## Differential Analyzer Laboratory

Marshall's two-integrator DA, nicknamed "Lizzie".

A **differential analyzer** is a mechanical device which solves differential
equations by simulating them on physical components. DAs were used extensively in the first half of the 20th century, before digital computers were able to solve differential
equations. Today, DAs are still useful for letting us *see* the way that a solution
to a differential equation develops over time. The abstract changes in mathematical
quantities can be visualized in physical movements and rotations within the DA.

The key component of a DA is the **integrator**, a mechanical device that takes
a mechanical representation of a derivative as input and returns a mechanical
representation of the net change as output. The number of integrators in a DA tells what
kind of differential equations it can solve. A DA with two integrators can solve a single
second-order ODE, or a system of two first-order ODEs. A DA with four integrators can
solve a system of two second-order ODEs, or a single second-order ODE with a forcing
term that itself is the solution of a second-order ODE.

A DA is entirely analog. The output consists of a plot of a solution drawn on paper.

More information about differential analyzers can be found on the
Wikipedia article.

### Contact Information

**Dr. Bonita Lawrence **

Differential Analyzer Laboratory

Smith Hall 311

Division of Mathematics

One John Marshall Drive

Huntington, WV 25755-2560

304.696.3285

An overhead view of "Art".

Two integrators on the lab's main four-integrator DA, nicknamed "Art" in honor of
Arthur Porter.