3 Properties of Laplace Transforms: Linearity, Existence, and Inverses
The Laplace Transform has several nice properties that we describe in this video:
1) Linearity. The Laplace Transform of a linear combination is a linear combination of Laplace Transforms. This will be very useful when applied to linear differential equations
2) Existence. When functions are reasonably nice - something we will call of exponential order - then the Laplace Transform converges.
3) Inverses. For L(f(t)=F(s), there is a unique f(t) for any given F(s). What this means is that we can define an inverse Laplace Transform.
This is the second video on Laplace Transforms in my Differential Equations Playlist: • Laplace Transforms and Solving ODEs
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