SylabUZ
Nazwa przedmiotu | Lecture I-A |
Kod przedmiotu | 13.7-WF-FiAT-W-I-F- 18 |
Wydział | Wydział Fizyki i Astronomii |
Kierunek | Fizyka i Astronomia |
Profil | ogólnoakademicki |
Rodzaj studiów | trzeciego stopnia z tyt. doktora |
Semestr rozpoczęcia | semestr zimowy 2018/2019 |
Semestr | 2 |
Liczba punktów ECTS do zdobycia | 3 |
Typ przedmiotu | obowiązkowy |
Język nauczania | angielski |
Sylabus opracował |
|
Forma zajęć | Liczba godzin w semestrze (stacjonarne) | Liczba godzin w tygodniu (stacjonarne) | Liczba godzin w semestrze (niestacjonarne) | Liczba godzin w tygodniu (niestacjonarne) | Forma zaliczenia |
Wykład | 30 | 2 | - | - | Egzamin |
The goal of the course is to acquaint the students with some of the selected methods of the dynamical systems that are described using ordinary differentia equations systems. The course will present basic notions of the theory of differential equations. Students will learn various types of equations and their solution methods. One of the most important goals will be to present the practical methods of the study of certain equation systems that appear in physics, astronomy and other applied sciences.
Knowledge of calculus and aglebra on the at the academic level for science or technical courses.
Knowledge of basic physics on the academic level.
Knowledge of theoretical mechanics.
Ordinary differential equations:
phase curves and integral curves , first integral, phase portrait
types of equations
linear differentia equations
equilibrium points and their classification; normalization
stability
numerical integration methods
Lapunov’s exponents and deterministic chaos
Mechanics of material points and solids:
Lanrange and Hamilton equations
stability of equilibrium points in mechanicsl systems
chaos in mechanical systems
separatrix spliting amd Mielnikov method
Traditional lecture using multimedia presentations.
Opis efektu | Symbole efektów | Metody weryfikacji | Forma zajęć |
Writen test.
Passing criterium – a positive grade from the test that involves questions/exercises of various degrees of difficulty.
[1] Perko, Lawrence. 2001. Differential Equations and Dynamical Systems. Vol. 7. Texts in Applied Mathematics. New York, NY: Springer New York. http://link.springer.com/10.1007/978-1-4613-0003-8.
[2] Walter, Wolfgang. 1998. Ordinary Differential Equations. Vol. 182. Graduate Texts in Mathematics. New York, NY: Springer New York. http://link.springer.com/10.1007/978-1-4612-0601-9.
[3]. Schuster, Chaos deterministyczny, PWN, Warszawa 1993.
[4] Florian, Scheck. Mechanics: From Newton’s Laws to Deterministic Chaos. 3rd ed. New York, NY: Springer Verlag, 1999.
[1] W.I. Arnold, Równania różniczkowe zwyczajne, PWN 1975.
[2] W. I. Arnold, Teoria Równań Różniczkowych, PWN, 1983.
Zmodyfikowane przez dr Joanna Kalaga (ostatnia modyfikacja: 11-07-2018 13:07)