All Science Fair Projects

Science Fair Project Encyclopedia for Schools!

 Search    Browse    Forum  Coach    Links    Editor    Help    Tell-a-Friend    Encyclopedia    Dictionary

Science Fair Project Encyclopedia

For information on any area of science that interests you,
enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
Or else, you can start by choosing any of the categories below.

Bromwich integral

In mathematics, the Bromwich integral or inverse Laplace transform of F(s) is the function f(t) which has the property

$\left\{\mathcal{L}f\right\}(s) = F(s),$

where $\mathcal{L}$ is the Laplace transform. The Bromwich integral is thus sometimes simply called the inverse Laplace transform.

The Laplace transform and the inverse Laplace transform together have a number of properties that make them useful for analysing linear dynamic systems.

The Bromwich integral, also called the Fourier-Mellin integral, is a path integral defined by:

$f(t) = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}F(s)e^{st}\,ds,\quad t>0,$

where the integration is done along the vertical line x=c in the complex plane such that c is greater than the real part of all singularities of F(s).

The name is for Thomas John I'Anson Bromwich (1875-1929).