Techniques of Asymptotic Analysis
These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown. In the hope that these notes might prove useful for reference purposes several additional sections have been included and also a table of contents and
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Joseph P. LaSalle Division of Applied Mathematics Brown University Providence, R.I. 02912
Lawrence Sirovich
Division of Applied Mathematics Brown University Providence, R.I. 02912
EDITORIAL STATEMENT The mathematization of all sciences, the fading of traditional scientific boundaries, the impact of computer technology, the growing importance of mathematicalcomputer modelling and the necessity of scientific planning all create the need both in education and research for books that are introductory to and abreast of these developments. The purpose of this series is to provide such books, suitable for the user of mathematics, the mathematician interested in applications, and the student scientist. In particular, this series will provide an outlet for material less formally presented and more anticipatory of needs than finished texts or monographs, yet of immediate interest because of the novelty of its treatment of an application or of mathematics being applied or lying close to applications. The aim of the series is, through rapid publication in an attractive but inexpensive format, to make material of current interest widely accessible. This implies the absence of excessive generality and abstraction, and unrealistic idealization, but with quality of exposition as a goal. Many of the books will originate out of and will stimulate the development of new undergraduate and graduate courses in the applications of mathematics. Some of the books will present introductions to new areas of research, new applications and act as signposts for new directions in the mathematical sciences. This series may serve as an intermediate stage of the publication of material which, through exposure here, will be further developed and refined and appear later in the Mathematics in Science Series of books in applied mathematics also published by SpringerVerlag and in the same spirit as this series. MANUSCRIPTS The Editors welcome all inquiries regarding the submission of manuscripts for the series. Final preparation of all manuscripts will take place in the editorial offices of the series in the Division of Applied Mathematics, Brown University, Providence, Rhode Island.
Published by SPRINGER SCIENCE+BUSINESS MEDIA, LLC
L. Sirovich
Techniques of Asymptotic Analysis With 23 Illustrations
Springer Science+Business Media, LLC 1971
Lawrence Sirovich Division of Applied Mathematics Brown University Providence, Rhode Island
AU rights reserved No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag_ 1971 by Springer Science+Business Media New York Originally published by Springer-Verlag New York • Heidelberg • Berlin in 1971 Softcover reprint ofthe hardcover Ist edition 1971 ©
Library of Congress Catalog Card Number 70-149141
ISBN 978-0-387-90022-3 ISBN 978-1-4612-6402-6 (eBook) DOI 10.1007/978-1-4612-6402-6
Applied Mathematical Sciences IVolume 2
PREFACE These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown.
In the hope tha
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