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Course info
KMA / MA3-A
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Course description
Department/Unit / Abbreviation
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KMA
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MA3-A
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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,
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
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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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 / -
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0 / -
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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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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 |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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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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KMA/MA3
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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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Lectures in English only.
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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Literature
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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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65
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Preparation for an examination (30-60)
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51
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Preparation for comprehensive test (10-40)
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30
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Preparation for formative assessments (2-20)
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10
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Total
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156
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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 basic notions of mathematical analysis to the extent of the course KMA/MA1, KMA/MA2. |
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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. Define a simple regular curve, its tangent and natural parametrization;
2. Define curve's integral of the first and second type;
3. Formulate Green's theorem;
4. Define gradient of a scalar field, divergence and curl of a vector field;
5. Define a smooth and closed surface;
6. Define and describe surface's integral of the first and second type;
7. Formulate Gauss theorem;
8. Formulate Stokes theorem;
9. Use curvilinear coordinates, contravariant a covariant vectors;
10. Define tensors of rank zero, one and two. |
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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 |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Multimedia supported teaching |
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