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Course info
KMA / MATA1
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Course description
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Department/Unit / Abbreviation
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KMA
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MATA1
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Mathematics 1
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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lecture
2
[Hours/Week]
practical class
2
[Hours/Week]
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Course credit prior to examination
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No
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Course credit prior to examination
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No
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / 0
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0 / 0
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0 / 0
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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not determined
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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| No. of hours of on-premise lessons |
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Evaluation scale |
A|B|C|D|E|F |
| Periodicity |
every year
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| Specification periodicity |
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Fundamental theoretical course |
No
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| Fundamental course |
No
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| Fundamental theoretical course |
No
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| Evaluation scale |
A|B|C|D|E|F |
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Substituted course
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None
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Preclusive courses
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KMA/MATH1 and KMA/XMAA1 and KMA/XMAT1 and KMA/2MAT1 and KMA/7MAT1
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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Elementary functions. Limit and continuity. Derivative. Applications.
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Requirements on student
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The course is finished by an examination consisting of written part and verbal part.
The evaluation of the course including the classification is carried out in accordance with the Study and Examination Regulations OU.
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Content
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1. Basic concepts. Interval, function, its domain, range and graph. Even and odd functions. Injection, surjection, inverse function.
2. Elementary functions and their inversions (power, exponential and goniometric functions).
3. Operations with functions (sum, product, quotient). Composition of functions.
4. Continuity, limit and their relation. Darboux's property. One-side limits. Improper limits. Sum, product and quotient of limits, limit of composed function.
5. Derivative. Its geometric and physical meaning - tangent, immediate velocity. Derivatives of elementary functions, rules for computing derivatives.
6. L'Hospital's rule. Higher order derivatives.
7. Monotonicity and convexity.
8. Local extrema, points of inflection.
9. Asymptotes of the graph of function. Sketch of the graph of function.
10. Sequences. Their properties and limit.
11. Supremum and infimum of a set. Limit points, upper and lower limits.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Basic:
Breviář vyšší matematiky
(Kalus, R. -- Hrivňák, D.)
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Basic:
Stewart, J. Calculus. [s.l.]: Thomson Brooks/Cole, 2008. ISBN 978-0-495-38362-8.
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Basic:
Hančl J., Šustek J. Matematická analýza I. skripta PřF OU.
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Extending:
K. Rektorys. Co je a k čemu je vyšší matematika, 1. vydání (Academia, Praha 2001).
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Extending:
Jarník, V. Diferenciální počet I. ACADEMIA Praha, 1976. ISBN cnb000021007.
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Extending:
Děmidovič, B. P. Sbírka úloh a cvičení z matematické analýzy. Havlíčkův Brod: Fragment, 2003. ISBN 80-7200-587-1.
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Recommended:
Rektorys,K. a kolektív. Přehled užité matematiky. SNTL Praha, 1981 nebo Prometheus Praha, 1995, 1981. ISBN 80-85849-92-5.
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Recommended:
Kopecký, M. -- Kubíček, Z. Vybrané kapitoly z matematiky. Praha: SNTL, 1981. ISBN cnb000047484.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Being present in classes
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52
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Self-tutoring
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40
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Consultation of work with the teacher/tutor (incl. electronic)
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10
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Preparation for an exam
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50
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Books of fiction reading in the Czech language
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20
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Total
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172
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Prerequisites
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
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knowledge of basic concepts of calculus and properties of functions
ability of proving general properties and rules in calculus
ability of giving an example illustrating some properties
ability of application of properties and theorems to solve problems in calculus
development of reading mathematical literature
competences of communication and studying
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
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| Written examination |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
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| Monologic (explanation, lecture, briefing) |
| Projection (static, dynamic) |
| Working with text (coursebook, book) |
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