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Main menu for Browse IS/STAG
Course info
KMA / M1S
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Course description
Department/Unit / Abbreviation
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KMA
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M1S
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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,
4
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]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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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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-
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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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302 / -
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0 / -
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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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1
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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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-
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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 |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
Yes
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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KMA/ZME1
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Preclusive courses
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N/A
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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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The aim of this course is a basic introduction to the fundamental concepts of mathematical analysis such as:
- infinite sequences and series of real numbers;
- functions of one real variable;
- differential calculus of functions of one variable;
- integral calculus of functions of one variable.
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Requirements on student
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Use rigorous arguments in calculus and be able to apply them in solving problems on the topics in the syllabus.
Credit: written test (required at least 50%)
Exam: witten and oral part.
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Content
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Week 1: Mathematical reasoning; sets and elementary operations;
Week 2: Sequences of real numbers and their properties;
Week 3: Methods of calculating a limit of a sequence;
Week 4: Series of real numbers; convergence criteria;
Week 5: Functions of one real variable and their properties;
Week 6: Local and global behaviour of a function; limits; algebra of limits;
Week 7: Continuity of a function at a point; points of discontinuity; continuity in a closed interval;
Week 8: Derivative and differential of a function, their geometrical and the physical meaning; differentiability and continuity of a function;
Week 9: Differentiation, product rule and chain rule; stationary points of a function; l'Hospital's rule;
Week 10: Higher order derivatives and differentials; Taylor's theorem;
Week 11: Indefinite integral; integration by parts and integration by substitution;
Week 12: Applications of differential and integral calculus in solving optimization and physical problems.
Week 13: Recapitulation
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Activities
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Fields of study
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Guarantors and lecturers
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-
Guarantors:
Ing. Jan Čepička, Ph.D. (100%),
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Lecturer:
Ing. Jiří Egermaier, Ph.D. (100%),
Doc. Ing. Jan Pospíšil, Ph.D. (100%),
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Tutorial lecturer:
Ing. Jan Čepička, Ph.D. (100%),
Ing. Jiří Egermaier, Ph.D. (100%),
Mgr. Martin Kopřiva (100%),
Ing. Lukáš Kotrla, Ph.D. (100%),
Doc. Ing. Jan Pospíšil, Ph.D. (100%),
Mgr. Radek Výrut (100%),
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Literature
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Recommended:
http://trial.kma.zcu.cz
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Recommended:
Matematická analýza
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Recommended:
Drábek, Pavel; Míka, Stanislav. Matematická analýza I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-558-8.
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Recommended:
Pultr, Aleš. Matematická analýza I. Praha : Matfyzpress, 1995. ISBN 80-8586-3-09-X.
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Recommended:
Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
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Recommended:
Míková, Marta; Kubr, Milan; Čížek, Jiří. Sbírka příkladů z matematické analýzy I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-568-5.
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Recommended:
Děmidovič, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. Havlíčkův Brod : Fragment, 2003. ISBN 80-7200-587-1.
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Recommended:
trial.zcu.cz
(-)
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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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Contact hours
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52
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Preparation for an examination (30-60)
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32
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Preparation for formative assessments (2-20)
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20
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Total
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104
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
There is no prerequisite for this course. Students should be familiar with a high school algebra and trigonometry. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
By the end of the course, a successful student should be able to:
1. Understand logical constructions and to be able to read mathematical text;
2. Use rigorous arguments in calculus and ability to apply them in solving problems on the topics in the syllabus;
3. Demonstrate knowledge of the definitions and the elementary properties of sequences, series and continuous and differentiable functions of one real variable;
4. Use both the definition of derivative as a limit and the rules of differentiation to differentiate functions;
5. Sketch the graph of a function using critical points, and the derivative test for increasing/decreasing and concavity properties;
6. Set up max/min problems and use differentiation to solve them;
7. Use l'Hospital's rule;
8. Evaluate integrals using techniques of integration, such as substitution and integration by parts;
9. Use developed theory in solving problems on physical systems.
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Skills demonstration during practicum |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Practicum |
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