Course: Mathematics 1

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Course title Mathematics 1
Course code KAP/MV1
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Cvrček Milan, PhDr. Ph.D.
  • Šimková Tereza, Mgr. Ph.D.
  • Bittner Václav, Mgr. Ph.D.
  • Tuček Richard, Mgr.
Course content
I.Functions 1. Introduction: terminology, notation. Sets od numbers. 2. Function. Graphs. Explicit, implicit and parametric functions. The definition, domain of the function. Function properties 3. Operations with functions. Inverse function. Linear, quadratic functions. 4. Further elementary functions. II. Introduction to differential calculus 5. Sequence, limit of sequences. Calculation of the limit. 6. Limit of a function. 5. Continuity. Continuous function, asymptotic behavior of functions. 7. Derivative of function. Geometric meaning of the definition. Derivatives of elementary functions. Derivative of sum and product functions. Derivative of inverse function. 8. Application of differential calculus:l'Hospitalovo rule. Extreme of function. 9. Points of inflection. Applications of derivatives to studying of graph of a function.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
  • Preparation for exam - 125 hours per semester
  • Class attendance - 56 hours per semester
Learning outcomes
The basic issues of mathematical analysis. Function, graph of a function, operations with functions. Survey of elementary functions of one real variable. Sequences. Limits of functions. Differentation, technique of derivation, applications
Basic knowledge of differential calculus.
Prerequisites
Mathematics -- the secondary level

Assessment methods and criteria
Oral exam, Written exam

Requirements on credit: two tests of the subject matter. The date of each test will be announced in advance by teacher. It is necessary to get score at least 50% for each test. Requirements on exam: Knowledge of problem solving, concepts and basic ideas.
Recommended literature
  • Bittnerová, D., Plačková G. Louskáček. Část 1, Diferenciální počet funkcí jedné reálné proměnné. Liberec : Technická univerzita v Liberci, 2005. ISBN 80-7083-984-8.
  • Hrubý D., Kubát J. Matematika pro gymnázia : diferenciální a integrální počet. Praha : Prometheus, 2004. ISBN 80-7196-210-4.
  • Kadeřábek J. Základy matematiky : Studijní texty pro distanční bakalářské studium - textilní marketing. Liberec : Technická univerzita v Liberci, 1999. ISBN 80-7083-367-X.
  • Nekvinda M., Vild J. Matematické oříšky 1.. Liberec : Technická univerzita v Liberc, 2006. ISBN 80-7372-017-5.
  • Nekvinda, M. Matematika. Část 1.. Liberec : Technická univerzita v Liberci, 2001. ISBN 80-7083-447-1.
  • Rektorys K. Přehled užité matematiky.. Praha : Prometheus, 2000. ISBN 80-7196-179-5.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Textile Engineering Study plan (Version): Textile marketing (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing Production and Management (ANG) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Textile Technologies, Materials and Nanomaterials (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Textile Technologies, Materials and Nanomaterials (2016) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Textile Technologies, Materials and Nanomaterials (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Textile Technologies, Materials and Nanomaterials (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Textile marketing (ANG) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Textile Technologies, Materials and Nanomaterials (2016) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing Production and Management of Clothing Trade (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Textile Engineering Study plan (Version): Textile Technologies, Materials and Nanomaterials (ANG) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Winter