Shifrin T. Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds

New York: John Wiley & Sons, Inc., 2005. — 504 p.Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs.
Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts.
Numerous exercises of varying levels of difficulty, both computational and more proof-oriented.
Exercises are arranged in order of increasing difficulty.