In mathematics, the Laplace–Carson transform, named after

Pierre Simon Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...

and John Renshaw Carson, is an

integral transform In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily charac ...

with significant applications in the field of

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

and engineering, particularly in the field of railway engineering.

Definition

Let

V(j,t)

be a

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-orie ...

and

p

complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...

variable. The Laplace–Carson transform is defined as: :

V^\ast(j,p) = p\int^_0 V(j,t) e^ \, dt

The inverse Laplace–Carson transform is: :

V(j,t) = \frac \int^_ e^ \frac \, dp

where

a_0

is a real-valued constant,

i\infty

refers to the imaginary axis, which indicates the integral is carried out along a straight line parallel to the imaginary axis lying to the right of all the singularities of the following expression: :

e^\frac

References

Integral transforms Differential equations Fourier analysis Transforms {{mathanalysis-stub

Definition

See also

References