Laplace transform [SEP] named after
Laplace transform
In mathematics, the Laplace transform is an integral transform named after its inventor Pierre-Simon Laplace (). It transforms a function of a real variable (often time) to a function of a complex variable (complex frequency). The transform has many applications in science and engineering.
The Laplace transform is similar to the Fourier transform. While the Fourier transform of a function is a complex function of a "real" variable (frequency), the Laplace transform of a function is a complex function
Laplace–Carson transform
In mathematics, the Laplace–Carson transform, named after Pierre Simon Laplace and John Renshaw Carson, is an integral transform with significant applications in the field of physics and engineering, particularly in the field of railway engineering.
Definition.
Let formula_1 be a function and formula_2 a complex variable. The Laplace–Carson transform is defined as:
The inverse Laplace–Carson transform is:
where formula_5 is a real-valued constant, formula_6 refers to the imaginary axis, which indicates the