| dc.description.abstract | Our purpose in writing a calculus text has been to help students learn at first hand
that mathematics is the language in which scientific ideas can be precisely formulated,
that science is a source of mathematical ideas that profoundly shape the development
of mathematics, and that mathematics can furnish brilliant answers to
important scientific problems. This book is a thorough revision of the text Calculus
with Applications and Computing by Lax, Burstein, and Lax. The original text was
predicated on a number of innovative ideas, and it included some new and nontraditional
material. This revision is written in the same spirit. It is fair to ask what new
subject matter or new ideas could possibly be introduced into so old a topic as calculus.
The answer is that science and mathematics are growing by leaps and bounds on
the research frontier, so what we teach in high school, college, and graduate school
must not be allowed to fall too far behind. As mathematicians and educators, our
goal must be to simplify the teaching of old topics to make room for new ones.
To achieve that goal, we present the language of mathematics as natural and
comprehensible, a language students can learn to use. Throughout the text we offer
proofs of all the important theorems to help students understand their meaning; our
aim is to foster understanding, not “rigor.”We have greatly increased the number of
worked examples and homework problems.We have made some significant changes
in the organization of the material; the familiar transcendental functions are introduced
before the derivative and the integral. The word “computing” was dropped
from the title because today, in contrast to 1976, it is generally agreed that computing
is an integral part of calculus and that it poses interesting challenges. These
are illustrated in this text in Sects. 4.4, 5.3, and 10.4, and by all of Chap. 8. But
the mathematics that enables us to discuss issues that arise in computing when we
round off inputs or approximate a function by a sequence of functions, i.e., uniform
continuity and uniform convergence, remains.We have worked hard in this revision
to show that uniform convergence and continuity are more natural and useful than
pointwise convergence and continuity. The initial feedback from students who have
used the text is that they “get it.”
This text is intended for a two-semester course in the calcu | en_US |
