Heaviside step function

Defines the Heaviside step function and computes its Laplace transform.

[salesv]

t' is just a dummy variable, if I have, for example, f(t') = t' it's the same as having f(t) = t, so it doesn't really matter what symbol you use for the argumente, the function, and the Laplace Transform, will be the same.

[marchlondon]

Really well explained ! thank you very much !
The only question I have is, How do you get in the very last end that the laplace transform of T' equals L(T) ?

I mean, how did u get this relationship of T' to T ?

Many thanks

[lasredchris]

For the sin function, how can you assume that for t values less than c, the function will be 0?

[ahyes]

For the last two integrals, are the lower bounds supposed to be zero or "c"?

[NathanSibs]

im not sure he actually meant t` turns into t. when we did this problem in class we used a u substitution instead of t`
so your ending should read e^(-s*c)*Laplace{f(u)}
thats how i understood it at least.

[germanelnica]

a pesar de ser latino le entendi a la explicación, lo único restante fue el ejemplo

[_hhk]

OK so I'm a pain in the ass but it's called the Heavieside function, named after the British mathematician Oliver Heavieside - hot heaviside.