This textbook offers a high-level introduction to multi-variable differential calculus. Differential forms are introduced incrementally in the narrative, eventually leading to a unified treatment of Green’s, Stokes’ and Gauss’ theorems. Furthermore, the presentation offers a natural route to differential geometry.

Contents:
Calculus of Vector Functions

Tangent Spaces and 1-forms

Line Integrals

Differential Calculus of Mappings

Applications of Differential Calculus

Double and Triple Integrals

Wedge Products and Exterior Derivatives

Integration of Forms

Stokes’ Theorem and Applications