Ordinary differential and difference eguations. 2400-M1IiERR

The basic notions of the theory of differential equations are derivative and differential which were introduced by G.W.Leibniz and I.Newton in 17th century. Since then we observe a fast progress in many domains of science. It seems that whenever we try to describe a dynamical process (evolution of a system) we have to use differential equations. The program of the Seminar is the following:
1. basic differential equations: equations with separated variables, first order linear equations, Bernoulli’s and Riccati’s equations, second order linear equations;
2.systems of linear equations with constant coefficients;
3. nonlinear systems of first order differential equations, critical points, phase portraits: introduction to qualitative theory of ordinary differential equation;
4. Lagrange and Hamilton equations;
5. difference equations and numerical solutions.

Course coordinators

Jagoda Kacprzak

Type of course

obligatory courses

Prerequisites (description)

(in Polish) Założenia wstępne: Student powinien posiadać umiejętność posługiwania się rachunkiem różniczkowym i całkowym oraz pojęciami algebry liniowej w zakresie kursu tych przedmiotów dla pierwszego roku WNE lub jakiegokolwiek wydziału o kierunku matematycznym, przyrodniczym lub technicznym.

Learning outcomes

Student knows basic types of ordinary differential equations, the basic methods of solutions of the equations and its systems, some examples of its applications to economic sciences and sociology.

Assessment criteria

Exam

Bibliography

A.Palczewski, Równania różniczkowe zwyczajne, WNT 2004;
H.Amann, Ordinary Differential Equations, Gruyter, Berlin 1990;
P.Hartman, Ordinary Differential Equations, J.Wiley and Sons, N.Y. 1964;
D.K.Arrowsmith, C.M.Place, Ordinary Differential Equations, A Qualitative Approach with Applications, Chapman and Hall, London 1982