My book on Vector Calculus was published by Springer in 1998. Note that the description on the Springer site that the author is a "young writer" may no longer be accurate. The book has a similar format and style to Differential Equations, Bifurcations and Chaos, with over 60 figures, worked examples, exercises, and summaries of key points at the end of each chapter.
Vector calculus provides a way to describe physical quantities in three-dimensional space and how these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus, including fluid dynamics, solid mechanics and electromagnetism.
The book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants.