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Differential equations

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-2421/01
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KRC76Mgr. Jiří Krček
SWA0013RNDr. Martin Swaczyna, Ph.D.
Summary
This objective presents the part of basic mathematical course in the bachelor degree.
Learning Outcomes of the Course Unit
This subject offers integrated view on mathematical methods and tools needed to a solution practical problems described by differential equations. The applications are oriented to the problem solving of engineering practice with regard to prevailing speciality of students. Established goals tend namely to following knowledges:
- an orientation in typology of ordianary and partial differential equations;
- acquirement of basic analytical methods for solving of ordinary DE;
- an use of selected numerical methods;
- an ability to perform adequate mathematical model of real problem.
Course Contents
1. Introduction: basic notions, solution of DE, Cauchy problem, exitence and uniqueness of solution.
2. Solving methods of ordinary first-order DE: separation of variables, linear and Bernoulli DE, direction field and othogonal trajectories; special types of 1st order ODE.
3.Simple numerical methods: Picard approximation, Euler method.
4. Applications: kinematic equations, evolution an logistic models.
5. Linear ODE of higher order I - homogeneous equations: structure and properties of solution, equations with constant coefficients.
6. Linear ODE of higher order II: complete equation with constant coefficients, equation with special right side; selected applications: mechanical vibrations, electrical circuits.
7. Systems of DE: linear systems, homogeneous systems with constant coefficients.
8. Non-homogeneous linear systems: structure of solution, analytical methods for solving.
9. Phase-mapping of solution of homogeneous 2nd order system, introduction to the stability theory.
10. The backgrounds of partial DE: basic notions, method of characteristics for the 1st order PDE.
11. Second order PDE: typology, important equations in mathematical physics.

Recommended or Required Reading
Required Reading:
VLČEK, J., Mathematical modeling - http://mdg.vsb.cz/portal/dr/U18Mod.pdf
AHMAD, S., AMBROSETTI, A.: A Textbook of Ordinary Differential Equations. Springer, 2014. ISBN 978-3-319-02129-4
VLČEK, J., VRBICKÝ, J. Diferenciální rovnice (Matematika IV), VŠB-TU Ostrava, 1997, 134 stran, ISBN 80-7078-438-5
VLČEK, J., Matematické modelování - http://mdg.vsb.cz/portal/dr/U18Mod.pdf
Recommended Reading:
LOGAN, J. D. A First Course in Differential Equations, Springer, 2011, 386 pp., ISBN 978-1-4419-7592-8
REKTORYS, K. et al. Přehled užité matematiky I, II, Prometheus, Praha, 2009 (7. vyd.), 720 stran, ISBN 978-80-7196-180-2
DRÁBEK, P., HOLUBOVÁ, G. Parciální diferenciální rovnice., Západočeská univerzita, Fakulta aplikovaných věd, Plzeň, 2001, 177 stran, ISBN: 80-7082-766-1
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 15
        ExaminationExamination70 21