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.