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Lecturer(s)
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Lášek António, prof. RNDr. Ph.D.
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Čižmář Jiří, doc. Ing. Ph.D.
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Novák Pavel, prof. Ing. Ph.D.
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Boháč Pavel, doc. RNDr. Ph.D.
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Course 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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Learning activities and teaching methods
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Lecture supplemented with a discussion, Lecture with practical applications, Seminar classes
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Contact hours
- 26 hours per semester
- Preparation for comprehensive test (10-40)
- 16 hours per semester
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| prerequisite |
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| Knowledge |
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| understanding basic principles of calculus of functions of one real variable: derivatives, differentials etc. |
| understanding basic principles of calculus of functions of one real variable: Newton integral, fundamental theorem of calculus etc. |
| understanding basic principles of linear algebra |
| Skills |
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| finding derivatives and primitives of real functions of one real variable |
| operations with vectors and matrices |
| calculating eigenvalues and eigenvectors for a given matrix |
| Competences |
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| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| classification of ordinary differential equations |
| formulation of basic initial and boundary value problems for ordinary differential equations. |
| knowledge of elementary methods for solving ordinary differential equations |
| Skills |
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| finding solutions of the ordinary differential equations of the first order |
| finding solutions of the ordinary differential equations of the n-th order with constant coefficients |
| finding solutions of the systems of linear differential equations of the first order |
| finding eigenvalues and eigenfunctions of basic types of eigenvalue problems |
| ability to apply ordinary differential equations and basic methods of their solutions to problems from practice |
| Competences |
|---|
| N/A |
| N/A |
| N/A |
| teaching methods |
|---|
| Knowledge |
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| Lecture supplemented with a discussion |
| Interactive lecture |
| Seminar classes |
| Skills |
|---|
| Lecture supplemented with a discussion |
| Interactive lecture |
| Seminar classes |
| Competences |
|---|
| Lecture supplemented with a discussion |
| Interactive lecture |
| Seminar classes |
| assessment methods |
|---|
| Knowledge |
|---|
| Test |
| Skills demonstration during practicum |
| Skills |
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| Test |
| Skills demonstration during practicum |
| Competences |
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| Test |
| Skills demonstration during practicum |
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Recommended literature
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Braun, Martin. Differential Equations and Their Applications. New York, 1992. ISBN 978-0-387-94330-5.
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Bronson, Richard; Costa, Gabriel B. Schaum's Outline of Differential Equations, Fifth Edition. New York, 2021. ISBN 978-1-2642-5882-6.
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Kufner, Alois. Obyčejné diferenciální rovnice. 1. vyd. Plzeň : Západočeská univerzita, 1993. ISBN 80-7082-106-X.
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Míka, Stanislav; Kufner, Alois. Okrajové úlohy pro obyčejné diferenciální rovnice. 2. upr. vyd. Praha : SNTL - Nakladatelství technické literatury, 1983.
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Mošna, František. Obyčejné diferenciální rovnice. Univerzita Karlova, Praha, 2019. ISBN 978-80-7603-090-9.
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Nagy, Jozef. Soustavy obyčejných diferenciálních rovnic : Vysokošk. příručka pro vys. školy techn. směru. 2., nezm. vyd. Praha : SNTL, 1983.
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Ráb, Miloš. Metody řešení obyčejných diferenciálních rovnic. Masarykova univerzita. Brno., 2012. ISBN 978-80-210-5816-3.
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Walter, Wolfgang. Ordinary Differential Equations. New York, 1998. ISBN 978-0-387-98459-9.
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