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Course info
KMA / ZME3
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Course description
Department/Unit / Abbreviation
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KMA
/
ZME3
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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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Integral Calculus and Series
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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
4
[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
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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 / -
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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
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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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KMA/ZM3
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Preclusive courses
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KMA/M3
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Prerequisite courses
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N/A
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Informally recommended courses
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KMA/ZME2 or KMA/ZM2
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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 : 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. Integral theorems. Function sequences,
Number and function series. Taylor's and Fourier's series
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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: Laplace transform, inverse transform, solving linear constant coefficient differential equations using Laplace transform
Week 2: Double integral, Fubini theorem. Methods to computation. Change of variables in a double integrals.
Week 3: Triple integral. Methods to computation.
Week 4: Scalar field, gradient, directional derivative.
Week 5: Vector fields, divergence and curl. Operator Laplace, Hamilton.
Week 6: Paths and parametrizations. Path integrals of scalar fields. Path integrals of vector fields,
Week 7: Parametrized surfaces. Surface integral of scalar and vector fields. Integration theorems of vector calculus.
Week 8: Series of real number, conergent and divergent series.
Week 9: Sequences of functions, point-wise and uniform konvergence.
Week 10-11: Power series and their convergence. Taylor's series
Week 12-13: Fourier series.
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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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-
Recommended:
Polák, Josef. Funkční posloupnosti a řady, Fourierovy řady. 1. vyd. Plzeň : Západočeská univerzita, 1995. ISBN 80-7082-224-4.
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Recommended:
Polák, Josef. Integrální a diskrétní transformace. 3.,přeprac. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-924-9.
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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:
Jirásek, František; Kriegelstein, Eduard; Tichý, Zdeněk. Sbírka řešených příkladů z matematiky : logika a množiny, lineární a vektorová algebra, analytická geometrie, posloupnosti a řady, diferenciální a integrální počet funkcí jedné proměnné. 2. nezměn. vyd. Praha : SNTL, 1981.
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Recommended:
Jirásek, František; Vacek, Ivan; Čipera, Stanislav. Sbírka řešených příkladů z matematiky II. 1. vyd. Praha : SNTL, 1989.
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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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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 formative assessments (2-20)
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24
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Preparation for an examination (30-60)
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56
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Contact hours
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78
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Total
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158
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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: |
Students should be familiar with basic notions of the course KMA/ZME1, KMA/ZME2. |
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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:
Evaluate double and triple integral, parametrization of curves and surfaces, evaluate line and surfece integral. Deal with function sequences and function series. Expend a function into Fourier series.
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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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