What Is Calculus About?, by W. W. Sawyer, New Mathematical Library
Four out of five stars
To his credit, Sawyer uses the example that is the easiest to understand when he is describing derivatives and how they represent a rate of change. That example is the position of a moving particle over time, how the velocity changes over time, how it is derived and the rate at which velocity changes over time. In other words, start with the formula for position, the first derivative is velocity and the second derivative the acceleration. The underlying algebra is as easy as it can be.
This is a physical principle that nearly everyone can understand, which makes it an excellent introduction to the basics of differential calculus. The problem is that this example is used to the point of overuse. The reader beginning their study of calculus will not understand how powerful it is, as there is little in the way of other examples where calculus is used to solve problems in the world.
The principles that are explained are handled very well, there is just not enough of them covered.