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ANALYTICAL GEOMETRY AND CALCULUSWITH VECTORS
CALCULUS
Analytic Geometry and Calculus, with Vectors
CALCULUS
Analytic Geometry and Calculus, with Vectors
Ralph Palmer Agnew
Professor of Mathematics
Department ofMathematics
Cornell University
McGraw-Hilt pany, Inc.
New York San Francisco Toronto London
CALCULUS
Analytic Geometry and Calculus, with Vectors
Copyright © 1962 by McGraw-Hill, Inc..411 Rights Reserved.
Printed in the United States of book, or parts
thereof, may not be reproduced in any form without
permission of the publishers.
Library of Congress Catalog Card Number: 61-18624
II
00595
Preface
There is an element of truth in the old saying that the Euler textbook
Introductio in 4nalysin Infinitorum (Lausannae, 1748) was the first great
calculus textbook, and that all elementary calculus textbooks published
since that time have been copied from Euler or have been copied from
books that were copied from , the greatest mathematician
of his day and in many respects the greatest mathematician of all time,
held sway when, except where the geometry of Euclid was involved, it
was not the fashion to try to base mathematical work upon accurately
formulated basic were the important things, and
meaningful formulations of axioms, postulates, definitions, hypotheses,
conclusions, and theorems either were not written or played minor roles.
Through most of the first half of the twentieth century, elementary
textbooks in our subject taught unexplained but "well motivated" intui-
tive ideas along with their for this approach to
calculus waned when it was realized that students were not nourished by
stews in which problems, motivations, fuzzy definitions, and fuzzy theo-
rems all boiled together while something approached something else with-
out ever quite getting the middle of the twentieth century,
precise formulations of basic concepts began to occupy