3 - Applications of First-Order Ordinary Differential Equations

Abstract

This chapter describes the applications of first-order ordinary differential equations. Many interesting problems involving population can be solved with first-order differential equations. These include the determination of the number of cells in a bacteria culture, the number of citizens in a country, and the amount of radioactive substance remaining in a fossil. First-order linear differential equations can also be used to solve a variety of problems that involve temperature. For example, a medical examiner can find the time of death in a homicide case, a chemist can determine the time required for a plastic mixture to cool to a hardening temperature, and an engineer can design the cooling and heating system of a manufacturing facility. Although distinct, each of these problems depends on a basic principle that is used to develop the associated differential equation. The motion of some objects can be determined through the solution of a first-order equation. The chapter explains some of the theory that is needed to set up the differential equation that models the situation.