Mathematics of Dynamic Processes
This chapter introduces conditions for the solvability of ordinary differential and difference equations, which will be fundamental in describing dynamic processes. In the constant coefficient cases, Laplace transforms and Z-transforms serve as the most commonly used solution methods. The chapter discusses their definitions and main properties. It introduces a very useful function transformation, known as Laplace transform. Dynamic systems with continuous time scale are usually modeled by a system of linear or nonlinear differential equations. Dynamic systems with discrete time scale are usually modeled by a system of difference equations. The solution of the difference equations represent the state of the dynamic system. The chapter develops conditions for the existence and the uniqueness of the solution of initial value problems of ordinary differential equations. It examines the solution of linear difference equations; the closed form solution introduced next is often applied in solving practical problems.