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Laplace Transform With Unit Step Functions :: Second Shifting/Translation Theorem
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In this video we discuss how to take Laplace Transforms of functions involving the unit step function.
The unit step function is a function that has a value of zero then takes a value of 1 (turns on) at some value 'a' and stays on forever after.
Graphical examples of functions involving unit steps are presented.
The second translation theorem tells us how to take the Laplace Transform of such functions.
The second shifting theorem in its first form is
L{f(t-a) U(t-a)} = F(s) e^(-as)
This form is more useful when taking inverse Laplace Transforms.
The second shifting theorem alternate form is
L{g(t)U(t-a)} = e^(-as) L{g(t+a)}
This form is more commonly encountered when computing the Laplace Transform.
-------------------------
I'm Jonathan, I'm excited to share with you what little I know about Laplace Transforms and unit step functions and how they're used.
Thanks for watching!
The unit step function is a function that has a value of zero then takes a value of 1 (turns on) at some value 'a' and stays on forever after.
Graphical examples of functions involving unit steps are presented.
The second translation theorem tells us how to take the Laplace Transform of such functions.
The second shifting theorem in its first form is
L{f(t-a) U(t-a)} = F(s) e^(-as)
This form is more useful when taking inverse Laplace Transforms.
The second shifting theorem alternate form is
L{g(t)U(t-a)} = e^(-as) L{g(t+a)}
This form is more commonly encountered when computing the Laplace Transform.
-------------------------
I'm Jonathan, I'm excited to share with you what little I know about Laplace Transforms and unit step functions and how they're used.
Thanks for watching!
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