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 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

"The characteristic features of the book are the abundance of worked examples, illustrated by nicely drawn suggestive gures and the excellent layout […]. There are also exercises at the end of each section. The book is clearly written, in a pleasant style, and can be recommended as a textbook for advanced calculus courses." - Tiberiu Trif in: Stud. Univ. Babes-Bolyai Math. 62 (2017), 2, S. 269-271