\" Preface
As in the previous editions， we have striven to present calculus in a way that is
as easy as possible for the student to understand as well as easy for the instructor
to present. Many changes， both large and small， have been made in this edition to
further these aims. One of the most important of these changes is in the problem
sets. Over half of the problems have been altered， and new ones have been added.
The_daew problems are， for the most part， problems that present the student with
sorr~hing of a challenge. Many of the alterations in the problems are minor
changes in the numbers; this has been done to prevent the students from making
use of \"files，\" assembled from previous editions. In addition， the problems have
been graded for difficulty by separating them (in most sections) into three parts，
labeled A， B， and C. The part labeled A consists of routine problems that every
student can be expected to do. Those problems labeled B are less routine but still
not a great challenge. The average student can be expected to work most of these.
The C problems present something of a challenge; only the better students can be
expected to work them. Of course， any such system of classification mu st be very
subjective; it must be considered as a rough guide only.
The approach to vectors has been reviewed and completely revised. The previ-
ously used definition of a vector as an equivalence class of directed line segments
was felt to be too abstract for the level set by the rest of the book. Thus， in this
edition， vectors are approached from an algebraic point of view that simplifies
their introduction.
In addition， a more conventional proof of the fundamental theorem of calculus
has been given.
However， the greatest change has occurred in the last few chapters on mul-
tivariate calculus. Chapters 20， 21， and 22 have been extensively revised and a
chapter on line and surface integrals has been added.
Retained from the previous editions are the wide variety of applications and the
important area of rapid curve sketching without the use of calculus. The recent
trend toward the consideration of curve sketching only in conjunction with cal-
culus is， in our view， unfortunate. A sketch is necessary for setting up most
integrals; and generally only a very rough sketch (without locating relative max-
ima， minima， or points of inflection) is needed. It is felt that a student who cannot
make such a sketch without resorting to differentiation is m a distinct disadvan-
tage. Thus， several sections are devoted to the sketching of curves without any
consideration of the derivative.
As in earlier editions， we have frequently been faced with direct opposition
between what is mathematically propel\" and what is pedagogically proper. As
mathematicians， we feel that we should use proper mathematics， but as teachers
we feel that to say that one is teaching when no one is learning is like saying that
one is selling when no one is buying. The view that we must use \"proper\"
mathematics at all costs is responsible for the cun ent wave of ultrarigorous texts
that begin with an epsilon-delta definition of limits， introduce the mean-value
theorem at an early stage， and give proofs of all theorems. The hoped-for
results--students who really understand the underlying concepts of calculus--
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