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Course info
KMA / MS2
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Course description
Department/Unit / Abbreviation
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KMA
/
MS2
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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 Mechanical Engineers 2
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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 + 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 |
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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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 :
differential models of dynamic systems; first-order differential equations and first-order systems; initial value problems; oscillation and equilibrium; fundamental, general and particular solutions; scalar functions of several variables, graphs and contour curves; vector functions; differential and integral calculus of functions of several variables; curve and surface integrals; differential and integral characteristics of vector fields.
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Requirements on student
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During semester, students have to write two assignments (8-th week, 12-th week) - it is necessary to obtain at least 50% points from these assignments.
The final examination 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.
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Content
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1. Differential models of dynamic systems; first-order differential equations and first-order systems;
2. Ordinary linear differential equations n-th order.
3. First and secod-order systems.
4. Scalar functions of several variables, limits, contunuity.
5. Differential calculus of functions of several variables.
6. Optimalization, local and constrained extrems.
7. Integral calculus of functions of several variables.
8. Curve and surface integrals.
9. Scalar and vector fields.
10. Vector functions, differential calculus of vector functions.
11. Differential and integral characteristics of vector fields.
12. Integral's theorems in the vector fields.
13. Integral with parameter.
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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:
Jarník, Vojtěch. Diferenciální počet II. Praha : Academia, 1976.
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Recommended:
Jarník, Vojtěch. Integrální počet. II. Praha : Nakladatelství Československé akademie věd, 1955.
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Recommended:
Brabec, Jiří; Hrůza, Bohuslav. Matematická analýza II. Praha : SNTL, 1986.
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Recommended:
Drábek, Pavel; Míka, Stanislav. Matematická analýza II. 3. nezm. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-528-6.
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Recommended:
Ivan, Ján. Matematika 2. 1. vyd. Bratislava : Alfa, 1989. ISBN 80-05-00114-2.
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Recommended:
Mašek, Josef. Řešené úlohy z matematiky : dvojné, trojné, křivkové a plošné integrály. 1. vyd. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-836-6.
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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:
server TRIAL
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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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78
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Preparation for an examination (30-60)
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38
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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/MS1. |
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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. Solve differential equation of first order and system of differential equations;
2. Solve initial problems;
3. Describe curves in Rn and work with them;
4. Determine properties of functions of more variables;
5. Compute directional and partial derivatives of functions of more variables;
6. Formulate basic min/max problems and solve them using differential calculus;
7. Evaluate double and triple integrals;
8. Compute curves integral;
9. Deal with differential and integral characteristic of vector fields. |
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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 |
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