文档介绍：A Course in
Advanced Calculus
Robert S. Borden
DOVER PUBLICATIONS, INC.
Mineola. New York
Copyright
Copyright © 1983 by Elsevier Science Publishing Co., Inc.
Copyright © 1998 by Robert S. Borden
All rights reserved under Pan American and International
Copyright Conventions.
Bibliographical Note
This Dover edition, first published in 1998, contains the unabridged
and slightly corrected text of the work first published by North
Holland/Elsevier Science Publishing Co., Inc., New York, in 1983. A
new chapter, "Tips and Solutions for Selected Problems," has been
prepared specially for this edition.
Library of Congress Cataloging-in-Publication Data
Borden, Robert S.
A course in advanced calculus I Robert S. Borden.
p. em.
"Contains the unabridged and slightly corrected text of the work
first published by North Holland/Elsevier Science Publishing Co.,
Inc., New York, in 1983. A new chapter, 'Tips and solutions for
selected problems,' has been prepared specially for this edition"•
. verso.
Includes bibliographical references and index.
ISBN 0-486-67290-5 (pbk.)
1. Calculus. I. Title.
~ 1997
515--dc21 97-43366
CIP
Manufactured in the United States of America
Dover Publications, Inc., 31 East 2nd Street, Mineola, 11501
To Mary
CONTENTS
Preface xi
CHAPTER 1 SETS AND STRUCTURES 1
Sets 1
Algebraic Structures 12
Morphisms 16
Order Structures 18
Problems 24
CHAPTER 2 LIMIT AND CONTINUITY IN En 30
Limit of a Function 30
Sequences in En 34
Limit Superior and Limit Inferior of a Function 39
Problems 41
CHAPTER 3 INEQUALITIES 48
Some Basic Inequalities 48
Problems 55
CHAPTER 4 LINEAR SPACES 58
Linear and Affine Mappings 58
Continuity of Linear Maps 64
Determinants 67
The Grassmann Algebra 72
Problems 74
CHAPTER 5 FORMS IN En 78
Orientation of Parallelotopes 78
I-Forms in En 84
YIll CONTENTS
Some Applications