Vector Calculus, Linear Algebra, and Differential Forms:

A Unified Approach

 Second edition, ISBN 0-13-041408-5, © Prentice Hall, 2002  
John H. Hubbard, professor of mathematics, Cornell University and the University of Provence  
Barbara Burke Hubbard,
winner of the prix d'Alembert for her book, The World According to Wavelets: the story of a mathematical technique in the making


If you have a copy of Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, we invite you to write with ``calculus book readers'' as the subject, to let us know what math course you are taking, or, if you are not using the book in a formal course, what your connection to mathematics is.

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Student Solution Manual

The Student Solution Manual contains detailed solutions to all odd-numbered exercises in Chapters 0-6 and to many in the Appendix. See sample solutions.

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What makes this book different?

This text covers most of the standard topics in multivariate calculus and a substantial part of a standard first course in linear algebra. If, in addition, one teaches the proofs in Appendix A, the book can be used as a textbook for a course in analysis.The organization and selection of material differs from the standard approach in four ways.

  • We integrate linear algebra and multivariate calculus.

  • We emphasize computationally effective algorithms, and prove theorems by showing that those algorithms really work. This better reflects the way this mathematics is used today, in both applied and in pure mathematics.

  • we use differential forms to generalize the fundamental theorem of calculus to higher dimensions. This gives one elegant theorem, the generalized Stokes's theorem, that works in all dimensions. In contrast, vector calculus requires special formulas, operators, and theorems for each dimension where it works.

  • We provide a new approach to Lebesgue integration.

See what students and professors have to say about Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. See the table of contents in pdf form (requires Acrobat Reader).



Instructors' Solution Manual

A revised version of the instructor's solution manual, incorporating corrections and some new solutions, is now available from Prentice Hall .  



If your are taking your first serious math course and don't have the book, you may find several brief excerpts useful; they are from Chapter 0: Preliminaries. They are in pdf format and can be read using Acrobat Reader.

The first discusses how to read mathematics. (Many students who never read their math texts in high school discover this doesn't work in college.)

The second explains why ``all eleven-legged alligators are orange with blue stripes'' is a true statement, as is ``all eleven-legged alligators are black with white stripes.''

The third gives the vocabulary of set theory (and a nice picture of Bertrand Russell shaving his image in the mirror.)


If you find an error in the text, please write with ``second edition errata'' as the subject. The errata list for the second edition was updated on June 7, 2003. Lists are available at

Errata Second Edition

Errata First Edition.

If you would like to be notified by e-mail when new errata are posted, please write Barbara Hubbard at

Familiar with the first edition? See

what's new in the second edition.

Book Two

A sequel book will be published by Matrix Editions. See the tentative

table of contents.

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Links for John Hubbard

His official Cornell University site

personal Cornell University site

books about differential equations

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Last updated August 24, 2003