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Course info
KMA / SNM1
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Course description
Department/Unit / Abbreviation
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KMA
/
SNM1
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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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Advanced Numerical Methods 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,
4
Cred.
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Type of completion
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Oral
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Type of completion
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Oral
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Time requirements
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Lecture
3
[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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3 / -
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1 / -
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1 / -
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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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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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KMA/ODR
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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 to introduce students to basic ideas of numerical methods for solving initial and boundary value problems for ordinary differential equations.
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Requirements on student
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The examination assessment includes quality of the semester work and oral examination results.
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Content
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Finite difference method, finite volume method and finite element method for solving boundary problems for ODEs and elliptic PDEs. Direct and iterative methods for discretized problems.
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Activities
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Fields of study
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Studentům je k dispozici kurz v Google Classroom se všemi podstatnými informacemi a materiály.
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Guarantors and lecturers
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Literature
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Basic:
LEVEQUE, Randall J. Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. Philadelphia, 2007. ISBN 978-0-898716-29-0.
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Basic:
Trangenstein, J. A. Numerical solution of elliptic and parabolic partial differential equations. Cambridge : Cambridge University Press, 2012. ISBN 978-0-521-87726-8.
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Recommended:
STRIKWERDA, John C. Finite difference schemes and partial differential equations. 2nd ed.. Society for Industrial and Applied Mathematics. Philadelphia, 2007. ISBN 978-0-898716-39-9.
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Recommended:
THOMAS, James William. Numerical partial differential equations: finite difference methods. Springer. Texts in applied mathematics 22. New York, 1995. ISBN 0-387-97999-9.
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Recommended:
MÍKA, Stanislav a PŘIKRYL, Petr. Numerické metody řešení eliptických úloh pro PDR. Plzeň: Západočeská univerzita, 2007.
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Recommended:
MÍKA, Stanislav a PŘIKRYL, Petr. Numerické metody řešení okrajových úloh pro ODR. Plzeň: Západočeská univerzita, 2007.
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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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39
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Preparation for an examination (30-60)
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40
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Team project (50/number of students)
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48
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Total
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127
|
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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: |
describe and explain basic numerical methods for solving nonlinear equations |
describe linear algebra problems (systems of equations, eigenvalues), approximation of a function (interpolation, least squares method), approximation of a derivative and a definite integral, and an initial value problem for an ordinary 1st order differential equation |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
formulate and solve basic problems of numerical mathematics using numerical methods, i.e. solve linear and nonlinear equations and their systems, determine eigenvalues, approximate functions in terms of interpolation and L2-approximation, approximate value of derivative and definite integral, solve initial value problem for 1st order ordinary differential equation |
používat počítačový software MATLAB nebo podobný a implementovat základní algoritmy numerických metod |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
describe and explain the principle of numerical methods for solving initial and boundary value problems for ordinary and elliptic partial differential equations, namely methods of converting the boundary value problem to the initial value problem, difference methods for boundary value problems, Galerkin type methods and finite element methods |
Skills - skills resulting from the course: |
analyze the obtained numerical results |
discuss convergence of methods (firing method and boundary condition transfer method, finite difference method and integral identity method, Galerkin and Ritz method, finite element method) |
use numerical methods to solve initial and boundary value problems for ordinary differential equations |
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: |
Oral exam |
Individual presentation at a seminar |
Seminar work |
Skills - skills achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
Oral exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Lecture supplemented with a discussion |
Textual studies |
Skills - the following training methods are used to achieve the required skills: |
Individual study |
Students' portfolio |
Task-based study method |
Competences - the following training methods are used to achieve the required competences: |
Task-based study method |
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