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Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach

ISBN 9780971576650

$84, hardcover, 818 pages, smythe-sewn binding, 8 x 10 inches  

Sept. 2009

4th edition

 book cover

Look inside this book

Click on the links below to see the table of contents, the first four pages of each chapter,   a few pages from later in each chapter, and the review exercises for each chapter. (Each section also has its own exercises.)

These pages are all copyrighted. If you find it unpleasant to read them online, you are welcome to print one copy for your use. For other uses, please write hubbard@matrixeditions.com to inquire about permission.

Files are in pdf unless otherwise noted.

Table of contents (html)

Table of contents  

Partial preface (html)

Preface (pdf)

Chapter 0 (Preliminaries): first 4 pages

Chapter 0: pages 22-23 (infinite sets)

Chapter 1 (Vectors, matrices, and derivatives): first 4 pages

Chapter 1: pages 148-149 (criteria for differentiability)

Review exercises for chapter 1

Chapter 2 (Solving equations):  first 4 pages

Chapter 2: pages 222-223 (eigenvectors and eigenvalues)

Chapter 2: pages 244-245 (Kantorovich's theorem)

Review exercises for chapter 2
Review exercises for chapter 2 (last page)

Chapter 3 (Manifolds, Taylor polynomials, quadratic forms, and curvature): first 4 pages

Chapter 3: pages 351-352 (constrained critical points)

Review exercises for chapter 3

Chapter 4 (Integration): first 4 pages

Chapter 4: pages 497-498 (Lebesgue integration)

Review exercises for chapter 4

Chapter 5 (Volumes of manifolds): first 4 pages

Chapter 5, pages 544-545 (Gauss's remarkable theorem)

Review exercises for chapter 5

Chapter 6 (Forms and vector calculus): first 4 pages

Chapter 6: pages 635-636  (the generalized Stokes's theorem)

Chapter 6: pages 675-676  (Poincaré's lemma)

Review exercises for chapter 6

Appendix: pages 683-686 (Arithmetic of real numbers)

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"Depth, clarity and ambition" - MAA Review of 3rd edition

Readers  praise first two editions

"A real gem" - review of the second edition in the MAA Monthly

"Superb on all counts" - review of the first edition in CHOICE