Differential Forms

“Guillemin and Haine’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, Brouwer’s fixed-point theorem, divergence theorem, and Stokes’s theorem … The exercises support, apply and justify the developing road map.” — CHOICE There 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.