The primary focus of this work is to discuss the mechanical action of the Marshall Differential Analyzer ( ART ) in a mathematical context. Differential Analyzers are primarily used to calculate the solutions to Differential Equations. A full account of the uses of Marshall\u27s Differential Analyzer is given. Furthermore, a pure mathematical justification of how the machine integrates (mechanical integration) is provided via an application of the Riemann Integral. Many simple example problems are detailed ultimately leading up to the calculation of nonlinear problems, more specifically, a nonlinear oscillator
