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The calculus has been one ofthe areas of mathematics with a large
number of significant applications since its formal development in
the seventeenth century. With the recent development of the digital
computer, the range of applications of mathematics, including the
calculus, has increased greatly and now includes many disciplines
that were formerly thought to be non quantitative. Some of the more
traditional applications have been altered, by the presence of a
computer, to an extent such that many problems hitherto felt to be
intractable are now solvable. This book has been written as a
reaction to events that have altered the applications of the
calculus. The use of the computer is made possible at an early
point, although the extent to which the computer is used in the
course is subject to the decision of the instructor. Some less
traditional applications are included in order to provide some
insight into the breadth of problems that are now susceptible to
mathematical solution. The Stieltjes integral is introduced to
provide for easier transition from the stated problem to its
mathematical formulation, and also to permit the use of functions
like step functions in later courses (such as statistics) with
relative ease. The course is designed to include all the background
material ordinarily associa ted with the first course in the
calculus, but it is also designed with the user in mind.
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