Lawrence (Rutgers University) Corwin & Robert (Yale University) Szczarba 
Calculus in Vector Spaces, Revised Expanded [PDF ebook] 

Calculus in Vector Spaces addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This second edition introduces, among other topics, the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and explains differential forms on Euclidean space, allowing for Green »s theorem, Gauss »s theorem, and Stokes »s theorem to be understood in a natural setting. Mathematical analysts, algebraists, engineers, physicists, and students taking advanced calculus and linear algebra courses should find this book useful.