1. Laplace Transforms & Applications - Definition of Laplace Transform
The Laplace Transform is a transformative tool that simplifies the analysis of linear time-invariant systems by converting complex differential equations in the time domain into simpler algebraic equations in the s-domain. It is particularly beneficial in fields like electrical engineering and control systems, providing solutions for initial value problems and dynamic modeling. The conditions under which the Laplace Transform exists involve piecewise continuity and exponential order of functions.
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