The Laplace transform

Module overview. This module is a mathematical section to establish a base for the theory of control systems. This is a tool and it is indispensable as most of linear system dynamics are described in a mapped space that can only be understood when the main theorems of the Laplace transform are known. The module contains only the essential results, which are explained by several examples from the area of differential equations and their solutions. Some additional mathematical details can be found in the mathematical appendix module. The correspondences of the Laplace transform are given in tabular form to be simply used for the forward and back transformation. Special focus is put on the solution of differential equations using the Laplace transform and on special signals, e.g. impulse or step.

Module objectives. When you have completed this module you should be able to:

1. Apply the Laplace transform to differential equations.
2. Solve linear differential equations.
3. Apply the main theorems of the Laplace transform.
4. Know how useful this techniques is to handle dynamical systems.

Module prerequisites. Mathematics: integrals, differential equations, complex numbers, rational and analytical functions.