Background
Hale, Jack K. was born on October 3, 1928 in Dudley, Kentucky, United States. Son of James Marion and Cora Lee (Kelly) Hale.
(The present book builds upon an earlier work of J. Hale, ...)
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( ¢,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 . . . . . . . . . . . .
http://www.amazon.com/gp/product/0387940766/?tag=2022091-20
(In recent years, due primarily to the proliferation of co...)
In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.
http://www.amazon.com/gp/product/1461287650/?tag=2022091-20
( Based on a Brown University course in applied mathemati...)
Based on a Brown University course in applied mathematics, this rigorous and demanding treatment focuses on specific analytical methods. It emphasizes nonlinear problems, acquainting readers with problems and techniques in ordinary differential equations. The material is presented in a manner that prepares students for informed research of differential equations, teaching them how to be more effective in studies of the current literature. In addressing the applied side of the subject, the text devotes considerable attention to specific analytical methods common to applications. Introductory chapters offer necessary background material by reviewing basic facts of analysis and covering the general properties of differential equations. Topics include two-dimensional systems, linear systems and linearization, perturbations of noncritical linear systems, simple oscillatory phenomena and the method of averaging, and behavior near a periodic orbit. Additional subjects include integral manifolds of equations with a small parameter, periodic systems with a small parameter, alternative problems for the solution of functional equations, and the direct method of Liapunov. Exercises appear at the end of each chapter, and the appendix contains a convenient reference for almost every periodic functions.
http://www.amazon.com/gp/product/0486472116/?tag=2022091-20
administrator mathematics educator research
Hale, Jack K. was born on October 3, 1928 in Dudley, Kentucky, United States. Son of James Marion and Cora Lee (Kelly) Hale.
Bachelor in Mathematics, Berea College, 1949; Doctor of Philosophy in Mathematics, Purdue University, 1953; Doctor of Science (honorary), Rijksuniveriteit-Gent, Belgium, 1983; doctor honoris causa, Stuttgart U., Federal Republic of Germany, 1988; doctor honoris causa, Technology U. Lisbon, 1991; doctor honoris causa, Rostoch U., Federal Republican Germany, 1999.
Instructor, Purdue University, West Lafayette, Indiana, 1949-1954; with, Sandia Corporation, Albuquerque, 1954-1957; with, Remington-Rand Univac, St. Paul, 1957-1958; with, Research Institute for Advanced Study, Baltimore, 1958-1964; professor division applied mathematics, Brown U., Providence, 1964-1989; chairman, Brown U., Providence, 1973-1976; Regents' professor, Georgia Institute Technology, Atlanta, 1988-1998; director Center for Dynamical Systems and Nonlinear Studies, Georgia Institute Technology, Atlanta, 1989-1998; regents professor emeritus, Georgia Institute Technology, since 1998.
( Based on a Brown University course in applied mathemati...)
(In recent years, due primarily to the proliferation of co...)
(The present book builds upon an earlier work of J. Hale, ...)
Fellow Royal Society Edinburgh (honorary), Brazilian Academy Science (correspondent). Member Polish Academy Science (foreign), American Mathematics Society, American Academy Mechanics, Brazilian Mathematics Society.
Married Hazel Reynolds.