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

ISBN 9780971576650

$87, hardcover, 818 pages, smythe-sewn binding, 8 x 10 inches  

Sept. 2015

5th edition

To order:  United States    To order: other countries

 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 most chapters, 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.

Table of contents 


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 145-147 (criteria for differentiability)

Review exercises for chapter 1

Chapter 2 (Solving equations)   first 4 pages

Chapter 2: pages 219-221 (eigenvectors and eigenvalues)

Chapter 2: pages 242-243 (Kantorovich's theorem)

Review exercises for chapter 2

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

Chapter 3: pages 349-350 (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

Review exercises for chapter 5

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

Chapter 6: pages 645-646  (the generalized Stokes's theorem)

Review exercises for chapter 6

Appendix: pages 704-706 (Arithmetic of real numbers)

To order:  United States    To order: other countries

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

Readers praise previous editions

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

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