| The students are acquainted with the basic terminology of probability theory, and are able to use the acquired knowledge in practical applications: identifying the suitable distribution and computing the probability of an event; computing the expectation and variance of a random variable; applying the law of large numbers, the central limit theorem and the Bayes' theorem in the appropriate circumstances and way. The students are acquainted with basic knowledge in differential equations and systems, and can use it in practical applications: computing the solution of a linear ordinary differential equation or system; identifying the equilibria of a dynamical system and classifying their stability.
|
Basic concepts of probability theory; conditional probability and Bayes theorem;
random variables, expected value and variance;
selection of univariate discrete and continuous probability distributions;
law of large numbers; central limit theorem.
Linear ODE with constant coefficients; systems of linear ODEs; solution of ODEs by series expansions; equilibria and stability of linear and nonlinear systems of ODEs;
|
