Course: Seminar of Differential Equations

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Course title Seminar of Differential Equations
Course code KMA/SDR
Organizational form of instruction Seminar
Level of course Bachelor
Year of study 1
Semester Winter and summer
Number of ECTS credits 2
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Holubová Gabriela, Doc. Ing. Ph.D.
  • Girg Petr, Doc. Ing. Ph.D.
  • Benedikt Jiří, Doc. RNDr. Ph.D.
  • Kotsu Matas Aleš, Ing. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
Lecture supplemented with a discussion, Lecture with practical applications, Seminar classes
  • Contact hours - 26 hours per semester
  • Preparation for formative assessments (2-20) - 10 hours per semester
  • Preparation for comprehensive test (10-40) - 16 hours per semester
prerequisite
professional knowledge
There is no prerequisite for this course. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M1 or KMA/MA1.
learning outcomes
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. Solve the eigenvalue problems; 7. Apply ordinary differential equations and their solutions to real problems.
teaching methods
Lecture supplemented with a discussion
Lecture with practical applications
Seminar classes
assessment methods
Test
Skills demonstration during seminar
Recommended literature
  • Kufner, Alois. Obyčejné diferenciální rovnice. 1. vyd. Plzeň : Západočeská univerzita, 1993. ISBN 80-7082-106-X.
  • Míka, Stanislav; Kufner, Alois. Okrajové úlohy pro obyčejné diferenciální rovnice. 2. upr. vyd. Praha : SNTL - Nakladatelství technické literatury, 1983.
  • Nagy, Jozef. Soustavy obyčejných diferenciálních rovnic : Vysokošk. příručka pro vys. školy techn. směru. 2., nezm. vyd. Praha : SNTL, 1983.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Medical Informatics (2015) Informatics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 1 Summer
Faculty of Education Studies in Mathematics (13) Mathematics courses 2 Summer
Faculty of Applied Sciences Computer Control of Systems and Processes (2015) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (1) Economy 1 Summer
Faculty of Applied Sciences Computer Systems (2016) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Applied Sciences Geomatics (2012) Construction industry, geodesy and cartography 3 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Scientific Computing and Modelling (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Computer Control of Systems and Processes (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computer Systems (2017) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Education Studies in Mathematics (15) Mathematics courses 2 Summer
Faculty of Applied Sciences Computer Systems (2016) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Mechanical Engineering - (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Applied Sciences Medical Informatics (2017) Informatics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 1 Summer
Faculty of Applied Sciences Systems for Identification, Security and Communication (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computer Control of Systems and Processes (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computer Modelling (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 3 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2012) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Information Technologies (2016) Informatics courses 1 Summer
Faculty of Applied Sciences Intelligent Man-Machine Communication (2016) Special and interdisciplinary fields 1 Summer
Faculty of Mechanical Engineering Design of Power Machines and Equipment (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2007) Economy 1 Summer
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 3 Summer
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 3 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Computer Modelling (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Intelligent Man-Machine Communication (2017) Special and interdisciplinary fields 1 Summer
Faculty of Education Studies in Mathematics (14) Mathematics courses 2 Summer
Faculty of Applied Sciences Computer Modelling (2014) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 1 Summer
Faculty of Applied Sciences Computer Systems (2013) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Computations and Design (2014) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computer Systems (2017) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Education Studies in Mathematics (1) Mathematics courses 2 Summer
Faculty of Applied Sciences Intelligent Man-Machine Communication (2015) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computations and Design (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Systems for Identification, Security and Communication (2015) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 1 Summer
Faculty of Applied Sciences Information Technologies (2015) Informatics courses 1 Summer
Faculty of Applied Sciences Information Technologies (2012) Informatics courses 1 Summer
Faculty of Applied Sciences Information Technologies (2017) Informatics courses 1 Summer
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 3 Summer
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 3 Summer
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 3 Summer
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Computations and Design (2017) Special and interdisciplinary fields 1 Summer
Faculty of Economics Information Systems Management (2013) Economy 1 Summer
Faculty of Applied Sciences Systems for Identification, Security and Communication (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computer Systems (2012) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Summer
Faculty of Applied Sciences Geomatics (2015) Construction industry, geodesy and cartography 3 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2015) Mathematics courses 1 Summer
Faculty of Applied Sciences Medical Informatics (2016) Informatics courses 1 Summer