Advanced Calculus: Differential Calculus and Stokes'' Theorem

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 Greens, 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