In a book written for mathematicians, teachers of mathematics,
and highly motivated students, Harold Edwards has taken a bold and
unusual approach to the presentation of advanced calculus. He
begins with a lucid discussion of differential forms and quickly
moves to the fundamental theorems of calculus and Stokes theorem.
The result is genuine mathematics, both in spirit and content, and
an exciting choice for an honors or graduate course or indeed for
any mathematician in need of a refreshingly informal and flexible
reintroduction to the subject. For all these potential readers, the
author has made the approach work in the best tradition of creative
mathematics.
This affordable softcover reprint of the 1994 edition presents
the diverse set of topics from which advanced calculus courses are
created in beautiful unifying generalization. The author emphasizes
the use of differential forms in linear algebra, implicit
differentiation in higher dimensions using the calculus of
differential forms, and the method of Lagrange multipliers in a
general but easy-to-use formulation. There are copious exercises to
help guide the reader in testing understanding. The chapters can be
read in almost any order, including beginning with the final
chapter that contains some of the more traditional topics of
advanced calculus courses. In addition, it is ideal for a course on
vector analysis from the differential forms point of view.
The professional mathematician will find here a delightful
example of mathematical literature; the student fortunate enough to
have gone through this book will have a firm grasp of the nature of
modern mathematics and a solid framework to continue to more
advanced studies.
"The most important feature is that it is fun it is fun to read
the exercises, it is fun to read the comments printed in the
margins, it is fun simply to pick a random spot in the book and
begin reading. This is the way mathematics should be presented,
with an excitement and liveliness that show why we are interested
in the subject."
The American Mathematical Monthly (First Review)
"An inviting, unusual, high-level introduction to vector
calculus, based solidly on differential forms. Superb exposition:
informal but sophisticated, down-to-earth but general,
geometrically rigorous, entertaining but serious. Remarkable
diverse applications, physical and mathematical."
The American Mathematical Monthly (1994) Based on the Second
Edition"
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