Continuous Dynamical Systems

fakultatywne

mieszany: w sali i zdalnie

The aim of the course is to provide students with the necessary information on the theory of autonomous dynamical systems, thanks to which they will be ready to apply the acquired knowledge to solve certain problems in various fields of science and practice.

Educational profile: general academic

Form of study: full-time

Mandatory item

Academic discipline: science and natural science, field of study in the arts and science: mathematics

Year of study: 1, semester: 2

Prerequisites: linear algebra, ordinary differential equations, mathematical analysis

lecture 30 hours. exercises 30 hours

Didactic methods: lectures, calculation exercises, consultations, work on literature, solving homework, discussions in problem groups.

ECTS points: 5

Student workload balance:

participation in lectures 15x2h = 30h

participation in exercises 15x2h = 30h

preparation for classes 7x2h = 14h

completion of solving tasks started during classes and preparation of notes after classes at home 10x3h = 30h participation in consultations 3x1h = 3h

preparation for the exam and participation in it 12h + 3h = 15h

preparation for tests 2x4h = 8h

Quantitative indicators

student workload related to classes requiring the direct participation of an academic teacher: 63 hours, 2 ECTS

[1] J.Diblík, M. Růžičková, E. Schmeidel, Równania różniczkowe zwyczajne II, stabilność rozwiązań, Wydawnictwo UwB 2023.

[2] G Bowtell, Dynamical Systems, Centre for Mathematical Science, City University London, 2011.

[3] Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, American Mathematical Society (AMS).

Directional learning outcomes:

KA7_WG02, KA7_WG03, KA7_WG04, KA7_WG05, KA7_WG06, KA7_UU01, KA7_UW02, KA7_UW06, KA7_UW13, KA7_UW14, KA7_KK01.

The student has in-depth knowledge of the theory of autonomous dynamical systems and their applications; Knows the limitations of his own knowledge and understands the need for further education; Can independently search for information on a given topic in the literature, understands names and mathematical terms in Polish and English; The student is prepared to apply the acquired knowledge in solving certain problems in various fields.

Classes - credit based on the results of two tests and activity and attendance at classes:

1. Colloquium results. It is necessary to obtain at least 50% of points from each colloquium.

2. Exercise activity. During the semester, you can receive a total of 10 points for active participation in the exercises.

3. Attendance at classes. Two unexcused absences from classes are allowed. Each subsequent absence must be justified with a relevant certificate or made up.

In the case of not getting 51%, it is possible to write a credit for the entire semester. This credit can be taken by persons who have obtained at least 30% of the points from the colloquia (calculated as the arithmetic mean).

The exam is written.

1. A student who has passed the exercises is admitted to the exam.

2. A total of 10 points can be awarded for active participation in the exercises - the instructor will suggest.

3. A total of 90 points can be obtained for the written part of the exam.

It consists of 3 parts containing theoretical questions.

So a student can get a total of 100 points from all parts. The final grade is in accordance with the presented grading scale:

90% -100% - rating: very good;

80% - 89% - rating: good plus;

70% - 79% - rating: good;

60% - 69% - rating: sufficient plus; 46% - 59% - rating: satisfactory; 0% - 45% - rating: unsatisfactory.

In the case of a small number of missing points to pass or a better grade (up to 5% of the exam points), an oral exam is possible.