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Course info
KMA / SM2E
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Course description
Department/Unit / Abbreviation
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KMA
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SM2E
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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 to Mathematics 2
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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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0 / -
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0 / -
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142 / -
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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 |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
S|N |
Substituted course
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KMA/SZM2
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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 goal is to acquaint the students with basic types of ordinary differential equations, with phenomena described by these equations, and with methods of solving these equations. Number and function series. Taylor's and Fourier's series.
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Requirements on student
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It is necessary to obtain at least 60% points of the assignments given by lecturer.
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Content
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Week 1-2: ODEs of the 1st order, nonlinear, linear. General and particular solutions, singular solutions. Formulation of the initial value problem. Methods of solving ODEs of the 1st order: direct integration, separation of variables, variation of parameters.
Week 3-6: Linear ODEs of higher orders - homogeneous, nonhomogeneous, with constant coefficients. Method of characteristic equation. Variation of parameters.
Week 7: Systems of ODEs of the 1st order.
Week 8 : Laplace transform. Inverse Laplace transform. Application to initial value problems for ODEs.
Week 10-11: Function series, point convergence, uniform convergence. Power series. Taylor series. Fourier series.
Week 12: Power and Fourier methods of solving boundary value problems.
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:
Jirásek, František; Kriegelstein, Eduard; Tichý, Zdeněk. Sbírka řešených příkladů z matematiky : logika a množiny, lineární a vektorová algebra, analytická geometrie, posloupnosti a řady, diferenciální a integrální počet funkcí jedné proměnn. Praha : SNTL, 1981.
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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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Recommended:
Mašek, Josef. Základy matematiky II : cvičení. 1. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-507-3.
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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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Preparation for formative assessments (2-20)
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10
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Preparation for comprehensive test (10-40)
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18
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Contact hours
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26
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Total
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54
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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/M1E. |
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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. Classify ordinary differential equations;
2. Formulate the basic initial and boundary value problems for ODEs;
3. Solve ODEs of the first order;
4. Solve linear ODEs of the n-th order with constant coefficients;
5. Solve systems of linear ODEs of the first order;
6. Deal with function sequences and function series.
7. Expend a function into Fourier series.
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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 |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Seminar |
Practicum |
Seminar classes |
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