SylabUZ
Nazwa przedmiotu | Differential Equations |
Kod przedmiotu | 11.1-WK-MATEP-DE-S22 |
Wydział | Wydział Matematyki, Informatyki i Ekonometrii |
Kierunek | Mathematics |
Profil | ogólnoakademicki |
Rodzaj studiów | pierwszego stopnia z tyt. licencjata |
Semestr rozpoczęcia | semestr zimowy 2022/2023 |
Semestr | 4 |
Liczba punktów ECTS do zdobycia | 5 |
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 |
Ćwiczenia | 30 | 2 | - | - | Zaliczenie na ocenę |
The main aim of this course is to familiarize students with the basic theory of ordinary differential equations: finding solutions of first-order and second-order ODE as well as first-order systems of ODE, the existence and the uniqueness of solutions of ODE, testing stability of critical points and making phase portraits of linear system in the plane.
Mathematical Analysis 1 and 2, Linear Algebra 1 and 2.
Lecture
Classes
1. Solving first-order ordinary differential equations: separable equations and the types of equations reducible to separable equations, linear equations, Bernoulli equations, Riccati equations, exact equations. Solving exercises related to physical phenomena which should be described in terms of Cauchy problems for ODE. (8 hours)
2. Solving exercises with the use of existence and uniqueness theorems of local solutions of initial problems for ODE. (3 hours)
3. Test. (2 hours)
4. Solving second-order ordinary differential equations by reducing them to first-order ordinary differential equations. Solving second-order linear ordinary differential equations. (5 hours)
5. Solving systems of first-order linear ordinary differential equations - computation of fundamental matrix. (5 hours)
6. Examination of stability of critical points of systems of first-order linear ODE. Sketching phase portraits. (5 hours)
7. Test. (2 hours)
Traditional lectures; classes with the lists of exercises to solve by students.
Opis efektu | Symbole efektów | Metody weryfikacji | Forma zajęć |
Classes: learning outcomes will be verified through homeworks and two tests consisted of exercises of different degree of difficulty. A grade determined by the sum of points from these homeworks and test is a basis of assessment.
Lecture: final exam. A grade determined by the sum of points from that exam is a basis of assessment.
A grade from the course is consisted of the grade from classes (50%) and the grade from the final exam (50%). To take a final exam, students must receive a positive grade from classes. To attain a pass in the course students are required to pass the final exam.
Zmodyfikowane przez dr Ewa Sylwestrzak-Maślanka (ostatnia modyfikacja: 16-12-2023 22:08)