### Course: Differential equations

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 Course title Differential equations NTI/DR Lecture + Lesson Bachelor not specified Winter 4 Czech Compulsory Face-to-face Course does not contain work placement None
Lecturer(s)
• Březina Jan, doc. Mgr. Ph.D.
Course content
Lectures: 1) Physical problems leading to ODR, basic methods for solution of ODR, Initial value problem for systems of ODR. 2) Higher order systems, Lipschitz functions, existence and uniqueness theorems. 3) Theory for linear systems, systems with constant matix, variation of constant for systems. 4) Explicit Euler method, theoretical properties of the numerical methods 5) Stability, stiff problems, implicit Euler method, Newton method for the systems of AE. 6) Runge-Kutta methods, explicit and implicit. 7) Boundary value problems, finitie diference method. Tutorials: 1) Repetition: linear algebra, eigenvalues, complex numbers 2) Physical problems leading to ODR. 3) Conversion of the higher order equation to the system. 4) Standard fundamental matrix - using eigenvectors. 5) Systems with complex eigenvalues. 6) Variation of constants. 7) Reserve. 8) Test. 9) Explicit and implicit Euler method, using Matlab. 10) Explicit and implicit Euler method, for systems. 11) Stability, stiff problems, examples. 12) Usage of Matlab's built-in solvers. 13) Finite difference method for boundary value problems. 14) Reserve. Evaluation of the individual work.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
• Class attendance - 42 hours per semester
• Preparation for exam - 39 hours per semester
• Preparation for formative assessments - 21 hours per semester
• Preparation for credit - 17 hours per semester
Learning outcomes
The course presents basic methods for solving ordinary differential equations and their systems. The course have two parts. The first part introduces elementary theoretical properties of the systems of the ordinary differential equations and their exact solutions. The second part is an introduction to the numerical methods.
Student will acquire theoretical prerequisites for solution systems of ordinary differential equations and a skill of their numerical solution using appropriate numerical methods.
Prerequisites
Unspecified

Assessment methods and criteria
Combined examination

Requirements for getting a credit are activity at the tutorials and successful passing of the tests. Examination is written and oral form.
Recommended literature
• Deuflhard, Peter, and Folkmar Bornemann. Scientific Computing with Ordinary Differential Equations. Springer Science & Business Media, 2012.
• J. E. Flaherty. Ordinary Differential Equations [online]. [cit. 2016-01-08]. Dostupné z: http://www.cs.rpi.edu/~flaherje/odeframe.html.
• Miroslav Feistauer. Základy numerické matematiky [online]. Praha: 56 s. [cit. 2016-01-08]. Dostupné z: http://www.karlin.mff.cuni.cz/~feist/ZNM-scripta.pdf.
• Nagy, J.:. Soustavy obyčejných diferenciálních rovnic.. Praha, MVŠT, SNTL, 1983.
• Vitásek, E. Numerické metody. Praha 1993.

 Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Applied Sciences in Engineering (2019) Category: Special and interdisciplinary fields 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Applied Sciences in Engineering (2016) Category: Special and interdisciplinary fields 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Automatic Control and Applied Computer Science (2016) Category: Special and interdisciplinary fields 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Mechatronics (2016) Category: Special and interdisciplinary fields 1 Recommended year of study:1, Recommended semester: Winter