DIFFERENCE EQUATIONS AND THEIR APPLICATIONS

Basic notions of ordinary difference equations. Linear ordinary difference equations of order one. Linear ordinary difference equations of order greater than one. Homogeneous and non-homogeneous ordinary difference equations with constant coefficients: general theory and solutions’ techniques. Linear ordinary difference equations with non-constant coefficients. Non-linear ordinary difference equations. Systems of linear ordinary difference equations. Stability of solutions of ordinary difference equations. Periodic solutions of ordinary difference equations. Partial difference equations of two variables. The methods of Lagrange, Laplace and separation of variables for the solution of partial difference equations of two variables. Applications in mathematics, numerical solution of differential equations, physics, economy, biology, social sciences, helath sciences, etc.