Laplace transform of sinhat & coshat | transform of hyperbolic trigonometric function l Shah Hussain

Learn Mathematics By Shah Hussain
"The Laplace Transform"
Today we are going to discuss an interesting topic of graduation level.
That is laplace transform.
▪The laplace transform is an efficient technique for solving linear differential equations with constant coefficients .We shall study it's basic properties and will apply them to solve initial value problems.
As the name suggests,

▪ Laplace Transform is an operator which transforms a function f of the variable t into a function F of the variable s.

"Let f be a real- valued piecewise continues function defined on [0,infinity). The laplace transform of f , denoted by L(f), is the function F defined by F(s)
Provided the improper integral in 1 converges.
▪The domain of F is the set of all real numbers s for which the above integral converges."

▪The transform operation transforms the given function f of the variable t into a new function F of the variable s

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▪The laplace transform exists only for certain class of functions.

▪Hope so you have understand it.
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