Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds

by Theodore Shifrin

Multivariable Mathematics combines linear algebra and multivariable calculus in a rigorous approach. The material is integrated to emphasize the role of linearity in all of calculus and the recurring theme of implicit versus explicit that persists in linear algebra and analysis.  In the text, the author addresses 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 including complete proofs.  By emphasizing the theoretical aspects and reviewing the linear algebra material quickly, the book can also be used as a text for an advanced calculus or multivariable analysis course culminating in a treatment of manifolds, differential forms, and the generalized Stokes’s Theorem.

Genres: Mathematics

512 pages, Hardcover

First published January 1, 2004

Reviews

[C. Hinsley]

This was an excellent introduction to advanced calculus; reading this made it much easier to get through Spivak's Calculus on Manifolds. Of particular interest is Chapter 8, on differential forms. The chapter works up to the Generalized Stokes' Theorem.

The exercises throughout this text are very good, and many have solutions in the book.

[Yunjiang Jiang]

Best introduction to multivariate calculus.