Transforms generally take a vector from one vector space to another. The neat thing is that you can pack concepts like functions into your vectors and calculus operations like integration and differentiation into your concept of a vector space.
The LaPlace transform lets you take a function from the normal calculus universe and map it into one where integration and differentiation are represented by a variable that gets multiplied or divided in. This lets you complete what might be a difficult or out-right impossible integration with algebra.
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