laplace_transform - Synonyms of laplace_transform | Antonyms of laplace_transform | Definition of laplace_transform | Example of laplace_transform | Word Synonyms API

Article	Example
Laplace transform	as solutions of differential equations but did not pursue the matter very far.
Laplace transform	In pure and applied probability, the Laplace transform is defined as an expected value. If is a random variable with probability density function , then the Laplace transform of is given by the expectation
Laplace transform	When one says "the Laplace transform" without qualification, the unilateral or one-sided transform is normally intended. The Laplace transform can be alternatively defined as the "bilateral Laplace transform" or two-sided Laplace transform by extending the limits of integration to be the entire real axis. If that is done the common unilateral transform simply becomes a special case of the bilateral transform where the definition of the function being transformed is multiplied by the Heaviside step function.
Laplace transform	The bilateral Laplace transform is defined as follows,
Laplace transform	The Laplace transform converges absolutely if the integral
Laplace transform	This ROC is used in knowing about the causality and stability of a system.
Laplace transform	Because of this property, the Laplace variable is also known as "operator variable" in the domain: either "derivative operator" or (for "integration operator". The transform turns integral equations and differential equations to polynomial equations, which are much easier to solve. Once solved, use of the inverse Laplace transform reverts to the time domain.
Laplace transform	Given the functions and , and their respective Laplace transforms and ,
Laplace transform	The Laplace transform can be viewed as a continuous analogue of a power series. If is a discrete function of a positive integer , then the power series associated to is the series
Laplace transform	where is a real variable (see Z transform). Replacing summation over with integration over , a continuous version of the power series becomes