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Serious mathematics, written with the reader in mind. Matrix Editions Current Books Teichmüller Theory Vol1 Functional Analysis Vol1 Vector Calculus 4th edition Solving Linear Systems Vector Calculus 3rd edition Student Solution Manual for 4th edition Student Solution Manual for 3rd edition Solution Manual for 2nd edition Future Books Sign up to be notified Dynamics: Introductory Lectures Teichmüller Theory Vol 2 Functional Analysis Vol 2 Advanced Calculus Complex Dynamics War and Peace in America, 1853-1868 Errata Math Links Math in literature Other Books

Matrix Editions current books 4th edition  Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach John Hubbard and Barbara Burke Hubbard 818 pages, hardcover, smythe-sewn binding, 8 x 10 inches $79. Sept. 2009 ISBN 9780971576650 "Superb on all counts" - review in CHOICE (review of 1st edition) "A real gem" - review of 2nd edition, MAA Monthly More reviews and reader praise for first three editions Reprinting of 4th edition The 4th edition now exists in two printings. All copies ordered from our web site August 22, 2012  or later will be the second printing.  Some bookstores may still have the first printing.    To determine which printing you have, look at the copyright page.  If the numbers under ``Printed in the United States of America'' decrease from 10 to 1, it is the first printing.  If they decrease from 10 to 2, it is the second printing. The second printing corrects all errata known at time of printing. When we ran low on copies of the first printing, we chose not to make it a new edition, so that students can use both printings in a single classroom.  The result is that there are some discrepancies in numbering, particularly in Sections 4.3 and  4.4.  Correspondences between the two printings are described in the table of correspondences, which is in pdf. Why a new edition?  The main impetus was that we finally hit on what we consider the right way to define orientation of manifolds. The new approach, based on direct bases, is simpler than the previous, but still covers the case of 0-dimensional manifolds (i.e., points). In addition, the new edition provides a proof of Gauss's  remarkable theorem.  This theorem, also known as the  ``Theorema Egregium'',  justifies the statement (section 3.8)  that Gaussian curvature measures to what extent pieces of a surface can be made flat, without stretching or deformation.  All the other proofs we know of this theorem require advanced techniques;  the proof we added to section 5.4 uses only the techniques developed in this book. a justification of the statement in section 3.8 that the mean curvature measures how far a surface is from being minimal  classifying constrained critical points using the augmented Hessian matrix (section 3.7) a proof of Poincare's lemma for arbitrary forms rather than just 1-forms, based on the cone operator (section 6.12) a discussion of Faraday's experiments in section 6.11 on electromagnetism  a trick for finding Lipschitz ratios for polynomial functions (example 2.8.12) We have also added new examples and exercises, deleted some weaker examples and exercises, and corrected errata. Preface (excerpt in html, with link to complete preface in pdf) To order (for books shipped to the United States) To order (for books shipped to other countries) Student Solution Manual for 4th edition Math programs used in the book Table of contents (in html) Look inside this book (sample pages, mostly in pdf) For errata listings, go to errata