9.1 Modelling with Differential Equations Overview
University of Toronto St. George
9.1 Differential Equations
Modeling With Differential Equations: Overview
Differential Equation: contains an unknown function and one or more of its derivative
Second order differential equation involves second derivatives
Models of Population Growth
Rate of population growth: based on the assumption that population growth rate is
proportional to the population size. K is the proportionality constant.
Model for the Motion of a Spring
Restoring force: , where k is a positive constant and is the length stretched from its natural
length. The force is proportional to .
Newton’ second law states: ; rearranging: