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Course info
KMA / M3S
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Course description
Department/Unit / Abbreviation
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KMA
/
M3S
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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 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,
4
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
2
[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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120 / -
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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 |
Yes
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Fundamental course |
No
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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 aim of this course is an introduction to the concepts of advanced mathematical analysis such as:
- differential calculus of functions of more variables;
- optimization problems;
- integral calculus of functions of more variables;
- curves and vector functions;
- partial differential equations.
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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: Functions of more variables and their properties (recapitulation).
Week 2: Differential calculus of functions of more variables, partial derivatives, gradient.
Week 3: Higher order partial derivatives. Chain rule, derivatives of implicit functions.
Week 4: Fundamental optimization probles in Rn. Stationary points, local extrema.
Week 5: Double integral, Fubini theorem. Methods to computation.
Week 6: Change of variables in a double integrals
Week 7: Triple integral, methods to computation. Change of variables.
Week 8-9: Vector functions of one scalar variable.
Week 10-11: Introduction to partial differential equations. Formulation of fundamental problems.
Week 12: Classification of basic types of partial differential equations.
Week 13: Recapitulation
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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:
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:
Jana Musilová a Pavla Musilová. Matematika II/1. Brno, 2012. ISBN 978-80-214-4071-5.
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Recommended:
Jana Musilová a Pavla Musilová. Matematika II/2. Brno, 2012. ISBN 978-80-214-4071-5.
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Recommended:
Ivan, Ján. Matematika 2. 1. vyd. Bratislava : Alfa, 1989. ISBN 80-05-00114-2.
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Recommended:
Matematika 3 pro FST
(Petr Tomiczek)
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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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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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52
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Preparation for an examination (30-60)
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32
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Preparation for formative assessments (2-20)
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20
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Total
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104
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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/M2S. |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
1. Používat základní techniky integrálního počtu funkcí jedné proměnné a aplikovat je na úlohy z praxe. 2. Rozvinout funkci do Taylorovy nebo Fourierovy řady. 3. Formulovat základní počáteční a okrajové úlohy pro obyčejné diferenciální rovnice. 4. Řešit rovnice prvního řádu a soustavy lineárních rovnic prvního řádu. 5. Řešit lineární rovnice vyšších řádů s konstantními koeficienty. 6. Aplikovat diferenciální rovnice a znalost jejich řešení na úlohy z praxe. 7. Pracovat s funkcemi více proměnných. 8. Používat základní pojmy diferenciálního kalkulu funkcí více proměnných (parciální derivace, gradient) |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
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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. Compute directional and partial derivatives of functions of more variables;
2. Formulate basic min/max problems and solve them using differential calculus;
3. Evaluate double and triple integrals;
4. Work with curves and vector functions;
5. Formulate fundamental problems for partial differential equations;
6. Classify basic types of partial differential equations.
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Skills - skills resulting from the course: |
1. Počítat derivace ve směru a parciální derivace funkcí více proměnných; 2. Vyřešit základní úlohy na maximum, resp. minimum 3. Počítat dvojné a trojné integrály; 4. Pracovat s křivkami a vektorovými funkcemi; 5. Formulovat základní úlohy pro parciální diferenciální rovnice; 6. Klasifikovat základní parciální diferenciální rovnice |
Competences - competences resulting from the course: |
N/A |
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: |
Combined exam |
Test |
Skills demonstration during practicum |
Skills - skills achieved by taking this course are verified by the following means: |
Skills demonstration during practicum |
Combined exam |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Practicum |
Interactive lecture |
Competences - the following training methods are used to achieve the required competences: |
Seminar |
Lecture supplemented with a discussion |
Interactive lecture |
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