New textbook: Vector and Geometric Calculus, by Alan Macdonald. It is intended for the sophomore vector calculus course or for independent reading.
It is a sequel to Macdonald’s Linear and Geometric Algebra. That text is a prerequisite for this one.
Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world.
The book contains a chapter on differential geometry.
Further information is available at the book’s web site:
Source: A. Macdonald, macdonal_AT_luther.edu, Email on 20 Dec. 2012.