Macdonald A. Vector and Geometric Calculus 2012

Textbook in PDF format

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. It is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one.
Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways.
Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world.
Differential geometry is used today in many disciplines. A final chapter is devoted to it