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Lecturer(s)
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Moravcová Fanny, Ph.D.
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Holeček Miroslav, Doc. Dr. RNDr.
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Course content
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1. Dimensions, unities, basic variables, basic variables, dimensional independence and dependence. 2. Dimensional independence and dependence: exercises. 3. Pi-theorem (introduction, development, and examples). 4. Physical similitude 5. Self-similitude 6. Dynamic systems with one degree of freedom, equilibrium point, bifurcation 7. Dynamic systems with two degress of freedom, atractors 8. An example of dynamic system: Van Der Pol oscillator 9. Other examples: Lotka-Voterra system, retarded fall 10. Approximation for solving problems in physics: residua method, Galerkin method 11. Finite element method (1) 12. Finite element method (2) 13. Exhibitions of uses of some software products
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Learning activities and teaching methods
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Lecture supplemented with a discussion
- Preparation for an examination (30-60)
- 60 hours per semester
- Contact hours
- 26 hours per semester
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| prerequisite |
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| Knowledge |
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| The students know basic methods for solving linear differential equations, basic rules for solving systems of linear equations, Taylor development, matrix and vector calculus (calculus of eigenvalues). |
| learning outcomes |
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| The students will be able to analyze a problem in physics, to choice the suitable variables and to verify their supposition using the dimensional analysis. They will be able to rewrite the equations of the physical problem in a adimensional form. They will be able to study the equilibrium points of the solution, to dispute their stability and the eventual bifurcations of the trajectories in dynamical case. They will be also familiarized with the finite element method for approximating solution of static problems. |
| teaching methods |
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| Lecture supplemented with a discussion |
| assessment methods |
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| Written exam |
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Recommended literature
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Barenblatt, G.I. Similarity, Self-Similarity, and Intermediate Asymptotics. New York, 1977.
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Krempaský, Július. Synergetika : v astrofyzike, chémii, biológii, ekológii, medicíne, ekonómii a v sociológii. Vyd. 1. Bratislava : Veda, 1988.
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Slavík, Jan. Teoretická mechanika : moderní přehled. I. díl. 1. vyd. Plzeň : Pedagogická fakulta Západočeské univerzity, 1994. ISBN 80-7043-105-9.
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Slavík, Jan. Teoretická mechanika : moderní přehled. II.. 1. vyd. Plzeň : Pedagogická fakulta Západočeské univerzity, 1995. ISBN 80-7043-158-X.
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