Edwards Harold M. Advanced Calculus. A Differential Forms Approach

Reprint of the 1994 Edition. — Birkhauser, 2014. — 528 p. — ISBN: 978-0-8176-8411-2.This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.