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Course info
KMA / ME4
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Course description
Department/Unit / Abbreviation
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KMA
/
ME4
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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 for Electrical Engineers 4
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Form of course completion
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Pre-Exam Credit
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Form of course completion
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Pre-Exam Credit
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Accredited / Credits
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Yes,
3
Cred.
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Type of completion
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-
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Type of completion
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-
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Time requirements
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Lecture
2
[Hours/Week]
Tutorial
1
[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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NO
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Language of instruction
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Czech
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Occ/max
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|
|
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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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NO
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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YES
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Repeated registration
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YES
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Timetable
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Yes
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Semester taught
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Winter + Summer
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Semester taught
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Winter + Summer
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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
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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 |
S|N |
Periodicity |
každý rok
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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 |
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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KMA/ME1
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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 main aim of this course is to give students a good insight into the following areas : Differential calculus in Rn, optimalization in R2. Integral calculus in R2 and R3. Vector differential calculus. Curves and Surfaces. Line and surface integrals. Gradient of a scalar field, divergence and curl of a vector field. Divergence theorem of Gauss. Stokes theorem. Greens theorems.
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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 60%)
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Content
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Week 1: Functions of several variables, their graph, partial derivatives, total differential..
Week 2: Higher order partial derivatives.
Week 3: Fundamental notions of min/max theory in Rn;
Week 4: Double integral, Fubini theorem. Methods to computation.
Week 5: Change of variables in a double integrals
Week 6: Triple integral, methods to computation. change of variables.
Week 7: Scalar field, gradient, directional derivative.
Week 8: Vector fields, divergence and curl. Operator Laplace, Hamilton.
Week 9: Paths and parametrizations. Path integrals of scalar fields.
Week 10: Path integrals of vector fields,
Week 11: Surface integral of scalar fields.
Week 12: Surface integral of vector fields.
Week 13: Integration theorems of vector calculus
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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:
Polák, Josef. Funkční posloupnosti a řady ; Fourierovy řady. 2. upr. vyd. Plzeň : Západočeská univerzita, 2004. ISBN 80-7043-282-9.
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Basic:
Polák, Josef. Integrální a diskrétní transformace. 3.,přeprac. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-924-9.
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Basic:
Polák, Josef. Matematická analýza v komplexním oboru. 2., upr. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-923-0.
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Basic:
Polák, Josef. Matematická analýza v komplexním oboru II/. 1. vyd. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-700-9.
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Recommended:
Drábek, Pavel; Míka, Stanislav. Matematická analýza II.. 4. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-977-X.
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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:
Mašek, Josef. Sbírka úloh z matematiky : diferenční rovnice a transformace Z. 1. vyd. Plzeň : ZČU, 1998. ISBN 80-7082-457-3.
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Recommended:
Mašek, Josef. Sbírka úloh z matematiky : integrální transformace. 1. vyd. Plzeň : ZČU, 1993. ISBN 80-7082-117-5.
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Recommended:
Studijní materiály
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Recommended:
trial.kma.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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39
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Preparation for comprehensive test (10-40)
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25
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Preparation for formative assessments (2-20)
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15
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Total
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79
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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: |
No particular prerequisites specified. |
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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: compute partial derivatives of functions of more variables, formulate basic min/max problems of Rn, define and use scalar and vector fields, evaluate double and triple integrals, change of variables in a double and triple integrals, integration along paths and over surfaces.
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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 |
Task-based study method |
Self-study of literature |
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