Differential Equations by Kake L Pugh

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I've forgotten what a differential equation is

Remember Newton's Second Law?

Force = Mass x Acceleration

or,

f = ma

where f stands for Force, m for Mass, and a for Acceleration.

or,

f = m dv
dt
which can be written as
dv
dt
 = f
m
because acceleration is the rate of change of velocity, v. And what we have there is a differential equation. The left-hand side isn't exactly a fraction, dv divided by dt; that's just a way of showing that the equation tells you how fast v changes over time, rather than what the fixed value of v is.

The way it works, suppose m=1 and f=2. Then f/m=2, so v increases by 2 every second. So you know that if v starts at 0, then after 4 seconds v=8.

This is a pretty easy differential equation, so easy in fact, that if (as we suppose here) f and m have fixed values, we can solve it in our heads to see what v is at any particular time, even time 1,000,000. The differential equations that mathematical biologists work with are more complicated, so we can only solve them approximately, on computers.

Equations translated from TEX by TTH, version 0.9.
29 August 1997