Laplace Transforms : Theory, Problems, and Solutions

The Laplace transform is named after mathematician and astronomer Pierre-Simon Laplace, who used a similar transform in his work on probability theory. The Laplace Transform is a widely used integral transform in mathematics with many applications in science and engineering. The Laplace Transform can be interpreted as a transformation from time domain where inputs and outputs are functions of time to the frequency domain where inputs and outputs are functions of complex angular frequency.Laplace Transform methods have a key role to play in the modern approach to the analysis and design of engineering system Laplace transformation provides a powerful means to solve linear ordinary differential equations in the time domain, by converting these differential equations into algebraic equations. Laplace transformation belongs to a general area of mathematics called operational calculus which focuses on the analysis of linear systems.Laplace Transform is widely used by electronic engineers to solve quickly differential equations occurring in the analysis of electronic circuits.