MU:MU24055 Qualitative Methods for ODE - Course Information

MU24055 Qualitative Methods for Ordinary Differential Equations

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. Roman Popovych, D.Sc. (lecturer)
doc. RNDr. Jana Kopfová, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Jana Hantáková, Ph.D.
Mathematical Institute in Opava

Timetable

Thu 11:25–13:00 RZ

• Timetable of Seminar Groups:

MU24055/01: Wed 9:45–11:20 RZ, J. Kopfová

Prerequisites (in Czech)

TYP_STUDIA(N)

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Geometry and Global Analysis (programme MU, NMgr-M)
• Mathematical Analysis (programme MU, NMgr-M)
• Mathematical Modelling (programme MU, NMgr-M)

Course objectives

This is an advanced course of the theory of ordinary differential equations. The global and qualitative characteristics of ordinary differential equations and their systems will be investigated. The main focus will be on the asymptotic behavior of the different types of solutions and their stability.

Syllabus

• 1. Qualitative analysis of ordinary first-order differential equations (monotonicity and convexity of solutions, Barrow's formula)
  2. Stability (Lyapunov function, Lyapunov exponent, stability of the linearized system)
  3. Geometry of solutions of autonomous systems of differential equations in the plane (vector field index relative to the Jordan curve, Umlaufsatz, methods for finding cyclical solutions)
  4. Geometry of solutions of autonomous systems of differential equations in the 3-dimensional space (Lorenz's strange attractor)
  5. Qualitative analysis of solutions of non-autonomous systems of differential equations (non-unique solutions, the equation of pendulum)

Literature

required literature
• G. Teschl. Ordinary differential equations and dynamical systems. Providence, 2012. info
• P. Hartman. Ordinary Differential Equations. Baltimore, 1973. info

recommended literature
• T. Bárta, D. Pražák. OBYČEJNÉ DIFERENCIÁLNÍ ROVNICE, sbírka úloh a řešených příkladů. URL info
• J. Andres, J. Fišer. Obyčejné diferenciální rovnice 3: úvod do teorie stability. Olomouc, 2015. URL info
• L. S. Pontrjagin. Ordinary differential equations. Massachusetts, 1696. info

Language of instruction

English

Further comments (probably available only in Czech)

Study Materials
The course can also be completed outside the examination period.

Teacher's information

To obtain the course credit prior to examination, at least 3 problems are to be solved (a solution of a problem during the exercise or a homework). The exam is oral.

• Enrolment Statistics (Winter 2022, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2022/MU24055