Calculus in Vector Spaces

Addressing linear algebra from the basics to the spectral theorem and examining a host of topics in multivariable calculus, including differentiation, integration, maxima and minima, the inverse and implicit function theorems, and differential forms, this thoroughly revised Second Edition of an invaluable reference/text - widely successful through five printings - continues to provide unified, integrated coverage of the two fields.
Demonstrating that mathematics is a noncompartmentalized discipline of interrelated subjects, Calculus in Vector Spaces, Second Edition introduces the derivative as a linear transformation ... presents linear algebra in a concrete context based on complementary ideas in calculus ... explains differential forms on Euclidean space permitting Green's theorem, Gauss's theorem, and Stokes's theorem to be understood in a natural setting ... gives a new clarification of compactness as defined in terms of coverings and in terms of sequences ... supplies a novel treatment of eigenvalues and eigenvectors ... and more.

Lawrence J. Corwin was Professor of Mathematics at Rutgers University, New Brunswick, New Jersey, until his death in 1992.