Cartan differential calculus11/9/2023 ![]() ![]() With the exception of Chapter 9, which is a bow to the topics in the calculus of one variable that are traditionally covered in advanced calculus courses, the book is permeated with the use of differential forms. I wrote the book because I believed that differential forms provided the most natural and enlightening approach It is at their suggestion that the subtitle "A Differential Forms Approach" has been added. With that edition exhausted and with Krieger having decided not to do a new printing, I am enormously gratified by Birkhauser Boston's decision to add this title to their fine list, to restore it to its original, easy-toread size, and to direct it to an appropriate audience. This edition enjoyed modest but steady sales for over a decade. When the original publisher gave up on the book, it was republished, with corrections, by the Krieger Publishing Company. Ironically, my subsequent books-Riemann 's Zeta Function, Fermat's Last Theorem and Galois Theory-sold many more copies than the original edition of Advanced Calculus, even though they were written with no commercial motive at all and were directed to a narrower group of readers. The only other way a potential reader could learn of the book's existence was to read an advertisement or to encounter one of the publisher's salesmen. It received a favorable telegraphic review of a few lines in the American Mathematical Monthly, and that was it. I have never regretted the effort that I expended in the pursuit of this hopeless dream-only that the book was published as a textbook and marketed as a textbook, with the result that the case for differential forms that it tried to make was hardly heard. ![]() My original plan had been to write a small supplementary textbook on differential forms, but overly optimistic publishers talked me out of this modest intention and into the wholly unrealistic objective (especially unrealistic for an unknown 30-year-old author) of writing a full-scale advanced calculus course that would revolutionize the way advanced calculus was taught and sell lots of books in the process. The book was born in 1969 as an "innovative textbook"-a breed everyone claims to want but which usually goes straight to the orphanage. With this new edition, I hope it has reached a secure middle age. Preface to the 1994 Edition My first book had a perilous childhood. Printed and bound by Quinn-Woodbine, Woodbine, NJ Printed in the USA Special requests should be addressed directly to Birkhauser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139, U.S.A. Permission to photocopy for internal or personal use of specific clients is granted by Birkhauser Boston for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to CCC, 21 Congress Street, Salem, MA 01970, U.S.A. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. Edwards Reprinted 1994 with corrections from the original Houghton Mifflin edition.Ĭopyright is not claimed for works of U.S. Advanced calculus : a differential fonns approach / Harold M. Library of Congress Cataloging In-Publication Data Edwards, Harold M. Edwards Courant Institute New York University New York, NY 10012 Advanced Calculus A Differential Forms Approach ![]()
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