Linear Multivariable Systems
This text was developed over a three year period of time (1971- 1973) from a variety of notes and references used in the presentation of a senior/first year graduate level course in the Division of En gineering at Brown University titled Linear System Th
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Lawrence Sirovich Division of Applied Mathematics Brown University
Joseph P. LaSalle Division of Applied Mathematics Brown University Providence, R. I. 02912
Gerald B. Whitham Applied Mathematics Firestone Laboratory California Institute of Technology
New York, N.Y. 10012
Providence, R. I. 02912
Pasadena, CA. 91109
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 aU create the need both in education and research for hooks 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 all 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 will often serve as an intermediate stage of the publication of material which, through exposure here, will he further developed and refined and appear later in one of Springer-Verlag's other mathematical 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. SPRINGER-VERLAG NEW YORK INC., 175 Fifth Avenue, New York, N.Y. 10010 Printed in U.S.A.
Applied Mathematical Sciences! Volume 11
Applied Mathematical Sciences EDITORS
Fritz John Joseph P. laSalle
Lawrence Sirovich Gerald B. Whitham
F. John PARTIAL DIFFERENTIAL EQUATIONS ISBN 0·387·90021·7 L. Sirovich TECHNIQUES OF ASYMPTOTIC ANALYSIS ISBN 0·387·90022·5
J. Hale
FUNCTIONAL DIFFERENTIAL EQUATIONS ISBN 0·387·90023·3
J. K. Percus COMBINATORIAL METHODS ISBN 0·387·90027·6 R. von Mises and K. O. Friedrichs FLUID DYNAMICS ISBN 0·387·90028·4 W. Freiherger and U. Grenander A SHORT COURSE IN COMPUTATIONAL PROBABILITY AND STATISTICS ISBN 0·387·90029·2 A. C. Pipkin LECTURES ON VISCOELASTICITY THEORY ISBN 0·387·90030·6 K. O. Friedrichs SPECTRAL THEORY OF OPERATORS IN HILBERT SPACE ISBN 0·387·90076·4
A. H. Stroud
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