Difference equations, their applications and estimation theory

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

The series of lectures is devoted to difference equations and estimation theory. The methods of solving linear and nonlinear difference equations and behaviour of their solutions are presented. In the second part are discussed estimators of statistical parameters and their properties. The methods of point estimation and construction of confidence intervals are presented.

Requirements:

Syllabus of lectures:

1.Linear difference equations and their methods of solving

2.Nonlinear difference equations and chaotic behaviour of their solutions.

3.Applications of difference equations in physics and elsewhere

4.Point estimation and properties of estimator

5.Confidence intervals and their properties

Syllabus of tutorials:

Study Objective:

Knowledge:

Knowledge of types of difference equations and their solving methods. Knowledge of the basics theorem about difference equations and their chaotic behaviour. Knowledge of properties of estimators and methods of their finding.

Abilities:

Ability to calculate a solution of linear difference equation of the first and second order with constant coefficients. Ability to find a solution of special types of nonlinear difference equations. Ability to find the confidence interval for important statistical parameters.

Study materials:

1. H. Levy F. Lessman, Finite Difference Equations, Dover, London (1961)

2. V. Lakshmikantham and D. Trigante, Theory of Difference Equations: Numerical Methods and Applications, Mathematics in Science and Engineering, 181, Academic Press, Boston (1988)

3. D. O. Wackerly, W. Mendenhall, R. L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press (2011)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: