Mathematics in motion: Linear systems of differential equations on the differential analyzer.

摘要

In this work, I will provide an introduction to the differential analyzer, a machine designed to solve differential equations through a process called mechanical integration. I will give a brief historical account of differential analyzers of the past, and discuss the Marshall University Differential Analyzer Project. The goal of this work is to provide an analysis of solutions of systems of differential equations using a differential analyzer. In particular, we are interested in the points at which these systems are in equilibrium and the behavior of solutions that start away from equilibrium. After giving a description of linear systems of autonomous differential equations and the traditional analytical method for finding a solution, I will run some of these systems on the differential analyzer. With this visual approach, we look at the behavior of the rates of change to study the equilibrium solutions. I want to give a mechanical description of the relationship between the equations of the system.