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Main menu for Browse IS/STAG
Course info
KMA / SDR
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Course description
Department/Unit / Abbreviation
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KMA
/
SDR
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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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Seminar of Differential Equations
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Form of course completion
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Pre-Exam Credit
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Form of course completion
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Pre-Exam Credit
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Accredited / Credits
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Yes,
2
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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Seminar
2
[Hours/Week]
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Course credit prior to examination
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No
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Course credit prior to examination
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No
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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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NO
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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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20 / -
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65 / -
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24 / -
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Included in study average
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NO
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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
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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 |
S|N |
Periodicity |
každý rok
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Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
Yes
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Fundamental theoretical course |
Yes
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Evaluation scale |
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 seminar represents the first introduction to ordinary differential equations. The student obtains an overview of basic types of ordinary differential equations and of phenomena that can be described by these equations. The student becomes acquainted with elementary methods of solving linear initial and boundary value problems and partially also with special types of nonlinear problems.
The seminar assumes the knowledge of mathematical analysis within the range of lectures KMA/M1. It is recommended to KMA/MA2, KMA/M2.
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Requirements on student
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written test (required at least 50%)
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Content
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Week 1: Differential equations as models of real world processes. Basic notation. Qualitative analysis of population models.
Week 2: Cauchy problem for equations of the 1st order. Euler method of numeric integration. Equations with separable variables.
Week 3: Cauchy problem for equations of the 1st order. Homogeneous equation. Substitution.
Week 4: Cauchy problem for equations of the 1st order. Geometric interpretation and orthogonal curves.
Week 5: Linear problems of the 1st order. Homogeneous equations. Variation of parameters for non-homogeneous equations.
Week 6: Linear problems of the n-th order. Fundamental system.
Week 7: Linear problems of the n-th order. Variation of parameters.
Week 8: Linear equations with constant coefficients. Characteristic equation.
Week 9: Linear equations with constant coefficients. Particular integral.
Week 10: Euler equation.
Week 11: Boundary value problems. Eigenvalues and eigenfunctions.
Week 12: Systems of differential equations.
Week 13: Nonlinear equations - special types.
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Activities
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Fields of study
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Guarantors and lecturers
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-
Guarantors:
Prof. Ing. Petr Girg, Ph.D. (100%),
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Tutorial lecturer:
Doc. Ing. Radek Cibulka, Ph.D. (100%),
Ing. Jan Čepička, Ph.D. (100%),
Prof. Ing. Petr Girg, Ph.D. (100%),
Doc. RNDr. Petr Stehlík, Ph.D. (100%),
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Literature
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Basic:
Matematická analýza II
(Tomiczek, Petr)
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Basic:
Obyčejné diferenciální rovnice
(Krajc, B., Beremlijski, P.)
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Recommended:
Ráb, Miloš. Metody řešení obyčejných diferenciálních rovnic. Masarykova univerzita. Brno., 2012. ISBN 978-80-210-5816-3.
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Recommended:
Kufner, Alois. Obyčejné diferenciální rovnice. 1. vyd. Plzeň : Západočeská univerzita, 1993. ISBN 80-7082-106-X.
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Recommended:
Mošna, František. Obyčejné diferenciální rovnice. Univerzita Karlova, Praha, 2019. ISBN 978-80-7603-090-9.
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Recommended:
Míka, Stanislav; Kufner, Alois. Okrajové úlohy pro obyčejné diferenciální rovnice. 2. upr. vyd. Praha : SNTL - Nakladatelství technické literatury, 1983.
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Recommended:
Nagy, Jozef. Soustavy obyčejných diferenciálních rovnic : Vysokošk. příručka pro vys. školy techn. směru. 2., nezm. vyd. Praha : SNTL, 1983.
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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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26
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Preparation for comprehensive test (10-40)
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16
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Preparation for formative assessments (2-20)
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10
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Total
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52
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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 základním principům z oblasti diferenciálního počtu funkcí jedné proměnné |
rozumět základním principům z oblasti integrálního počtu funkcí jedné proměnné |
rozumět základním principům z oblasti lineární algebry |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
derivovat a integrovat funkce jedné proměnné |
ovládat aritmetické operace s vektory a maticemi |
pro zadanou matici vypočítat vlastní čísla a vlastní vektory |
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: |
klasifikovat obyčejné diferenciální rovnice |
formulovat základní počátečně a okrajové úlohy pro obyčejné diferenciální rovnice |
popsat a vysvětlit elementární metody řešení obyčejných diferenciálních rovnic |
Skills - skills resulting from the course: |
řešit rovnice prvního řádu |
řešit lineární rovnice n-tého řádu s konstantními koeficienty |
řešit soustavy lineárních diferenciálních rovnic prvního řádu |
řešit úlohy na vlastní čísla |
aplikovat obyčejné diferenciální rovnice a jejich řešení na úlohy z praxe |
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: |
Test |
Skills demonstration during practicum |
Skills - skills achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Test |
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 supplemented with a discussion |
Interactive lecture |
Seminar classes |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Interactive lecture |
Seminar classes |
Competences - the following training methods are used to achieve the required competences: |
Lecture supplemented with a discussion |
Interactive lecture |
Seminar classes |
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