Review of
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.
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