TABLE OF CONTENTS This chapter introduces the basics of differential and integral calculus. It is intended for readers who need an introduction or an accelerated review of this topic. Readers with a strong mathematical background may skip this chapter. Others may find it useful, as well as a convenient source for review.
Calculus is the branch of mathematics that is concerned with concepts such as the rate of change, the slope of a curve at a particular point, and the calculation of an area bounded by curves. Many principles governing physical processes are formulated in terms of rates of change. Calculus is also widely used in the study of statistics and probability.
The fundamental concept of calculus is the theory of limits of functions. A function is a defined relationship between two or more variables. One variable, called dependent variable, approaches a limit as another variable, called independent variable, approaches a number or becomes infinite. In calculus, we are interested in related variables. For instance, the amount of postage required to mail a package is related to its weight. Here, the weight of the package is considered the independent variable, and the amount of postage is considered the dependent variable.
The two branches into which elementary calculus is usually divided, are the differential calculus, based on the limits of ratios, and the integral calculus, based on the limits of sums.
Suppose that the dependent variable, denoted as y, is a function of...
