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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Introduction to Functional Differential Equations (Paperback, Softcover reprint of the original 1st ed. 1993)
Loot Price: R2,431
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Introduction to Functional Differential Equations (Paperback, Softcover reprint of the original 1st ed. 1993)
Series: Applied Mathematical Sciences, 99
Expected to ship within 10 - 15 working days
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The present book builds upon an earlier work of J. Hale, "Theory of
Func tional Differential Equations" published in 1977. We have
tried to maintain the spirit of that book and have retained
approximately one-third of the material intact. One major change
was a complete new presentation of lin ear systems (Chapters 6 9)
for retarded and neutral functional differential equations. The
theory of dissipative systems (Chapter 4) and global at tractors
was completely revamped as well as the invariant manifold theory
(Chapter 10) near equilibrium points and periodic orbits. A more
complete theory of neutral equations is presented (see Chapters 1,
2, 3, 9, and 10). Chapter 12 is completely new and contains a guide
to active topics of re search. In the sections on supplementary
remarks, we have included many references to recent literature,
but, of course, not nearly all, because the subject is so
extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents
Preface............................................................
v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear
differential difference equations . . . . . . . . . . . . . . 11 .
. . . . . 1.1 Differential and difference equations. . . . . . . .
. . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded
differential difference equations. . . . . . . . . . . . . . . . 13
. . . . . . . 1.3 Exponential estimates of x( cents, f) . . . . . .
. . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The
characteristic equation . . . . . . . . . . . . . . . . . . . . . .
. . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . .
. . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . .
. . 1.6 The variation-of-constants
formula............................. 23 1. 7 Neutral differential
difference equations . . . . . . . . . . . . . . . . . 25 . . . . .
. . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . .
. . . . . . . . 34 . . . . . . . . . . . . . 2. Functional
differential equations: Basic theory . . . . . . . . 38 . . 2.1
Definition of a retarded equation. . . . . . . . . . . . . . . . .
. . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and
continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation
of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44
. . . . . . . . . . . ."
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