'Guillemin and Haineâ (TM)s goal is to construct a well-documented road
map that extends undergraduate understanding of multivariable calculus
into the theory of differential forms. Throughout, the authors emphasize
connections between differential forms and topology while making
connections to single and multivariable calculus via the change of
variables formula, vector space duals, physics; classical mechanisms,
div, curl, grad, Brouwerâ (TM)s fixed-point theorem, divergence theorem,
and Stokesâ (TM)s theorem ... The exercises support, apply and justify
the developing road map.'CHOICEThere already exist a number of excellent
graduate textbooks on the theory of differential forms as well as a
handful of very good undergraduate textbooks on multivariable calculus
in which this subject is briefly touched upon but not elaborated on
enough.The goal of this textbook is to be readable and usable for
undergraduates. It is entirely devoted to the subject of differential
forms and explores a lot of its important ramifications.In particular,
our book provides a detailed and lucid account of a fundamental result
in the theory of differential forms which is, as a rule, not touched
upon in undergraduate texts: the isomorphism between the Čech cohomology
groups of a differential manifold and its de Rham cohomology groups.
