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Solutions of problems of classical variational calculus, Finding and Examination of Extreme of functionals.
Formulation of a variational problem and determination of their properties. Modern variational calculus. Application
of variational methods to the solution of boundary value problems. Applications in problems of mathematical
physics.
Last update: Kapsa Vojtěch, RNDr., CSc. (02.05.2018)
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The aim of this course is to deepen and broaden knowledge of variational methods with applications in physics. Last update: Augustovičová Lucie, doc. Ing., Ph.D. (02.05.2018)
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The course credit is awarded for participation and exercise activity. Lack of participation can not be compensated by other means. Course credit is a condition of admission to the exam. The exam is oral and the requirements correspond to the syllabus of the subject in the range that was presented at the lecture. Last update: Augustovičová Lucie, doc. Ing., Ph.D. (02.05.2018)
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Last update: Kapsa Vojtěch, RNDr., CSc. (02.05.2018)
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lecture and excercise Last update: Kapsa Vojtěch, RNDr., CSc. (02.05.2018)
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1. Introduction and motivational examples 2. Fundamental lemma of variational calculus 3. Extreme of functional, Euler-Lagrange equations 4. Conditions for the existence of extreme of functional 5. Sturm-Liouville problem and quadratic functional 6. Sobolev spaces 7. Weak solution of boundary value problems for elliptic equations 8. Lax-Milgram theorem 9. Rayleigh-Ritz method 10. Hamilton's principle for discrete systems 11. Hamilton's principle for continuous systems 12. Stability of dynamical systems
The exercises include the solution of specific tasks of the variational calculus - e.g. the problem of the shortest line, the brachistochrone problem, the shape of a liquid drop, the soap film between two coaxial circular rings, the rod deflection, the static deflection of an elastic string, applications of Hamilton’s principle Last update: Augustovičová Lucie, doc. Ing., Ph.D. (02.05.2018)
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