**Laplace Transforms**

The use of Laplace transforms can greatly simplify the solution of models representing very complicated physical systems. Scientist has the ability to calculate inverse Laplace transforms numerically which makes this elegant technique easily accessible. Scientist can be used to simulate systems expressed in terms of Laplace transforms, or fit data to models expressed as Laplace transforms. This is especially useful when inverse Laplace transformation is difficult or even impossible analytically. This example is from the study of pharmacokinetics, this technique is equally useful in electrical engineering and other fields.

In this example we use Scientist to study administration of a drug by
infusion for a finite time. The model can be expressed in terms of the
Laplace transform as follows, where **K0** is the infusion rate
and **TAU** is the time at which infusion is stopped.

In order to solve the equations and calculate the results we run a simulation from time T = 0 to time T = 24 with 48 intervals by setting the independant parameter range and number of intervals in the variable and parameter interface as shown.

Scientist runs the simulation and places the calculated values in a spreadsheet. Using the quick chart function we can quickly graph the results of the calculation.