McGraw-Hill - Advanced Calculus ...

McGraw-Hill - Advanced Calculus (Schaum's Outlines, Handbooks

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Theory and Problems of
ADVANCED
ROBERT WREDE, Ph.D.
MURRAY R. SPIEGEL, Ph.D.
Former Professor and Chairman of Mathematics
Rensselaer Polytechnic Institute
Hartford Graduate Center
Schaum’s Outline Series
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CALCULUS
Second Edition
Copyright © 2002, 1963 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of
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DOI: 10.1036/0071398341
A key ingredient in learning mathematics is problem solving. This is the strength, and no doubt
the reason for the longevity of Professor Spiegel’s advanced calculus. His collection of solved
and unsolved problems remains a part of this second edition.
Advanced calculus is not a single theory. However, the various sub-theories, including
vector analysis, infinite series, and special functions, have in common a dependency on the
fundamental notions of the calculus. An important objective of this second edition has been to
modernize terminology and concepts, so that the interrelationships become clearer. For exam-
ple, in keeping with present usage fuctions of a real variable are automatically single valued;
differentials are defined as linear functions, and the universal character of vector notation and
theory are given greater emphasis. Further explanations have been included and, on occasion,
the appropriate terminology to support them.
The order of chapters is modestly rearranged to provide what may be a more logical
structure.
A brief introduction is provided for most chapters. Occasionally, a historical note is
included; however, for the most part the purpose of the introductions is to orient the reader
to the content of the chapters.
I thank the staff of McGraw-Hill. Former editor, Glenn Mott, suggested that I take on the
project. Peter McCurdy guided me in the process. Barbara Gilson, Jennifer Chong, and
Elizabeth Shannon made valuable contributions to the finished product. Joanne Slike and
Maureen Walker accomplished the very di
cult task of combining the old with the new
and, in the process, corrected my errors. The reviewer, Glenn Ledder, was especially helpful
in the choice of material and with comments on various topics.
R
OBERT
C. W
REDE
iii
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