310-2117/02 – 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
Year1Semesterwinter
Study languageCzech
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.
LAM0028 RNDr. Alžběta Lampartová
MUL0086 RNDr. PhDr. Ivo Müller, Ph.D.
RIE0053 Mgr. Tomáš Riemel
SVO19 Mgr. Ivona Tomečková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 16+10

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

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 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.

E-learning

http://mdg.vsb.cz/portal/

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.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures ================= I. Functions of one real variable (4 h) ------------------------------------------------ Definition, graph and basic properties. Elementary functions. Operations with functions. Parametric and implicit functions. Limit of the function, continuous functions. II. The calculus (6 h) ------------------------------------------------ Definition of the derivative, basic rules for differentiation. Parametric differentiation, higher-order derivatives. Applications of the derivatives: tangent line, Taylor polynomial, extremes of a function, behaviour of the graph (monotony, convexity, critical and inflection points), inverse functions, computation of limits by l'Hospital rule, asymptotes. III. Linear algebra and Analytic geometry (6 h) ------------------------------------------------ Systems of linear equations, Gaussian elimination. Matrices, rank of a matrix. Matrix inversion, Determinant, its computation and properties. Cramer rule. Analytic geometry in Euclidean space. Dot product and cross product. Line and plane in 3D-Euclidean space. Tutorials: ================= 1. Pre-calculus. simplifying of algebraic expressions, rules for computation of powers, exponentials, logarithms, solution of (in)equalities. 2. Domains of functions of one real variable. 3. Graphs and properties of elementary functions . 4. Differentiation: rules of computation (for any variable), simplifying, chain rule. 5. Analytic geometry in Euclidean space.

Conditions for subject completion

Part-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 (20) 5
                Computing of the derivatives Written test 10  5
                Semestral project Semestral project 10  0
        Examination Examination 80 (80) 30 3
                Practical part Written examination 60  25
                Theoretical part Written test 20  5
Mandatory attendence participation: 75% of the lessons

Show history

Conditions for subject completion and attendance at the exercises within ISP: Written test on derivatives of elementary functions and submission of homework, attndance is not required.

Show history

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2024/2025 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2024/2025 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2024/2025 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2024/2025 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2023/2024 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2023/2024 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2023/2024 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2023/2024 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2023/2024 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2022/2023 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2022/2023 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2022/2023 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2022/2023 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2022/2023 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2021/2022 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2021/2022 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2021/2022 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2023/2024 Winter
2022/2023 Winter
2021/2022 Winter