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Course info
KMA / MA3
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Course description
Department/Unit / Abbreviation
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KMA
/
MA3
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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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Mathematical Analysis 3
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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,
5
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
3
[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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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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15 / -
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2 / -
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0 / 10
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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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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 |
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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None
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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 course is intended to give students a good insight into the following areas : Vector differential calculus. Curves and Surfaces. Line and surface integrals. Gradient of a scalar field, divergence and curl of a vector field. Transformation of coordinate systems. Vector and tensor fields. Transformation rules for tensors. Divergence theorem of Gauss. Stokes theorem. Greens theorems. Formulation of physical laws.
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Requirements on student
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During semester, students have to write two assignments - it is necessary to obtain at least 50% points from these assignments.
The final examination is in the form of a written exam (18-20 points - grade 1,
14-17 points - grade 2, 10-13 points - grade 3, 0 - 9 points - grade 4) which is supplemented by an oral examination. All assessment tasks will assess the learning outcomes, especially, the ability to provide logical and coherent proofs of theoretical results and to analyze problems from the written part.
Detailed information may be found on the server http://home.zcu.cz/~tomiczek/vyuka.htm
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Content
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Vector differential calculus. Curves and Surfaces. Line and surface integrals. Gradient of a scalar field, divergence and curl of a vector field. Transformation of coordinate systems. Vector and tensor fields. Transformation rules for tensors. Divergence theorem of Gauss. Stokes theorem. Greens theorems. Formulation of physical laws.
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Activities
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Fields of study
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Guarantors and lecturers
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-
Guarantors:
RNDr. Petr Tomiczek, CSc. (100%),
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Lecturer:
Oscar Iván Agudelo Rico, PhD (100%),
RNDr. Petr Tomiczek, CSc. (100%),
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Tutorial lecturer:
Oscar Iván Agudelo Rico, PhD (100%),
RNDr. Petr Tomiczek, CSc. (100%),
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Literature
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Recommended:
http://home.zcu.cz/~tomiczek/Karty.htm
(Tomiczek, Petr)
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Recommended:
Míka, Stanislav. Matematická analýza III : tenzorová analýza. 1. vyd. Plzeň : Západočeská univerzita, 1993. ISBN 80-7082-115-9.
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Recommended:
F.Jirásek,S.Čipera,M.Vacek. Sbírka řešených příkladů z matematiky II. Praha, 1989. ISBN 80-03-00187-0.
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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:
Spiegel Murray R. Schaum's Outline of Theory and Problems of Vector Analysis and An Introduction to Tensor Analysis. McGraw-Hill Book Company, Singapure, 1959. ISBN 0-07-084378-3.
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Recommended:
Boček, Leo. Tenzorový počet. 1. vyd. Praha : SNTL, 1976.
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Recommended:
Zachariáš, Svatopluk. Úvod do vektorové a tenzorové analýzy. 1. vyd. Plzeň : ZČU, 1998. ISBN 80-7082-445-X.
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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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Preparation for comprehensive test (10-40)
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20
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Preparation for an examination (30-60)
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35
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Preparation for formative assessments (2-20)
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10
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Contact hours
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65
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Total
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130
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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: |
definovat derivaci funkce jedné reálné proměnné |
popsat diferenciál funkcí více proměnných |
popsat matici přechodu od báze k bázi |
rozpoznat směrnicový, obecný a parametrický tvar přímky |
vysvětlit obsah Fubiniovy věty |
vysvětlit pojem tečna ke grafu |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
derivovat funkce více reálných proměnných |
parametrizovat přímku, kružnici a elipsu |
spočítat determinant |
spočítat vektorový součin dvou vektorů |
spočítat vícenásobné integrály |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
formulovat Greenovu větu, Stokesovu a Gaussovu větu |
charakterizovat jednoduchou regulární křivku a popsat přirozenou parametrizaci křivky |
popsat křivkový a plošný integrál 1. a 2. druhu |
popsat křivočarou, sdruženou bázi, kontravariantní a kovariantní souřadnice vektoru a tenzor nultého až druhého řádu |
popsat operátory skalárních a vektorových polí a jejich geometrický a fyzikální význam |
Skills - skills resulting from the course: |
dokázat Greenovu, Stokesovu a Caussovu větu |
rozpoznat tenzory nultého až druhého řádu |
spočítat kovariantní a kontravariantní součadnice vektoru |
spočítat křivkové a plošné integrály |
spočítat tečnu ke grafu křivky a tečnou rovinu k ploše |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Continuous assessment |
Test |
Combined exam |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Continuous assessment |
Test |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Continuous assessment |
Test |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Task-based study method |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Interactive lecture |
Practicum |
Task-based study method |
Competences - the following training methods are used to achieve the required competences: |
Interactive lecture |
Practicum |
Task-based study method |
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