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

ISBN 978-0-9715766-3-6

$78, hardcover, 802 pages, smythe-sewn binding (the second edition, published by Prentice Hall, was $113.)

3rd edition


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 243-244 (Kantorovich's theorem)

Review exercises for chapter 2

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

Chapter 3: pages 350-351 (constrained critical points)

Review exercises for chapter 3

Chapter 4 (Integration): first 4 pages

Chapter 4: pages 498-499 (Lebesgue integration)

Review exercises for chapter 4

Chapter 5 (Volumes of manifolds): first 4 pages

Chapter 5, pages 531-532 (computing volumes of manifolds)

Review exercises for chapter 5

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

Chapter 6: pages 648-649 (the generalized Stokes's theorem)

Review exercises for chapter 6

Appendix: pages 673-676 (Arithmetic of real numbers)

Appendix: pages 720-723 (Stirling's formula and the central limit theorem)

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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