Proceeds from general to special, including chapters on vector analysis on manifolds and integration theory.
Here's a sample of other books in this Dover category
Introduction to Global Analysis by Donald W. Kahn This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.
Vector Analysis by Louis Brand This text was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into the subjects' manifold applications. 1957 edition. 86 figures.
Geometric Integration Theory by Hassler Whitney Geared toward upper-level undergraduates and graduate students, this treatment of geometric integration theory consists an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. 1957 edition.
