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Ordinary Differential Equations with Constant Coefficient
S. K. Godunov, The S. L. Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia
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Translations of Mathematical Monographs
1997; 282 pp; hardcover
Volume: 169
ISBN-10: 0-8218-0656-4
ISBN-13: 978-0-8218-0656-2
List Price: US$120
Member Price: US$96
Order Code: MMONO/169
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This book presents the theory of ordinary differential equations with constant coefficients. The exposition is based on ideas developing the Gelfand-Shilov theorem on the polynomial representation of a matrix exponential. Boundary value problems for ordinary equations, Green matrices, Green functions, the Lopatinskii condition, and Lyapunov stability are considered.

This volume can be used for practical study of ordinary differential equations using computers. In particular, algorithms and computational procedures, including the orthogonal sweep method, are described. The book also deals with stationary optimal control systems described by systems of ordinary differential equations with constant coefficients. The notions of controllability, observability, and stabilizability are analyzed, and some questions on the matrix Luré-Riccati equations are studied.

Readership

Graduate students and research mathematicians interested in ordinary differential equations, computer science, and systems theory and control.

Table of Contents

  • Matrix exponentials, Green matrices, and the Lopatinskii condition
  • Quadratic Lyapunov functions
  • Qualitative properties of problems and algorithmic aspects
  • Linear control systems
  • References
  • Index
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