Laplace Transforms

Laplace transforms are mathematical tools used to convert complex functions, often representing physical systems like electrical circuits or mechanical systems, from the time domain into a simpler form called the frequency domain. This transformation simplifies the process of analyzing how systems respond to inputs, such as signals or forces, by turning differential equations into algebraic equations. Once solved in this easier form, the inverse Laplace transform is used to translate the results back into the original time-based context. Overall, Laplace transforms streamline the analysis and design of dynamic systems across engineering and science.