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Course info
KMA / VPM1
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Course description
Department/Unit / Abbreviation
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KMA
/
VPM1
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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 1
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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,
5
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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4 / -
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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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Summer semester
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Semester taught
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Summer 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
|
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 as well as practical relevance, are not included in the basic courses of mathematical Bachelor study branches due to time and content 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 and ability to use the methods from the course on solving given problems.
The final examination is in the form of a written and oral exam. All assessment tasks will assess the learning outcomes.
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Content
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Major topics of this course include the following parts which are not scheduled in standard courses: nonlinear ordinary differential and difference equations, optimization, game theory, numerical methods for ordinary differential equations, modern methods for systems of linear equations, etc.
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Activities
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Fields of study
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Guarantors and lecturers
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-
Guarantors:
RNDr. Jonáš Volek, Ph.D. ,
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Lecturer:
Oscar Iván Agudelo Rico, PhD (100%),
RNDr. Jonáš Volek, Ph.D. (100%),
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Tutorial lecturer:
Oscar Iván Agudelo Rico, PhD (100%),
RNDr. Jonáš Volek, Ph.D. (100%),
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Literature
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Basic:
Strogatz, Steven H. Nonlinear Dynamics and Chaos. Reading, MA, USA, 1994. ISBN 0-201-54344-3.
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Extending:
Kuznetsov, Yuri A. Elements of Applied Bifurcation Theory. New York, USA, 1998. ISBN 0-387-98382-1.
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Extending:
Teschl, Gerald. Ordinary Diffferential Equations and Dynamical Systems. Providence, RI, USA, 2012. ISBN 978-0-8218-8328-0.
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Recommended:
Stoer, Josef; Bulirsch, Roland. Introduction to numerical analysis. 3rd ed. New York : Springer, 2002. ISBN 0-387-95452-X.
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Recommended:
Axelsson, Owe. Iterative solution methods. Cambridge : Cambridge University Press, 1996. ISBN 0-521-55569-8.
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Recommended:
Butcher, J. C. Numerical methods for ordinary differential equations. Chichester : John Wiley & Sons, 2003. ISBN 0-471-96758-0.
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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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40
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Undergraduate study programme term essay (20-40)
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40
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Total
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132
|
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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: |
understand fundamental principles of single-/multi-variable differentiable calculus |
understand fundamental principles of single-/multi-variable integral calculus |
understand fundamental principles of ODEs (IVPs for equations of first and second order, existence, basic methods of solving equations) |
understand fundamental principles of numerical methods |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
differentiate and integrate single-variable functions |
solve ODEs of first order by separation of variables |
solve IVPs and BVPs for linear ODEs of first and second order |
formulate and solve fundamental problems in numerical mathematics |
use MATLAB and/or similar mathematical software, implement fundamental algorithms of numerical methods |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
N/A |
N/A |
N/A |
aktivně se více specializovat v oblasti matematické analýzy a numerické matematiky, zejména v souvislosti s tématem bakalářské práce |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
be familiar with selected topics in mathematical analysis and numerical mathematics |
Skills - skills resulting from the course: |
work with mathematical models |
use methods of selected mathematical disciplines |
demonstrate fundamental statements of abstract theory by accurate examples and counterexamples |
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 |
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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