Using a dual presentation that is rigorous and comprehensive—yet exceptionaly student-friendly in approach—this text covers most of the standard topics in multivariate calculus and part of a standard first course in linear algebra. It focuses in underlying ideas, integrates theory and applications, offers a host of pedagogical aids, and features coverage of differential forms and an emphasis on numerical methods to prepare students for modern applications of mathematics.

Features and Benefits

NEW - Revised and expanded content - Including new discussions of functions; complex numbers; closure, interior, and boundary; orientation; forms restricted to vector spaces; and expanded discussions of subsets and subspaces of R^n; probability; change of basis matrix, and more, makes text now a little easier and clearer.

NEW - Approximately 875 exercises - 270 more exercises that the previous edition, reinforces students understanding of the material.

NEW - Approximately 294 examples - 50 more examples that the previous edition, deepens students understanding of concepts and theorems by allowing them to see each step of the process.

NEW - 50 more figures and tables than the previous edition, makes text a bit easier.

NEW - Student Solutions Manual, gives students detailed solutions to several hundred exercises and provides a source of additional examples.

Unified approach to vector calculus, linear algebra, and differential forms, gives students a better understanding of all three areas and shows how they all relate to each other.

Unique treatment of differential forms, shows students how differential forms in three dimensions translate into the language of vector calculus.

Stresses computationally effective algorithms—Both for computations and for underlying theory, illustrates for students how mathematics is done today.

More difficult and longer proofs in the appendix, allows more advanced students to use the book at a higher level and beginning students to focus on statements and becoming at ease with techniques rather than being intimidated by the technical details of proofs.

Emphasis on the correspondence between different mathematical languages, including algebra and geometry.

Presents material as more intuitive and conceptual.

Integrates theory and application.

Emphasizes computationally effective algorithms and proves theorems by showing that those algorithms really work.

Begins most chapters with a treatment of a linear problem, shows students how the methods apply to “corresponding” non-linear problems.

Instant exercises with solutions in footnotes, encourages students to read the text actively.