Introduction
Suppose a certain chemical company releases pollutants into a nearby river during the course of its production cycle. The function Y(t) models the amount, in gallons, of pollutant material dumped into a river at any given time t, measured in minutes.
1) What does Y'(t) represent?
2) What are the units of Y'(t)?
We have a flow meter that measures, at any time t, the rate at which pollutants are being released into the river. How could we find the amount of pollution in the river at t?
The Swiss mathematician Leonhard Euler, came up with a numerical method to approximate the solution for this type of problem. With his method, if we know the amount of pollutant material in the river when we first set up our device (initial condition) and the rate at which pollutants are added, we can approximate the amount of pollutant at any time t. Euler's method is a step-wise procedure which uses the initial value with the rate of change to construct a number of tangent lines leading to the desired value.