310-2117/03 – Mathematics 1 (M1)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits6
Subject guarantorRNDr. Jan Kotůlek, Ph.D.Subject version guarantorRNDr. Jan Kotůlek, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageEnglish
Year of introduction2021/2022Year of cancellation
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
JAH0037 Mgr. Monika Jahodová, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+4

Subject aims expressed by acquired skills and competences

Mathematics is an essential part of the engineering programmes. Nevertheless, it is not a a goal on its own, but rather a necessary tool for understanding the technical subjects. Therefore, we aim to both introducing the basic mathematical concepts and deepen the logical and analytical thinking of our students.

Teaching methods

Individual consultations
Other activities


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 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:

BIRD, J. O. Higher engineering mathematics. Eighth edition. London: Routledge, Taylor & Francis Group, 2017. ISBN 978-1-138-67357-1. NEUSTUPA, Jiří. Mathematics. 2. Vyd. Praha: Vydavatelství ČVUT, 2004. ISBN 80-01-02946-8. BĚLOHLÁVKOVÁ, Jana, Jan KOTŮLEK, Worksheets for Mathematics I. 1. vyd. Ostrava: VŠB-TUO, 2020.

Recommended literature:

ANDREESCU, Titu. Essential linear algebra with applications: a problem-solving approach. New York: Birkhäuser, [2014]. ISBN 978-0-8176-4360-7. HARSHBARGER, Ronald J. a REYNOLDS, James J. Calculus with applications. 2nd ed. Lexington: D.C. Heath, 1993. xiv, 592 s. ISBN 0-669-33162-7. James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

Way of continuous check of knowledge in the course of semester

Written and oral exam.



Other requirements

The exam consists of the following three parts: Computation of the derivatives of elementary functions (5 tasks, 15 minutes), the practical part (6 problems, 60 minutes, maximum 60 points) and the theoretical test with 10 questions (correct answer 2 points, no answer 0 points, wrong answer -1 point). A student has to compute correctly 3 derivatives, obtain at least 25 points at the practical part and at least 5 points at the theoretical test.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1. Functions of one real variable (definitions and basic properties). 2. Elementary functions. Parametric and implicit functions. 3. Limit of the function, continuous functions. Definition of the derivative. 4-5. Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives. 6-8. Applications of the derivatives. Tangent line, Taylor polynomial, extremes of a function. Behaviour of the graph. Monotonic functions. Convex and concave functions. Inverse functions. Computation of limits by l'Hospital rule. Asymptotes. 9. Systems of linear equations, Gaussian elimination 10. Matrices, rank of a matrix. Matrix inversion 11. Determinant, its computation and properties. Cramer rule. 12. Analytic geometry in Euclidean space. Dot product and cross product 13. Line and plane in 3D-Euclidean space. 14. Mutual positions and metric properties of subspaces in 3D-Euclidean space.

Conditions for subject completion

Full-time form (validity from: 2021/2022 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80  30 3
Mandatory attendence participation: 80 % of the lessons

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Conditions for subject completion and attendance at the exercises within ISP: Two intermediate tests during the semester, attendace can be compensated by submission of homework in the form determined by the teaching assistant.

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (B0713A070003) Energetics and Environments P English Ostrava 1 Compulsory study plan
2023/2024 (B0715A270012) Engineering P English Ostrava 1 Compulsory study plan
2022/2023 (B0713A070003) Energetics and Environments P English Ostrava 1 Compulsory study plan
2022/2023 (B0715A270012) Engineering P English Ostrava 1 Compulsory study plan
2021/2022 (B0713A070003) Energetics and Environments P English Ostrava 1 Compulsory study plan
2021/2022 (B0715A270012) Engineering P English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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