Shifting Laplace Transforms :: The First Translation Theorem for Laplace Transforms

In this video we discuss the first translation theorem for Laplace Transforms. The first translation theorem for Laplace Transforms shifts the transform of a function in the s-domain.

Multiplying by e^(at) produces a shift in the function F(s).

We present the theorem here as well as an example to demonstrate how to use it.

Furthermore, this theorem can be used in reverse when computing inverse transforms where the square must be completed for a quadratic in the denominator.

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I'm Jonathan, and Laplace Transforms are one of the most useful tools in solving differential equations. I hope this video helps shed light on the first translation theorem.

Thanks for watching!