Course description

Course description
Course abbreviation:
Course name:
Academic Year:
KMD/MA1-H
Mathematics 1
2016/2017
Page:
Printed:
Department/Unit / KMD / MA1-H
1/3
12.10.2016 18:33
Academic Year 2016/2017
Title Mathematics 1
Type of completion Course-credit
Accredited/Credits Yes, 5 Cred.
Type of completion
Number of hours Lecture 2 [HOD/TYD] Tutorial 2 [HOD/TYD]
Occ/max
Status A
Status B
Status C
Course credit prior to NO
0/-
0/-
0/-
Counted into average NO
0/-
0/-
Min. (B+C) students not determined
Repeated registration NO
Summer semester
Winter semester
258 / Timetable Yes
Language of instruction Czech
Semester taught Winter semester
Substituted course None
Preclusive courses N/A
Prerequisite N/A
Informally recommended courses N/A
Courses depending on this Course KMD/MA2-H
Course objectives:
Basic mathematical concepts. Foundations of the differential calculus, finite and infinite limits in finite and infinite points,
including left-hand and right-hand limits. Derivation and its applications, specially to continuity of a function. Basis of integral
calculus and Riemann integral. Number progressions. All items regarding to economic applications.
Requirements on student
Credit: regular attendance, passing of two tests, seminary work.
Content
A. Definitions of mapping and function
1. Introduction - used symbols, notations. Basic terms of sententional calculus. Number sets.
2. Mapping, basic terms (domain of definition, image of mapping, types of mapping). Real function, basic properties of functions
(monotony, bounded functions, even, odd).
3. Inverse function. Basic elementary functions (including cyclometric).
4. Other functions (absolute value, signum, entire function, Dirichlet's function). Real sequences.
B. Differential calculus
5. Limit of sequence (finite, infinite), theorems about limit, calculation of limit, number e.
6. Limit function, one-sided limits, limits at infinite points.
Continuity, properties of continuous functions.
7. Derivative, geometric applications, tangent line to a function.
Calculation of derivative, derivative of a composite function, derivative of an inverse function.
8. L'Hospital's rule. Monotony, local and global extreme of a function.
9. Convexity, concavity, point of inflexion. Applications of derivatives to studying of graph of a function.
10. Differential of a function. Taylor's formula.
C. Integral calculus
11. Primitive function and indefinite integral. Basic rules, method per partes, substitution method.
12. Integration by partial fractions.
13. Riemann definite integral, Newton-Leibniz's theorem. Infinite integral.
14. Number series, criterions of convergence, absolute convergence.
Prerequisites - other information about course preconditions
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Knowledge of mathematics at the high school level
Competences acquired
Basic knowledge of higher mathematics.
Guarantors and lecturers
• Guarantors:
doc. RNDr. Jaroslav Mlýnek, CSc.
• Lecturer:
RNDr. Daniela Bittnerová, CSc., RNDr. Jaroslava Justová, doc. RNDr. Jaroslav Mlýnek, CSc.
• Tutorial lecturer: Mgr. Daniela Bímová, Ph.D., RNDr. Daniela Bittnerová, CSc., RNDr. Jaroslava Justová, doc. RNDr.
Jaroslav Mlýnek, CSc.
• Seminar lecturer: RNDr. Daniela Bittnerová, CSc., doc. RNDr. Jaroslav Mlýnek, CSc.
Literature
•
•
•
•
•
Basic:
Basic:
Recommended:
Recommended:
Recommended:
•
•
•
•
Recommended:
Recommended:
Recommended:
Recommended:
Klůfa, J. - Coufal, J.:. Matematika 1, Ekopress.. Praha, 2003. ISBN 80-86119-76-9.
Kaňka, M. - Henzler J.:. Matematika 2, Ekopress.. Praha, 2003. ISBN 80-86119-77-7.
Vild, J. - Říhová, H.:. Diferenciální kalkul F1.. Liberec, 2002. ISBN 80-7083-552-4.
Vild, J. - Říhová, H.:. Integrální kalkul F1.. Liberec, 2005. ISBN 80-7083-587-7.
Bittnerová, D. - Plačková, G.:. Louskáček 1 - Diferenciální počet funkcí jedné reálné proměnné
(Sbírka úloh). Liberec, TUL 2006, 2007..
Bittnerová, D. - Plačková, G.:. Louskáček 2 - Integrální počet funkcí jedné reálné proměnné..
Nekvinda, M. - Vild, J.:. Matematické oříšky I. Liberec, 2000. ISBN 80-7083-762-4.
Rektorys, K. a další:. Přehled užité matematiky.. Praha, Prometheus, 2000. ISBN 80-85849-92-5.
Jirásek, F. - Kriegelstein, E. - Tichý, Z.:. Sbírka řešených příkladů z matematiky I.. Praha, 1990.
Time requirements
Activities
Class attendance
Preparation for credit
Semestral paper
Home preparation for classes
Time requirements for activity [h]
56
26
10
28
Total:
120
Teaching methods
Monological explanation (lecture, presentation,briefing)
Assessment methods
Combined examination
Course is included in study programmes:
Study Programme
Type of
Form of
Branch
Economics and
Management
Bachelor
Part-time Business Administration
Economics and
Management
Bachelor
Part-time Business Administration
Economics and
Management
Bachelor
Full-time Business Administration
Economics and
Bachelor
Full-time Business Administration
Stage St. plan v.
Year Block
1 2016 2016 Compulsory
K
courses - B.Sc.
1st year
1 2012 2016 Compulsory
K
courses - B.Sc.
1st year
1 2012 2016 Compulsory
courses - B.Sc.
1st year
1 2016 2016 Compulsory
Status R.year
R.
A
1
ZS
A
1
ZS
A
1
ZS
A
1
ZS
(c) IS/STAG , Portal - Course syllabus , 12.10.2016 18:33
Page:
Study Programme
Type of
Form of
Branch
Stage St. plan v.
Year Block
Management
Economics and
Management
Bachelor
Full-time Business Administration
Economics and
Management
Bachelor
Full-time Economics and Management 1 2013 2016
of International Trade
Economics and
Management
Lifelong
learning
Part-time Business Administration
1 PEC 2016
13
Full-time Managerial Informatics
1 2013 2016
System Engineering Bachelor
and Informatics
1 2016 2016
courses - B.Sc.
1st year
Povinné
předměty - Bc.
1. ročník
Compulsory
courses - B.Sc.
1st year
Compulsory
courses - B.Sc.
1st year
Compulsory
courses B.Sc. 1st year
3/3
Status R.year
R.
A
1
ZS
A
1
ZS
A
1
ZS
A
1
ZS
(c) IS/STAG , Portal - Course syllabus , 12.10.2016 18:33