Operational Calculus Approach for Solving Ordinary Differential Equations

Laplace transform method is studied in this chapter. It is an operation calculus method for finding solutions to differential equations, especially solutions to models in engineering. Problems solved using the Laplace transform are: LRC electrical problems with constant voltages and n-th order linear differential equations. In real life, systems may be governed by combinations of continuous and discrete characteristics, referred to as hybrid systems. In order to handle such systems effectively, the Laplace transform of discrete systems is also studied to complement the continuous systems.

Keywords: Hybrid systems, Laplace transform, LRC electrical problems, Maple examples, Milne transform, Operation calculus.