It turns out that most of the physical laws in the universe are concerned with rates of change.  For example, Newton's second law tells us about the rate at which the momentum of an object changes when a force is applied.  It is not concerned with the absolute values of the momentum of an object.  Rates of change are very familiar to us.  The quantity called velocity is just the rate of change of distance with time.  Likewise, acceleration is the rate of change of velocity with time.

To handle rates of change, we need to understand about calculus.  The first article provides a summary of some of the important results of differential calculus.  In the remaining articles, a number of interesting problems are considered.  The results of calculus are required to solve all of them - even those problems that seem relatively simple at first sight.  This is because it is easier to make statements about how the quantities of interest are changing, rather than about their absolute values.

So we will take a look at the refraction of light, reflection of light from mirrors, dogs chasing rabbits, and much more.  Many of these examples have been taken from G.F. Simmons' book called "Differential Equations".  However, the words and interpretation here are my own.  I have made no attempt at a rigorous mathematical treatment.  My aim is only to give a flavour of how maths is used to formulate problems, and then solve them.