Dynamical systems and optimal control. A friendly introduction.

This volume provides an elementary introduction of the mathematical modelling in those areas of Dynamical Systems and Control Theory that arise frequently in Economics. In the first part the fundamental aspects of matematical modelling are developed, dealing with both continuous time systems (differential equations) and discrete time systems (difference equations). Particular attention is devoted to equilibria, their classification in the linear case, and their stability. An effort has been made to convey intuition and emphasize connections and concrete aspects, without giving up, however, to the necessary theoretical tools. In the second part the basic concepts and techniques of Dynamical Optimization are introduced, covering from the first elements of Calculus of Variations to the variational formulation of the most common problems in deterministic Optimal Control, both in the continuous and discrete versions. The last chapter contains a brief introduction to Dynamical Programming.