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Course info
KMA / VPM2
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Course description
Department/Unit / Abbreviation
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KMA
/
VPM2
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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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Selected Topics in MA and NM 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
3
[Hours/Week]
Tutorial
1
[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, 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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2 / -
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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 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, 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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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 focused at parts of mathematical analysis and numerical mathematics that, despite their theoretical and practical relevance, are not included in the basic courses of mathematical Master study branches due to time constraints. The course aims to enable students interested in Continuous Mathematics to study one of its subfields in a deeper and more detailed way.
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Requirements on student
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During semester, students have to write several homework assignments which will demonstrate knowledge of theory, applications, proofs, algorithm designing and analysis. In addition, students elaborate a non-trivial individual assigned project.
The final examination is in the form of a written exam (70% of the grade) which is supplemented by an oral examination (30% of the grade). All assessment tasks will assess the learning outcomes, especially, the ability to provide logical and coherent proofs of chosen theoretical results and to use the methods from the course on solving given non-trivial problems.
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Content
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Major topics of this course include which are not scheduled in standard courses: nonlinear ordinary and partial differential and difference equations, functional analysis, optimization, numerical methods for ordinary and partial differential equations, modern methods for systems of linear equations, numerical modeling of complex phenomena.
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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:
Kelley, Walter G.; Peterson, Allan C. Difference equations : an introduction with applications. 2nd ed. San Diego : Harcourt Academic Press, 2001. ISBN 0-12-403330-X.
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Recommended:
Leveque, Randall J. Finite volume methods for hyperbolic problems. 1st ed. Cambridge : Cambridge University Press, 2002. ISBN 0-521-81087-6.
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Recommended:
Murray, J. D. Mathematical biology. 2nd ed. corr. Berlin : Springer, 1993. ISBN 3-540-57204-X.
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Recommended:
Quarteroni, Alfio; Valli, Alberto. Numerical approximation of partial differential equations. 2 corr. printing. New York : Springer-Verlag, 1979. ISBN 3-540-57111-6.
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Recommended:
Atkinson, Kendall; Han, Weimin. Theoretical numerical analysis : a functional analysis framework. New York : Springer, 2001. ISBN 0-387-95142-3.
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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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Graduate study programme term essay (40-50)
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50
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Presentation preparation (report) (1-10)
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10
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Preparation for an examination (30-60)
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50
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Total
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162
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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: |
rozumět principům a metodám z oblasti diferenciálního počtu funkcí jedné i více proměnných
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rozumět principům a metodám z oblasti integrálního počtu funkcí jedné i více proměnných |
rozumět principům a metodám z oblasti řešení okrajových a počátečně-okrajových úloh pro obyčejné a parciální diferenciální rovnice (existence řešení, základní metody řešení) |
rozumět principům numerických metod a základním postupům jejich analýzy (numerické metody lineární algebry, řešení nelineárních rovnic, numerické metody pro obyčejné a parciální diferenciální rovnice)
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Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
analyticky a numericky řešit základní okrajové a počátečně-okrajové úlohy pro obyčejné a parciální diferenciální rovnice |
navrhovat základní matematické modely, formulovat související úlohy, navrhovat základní numerické modely, metody a algoritmy |
algoritmizovat základní metody, používat počítačový software MATLAB nebo podobný a implementovat algoritmy numerických metod |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
aktivně se více specializovat v oblasti matematické analýzy a numerické matematiky, zejména v souvislosti s tématem diplomové práce |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
orientovat se ve vybraných partiích z oblastí matematické analýzy a numerické matematiky |
Skills - skills resulting from the course: |
pracovat s matematickými modely |
používat nástroje a metody vybraných matematických disciplín |
vhodnou kombinací příkladů a protipříkladů demonstrovat základní tvrzení abstraktní teorie |
Competences - competences resulting from the course: |
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 |
Seminar work |
Skills demonstration during practicum |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
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: |
Lecture |
Task-based study method |
Interactive lecture |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Task-based study method |
Interactive lecture |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Task-based study method |
Interactive lecture |
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