

There is no further requirements.


Subject has no prerequisities.


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

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  30
Mandatory attendence parzicipation: 80% of seminars

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS - MechEng - Bachelor Studies 2020/2021 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS FCE Bc-Mgr 2019/2020 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
Additional Subjects 2019/2020 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FMST 2019/2020 Full-time English Compulsory 601 - Study Office stu. block