### Course Introduction

*Calculus can be thought of as the mathematics of CHANGE. Because
everything in the world is changing, calculus helps us track those
changes. Algebra, by contrast, can be thought of as dealing with a large
set of numbers that are inherently CONSTANT. Solving an algebra
problem, like *y = 2x + 5*, merely produces a pairing of two
predetermined numbers, although an infinite set of pairs. Algebra is
even useful in rate problems, such as calculating how the money in your
savings account increases because of the interest rate *R*, such as *Y = X_{0}+Rt*, where*t* is elapsed time and *X_{0}_{ }*is the initial deposit. With compound interest, things get complicated for algebra, as the rate *R* is itself a function of time with *Y = X_{0 }+ R(t)t*.
Now we have a rate of change which itself is changing. Calculus came to
the rescue, as Isaac Newton introduced the world to mathematics
specifically designed to handle those things that change.*

*Calculus is among the most important and useful developments of human
thought. Even though it is over 300 years old, it is still considered
the beginning and cornerstone of modern mathematics. It is a wonderful,
beautiful, and useful set of ideas and techniques. You will see the
fundamental ideas of this course over and over again in future courses
in mathematics as well as in all of the sciences (e.g., physical,
biological, social, economic, and engineering). However, calculus is an
intellectual step up from your previous mathematics courses. Many of the
ideas you will gain in this course are more carefully defined and have
both a functional and a graphical meaning. Some of the algorithms are
quite complicated, and in many cases, you will need to make a decision
as to which appropriate algorithm to use. Calculus offers a huge variety
of applications and many of them will be saved for courses you might
take in the future.*

*This course is divided into five learning sections, or units, plus a
reference section, or appendix. The course begins with a unit that
provides a review of algebra specifically designed to help and prepare
you for the study of calculus. The second unit discusses functions,
graphs, limits, and continuity. Understanding limits could not be more
important, as that topic really begins the study of calculus. The third
unit introduces and explains derivatives. With derivatives, we are now
ready to handle all of those things that change mentioned above. The
fourth unit makes visual sense of derivatives by discussing derivatives
and graphs. The fifth unit introduces and explains antiderivatives and
definite integrals. Finally, the reference section provides a large
collection of reference facts, geometry, and trigonometry that will
assist you in solving calculus problems long after the course is over.*