Sir Isaac Newton.

That teachers and students of the Calculus have shown such a generous appre-
ciation of Granville’s “Elements of the Differential and Integral Calculus” has
been very gratifying to the author. In the last few years considerable progress
has been made in the teaching of the elements of the Calculus, and in this
revised edition of Granville’s “Calculus” the latest and best methods are exhib-
ited,methods that have stood the test of actual classroom work. Those features
of the first edition which contributed so much to its usefulness and popularity
have been retained. The introductory matter has been cut down somewhat
in order to get down to the real business of the Calculus sooner. As this is
designed essentially for a drill book, the pedagogic principle that each result
should be made intuitionally as well as analytically evident to the student has
been kept constantly in mind. The object is not to teach the student to rely
on his intuition, but, in some cases, to use this faculty in advance of analytical
investigation.
Graphical illustration has been drawn on very liberally.
This Calculus is based on the method of limits and is divided into two main
parts,Differential Calculus and Integral Calculus. As special features, attention
may be called to the effort to make perfectly clear the nature and extent of each
new theorem, the large number of carefully graded exercises, and the summa-
rizing into working rules of the methods of solving problems. In the Integral
Calculus the notion of integration over a plane area has been much enlarged
upon, and integration as the limit of a summation is constantly emphasized.
The existence of the limit e has been assumed and its approximate value calcu-
lated from its graph. A large number of new examples have been added, both
with and without answers. At the end of almost every chapter will be found
a collection of miscellaneous examples. Among the new topics added are ap-
proximate integration, trapezoidal rule, parabolic rule, orthogonal trajectories,
centers of area and volume, pressure of liquids, work done, etc. Simple practi-
cal problems have been added throughout; problems that illustrate the theory
and at the same time are of interest to the student. These problems do not
presuppose an extended knowledge in any particular branch of science, but are
based on knowledge that all students of the Calculus are supposed to have in
common.
The author has tried to write a textbook that is thoroughly modern and
teachable, and the capacity and needs of the student pursuing a first course
in the Calculus have been kept constantly in mind. The book contains more
material than is necessary for the usual course of one hundred lessons given in
our colleges and engineering schools; but this gives teachers an opportunity to
choose such subjects as best suit the needs of their classes. It is believed that
the volume contains all topics from which a selection naturally would be made
in preparing students either for elementary work in applied science or for more
advanced work in pure mathematics.