Differential equations

A rule for change can come before a formula for the changing quantity. A differential equation describes how a quantity changes without giving the quantity itself, so understanding its behavior means reconstructing a function from local information and starting conditions. As we do that, we’ll encounter new functions whose behavior grows out of the equations that define them. The resulting models show how surprisingly different behavior can emerge from simple rules, and why a solution must be judged against both its mathematical conditions and the situation it represents.