A Tutorial on Analog Computation: Computing Functions over the Reals

Abstract

The best known programmable analog computing device is the differential analyser. The concept for the device dates back to Lord Kelvin and his brother James Thomson in 1876, and was constructed in 1932 at MIT under the supervision of Vannevar Bush. The MIT differential analyser used wheel-and-disk mechanical integrators and was able to solve sixth-order differential equations. During the 1930's, more powerful differential analysers were built. In 1941 Claude Shannon showed that given a sufficient numbers of integrators the machines could, in theory, precisely generate the solutions of all differentially algebraic equations. Shannon's mathematical model of the differential analyser is known as the GPAC.