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MUM -
J
ANALYTIC
GEOMETRY
with
CALCULUS
ROBERT C. YATES
University of South Florida
Englewood Cliffs, N. J. PRENTICE-HALL, INC. 1961
Q 1961, by Prentice-Hall, Inc., Englewood
Cliffs, New Jersey. All rights reserved. No
part of this book may be reproduced in any
form, by mimeograph, or any other means,
withoutpermissioninwriting fromthe
publishers.
Library of Congress Catalog Card No. 61-9224
Printed in the United States of America
08488-C
Preface
In recent years analytic geometry and the calculus have bined into
one course for the first or second year of college mathematics, and several
excellent texts have been published for this purpose. However, these texts
give primary emphasis to the calculus with a correspondingly reduced
content in analytic geometry. As a consequence, many students are not
acquiring a sound knowledge of analytic facts and techniques. For this
reason, this book emphasizes a full-bodied treatment of analytic geometry
in which the fundamental principles of calculus are introduced and used in
a supporting role. The result is a text, to follow algebra and trigonometry,
in which the student is more adequately prepared for the subject matter
of calculus.
Certain features of the book are listed here as a guide to the reader
before he begins a detailed study of the text. In the geometry of the plane,
rectangular and polar coordinates are introduced at the same time and used
interchangeably throughout. Lines are characterized by direction numbers
for wider application and to facilitate transition to three-space geometry.
The concepts of derivative and its inverse are presented early so that their
applications to direction of a curve, motion of points, plane areas, tangents
and normals to surfaces and curves in three-space, and volumes bounded
by surfaces considerably enhance the subject matter. Discussion of the
conies begins with the fundamental consideration of plane sec