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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Hartman, Philip, 1915- Ordinary differential equations. Philadelphia : Society for Industrial and Applied Mathematics, ©2002 (DLC) 2002017641 (OCoLC)48817308 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Philip Hartman |

ISBN: | 0898715105 9780898715101 9780898719222 0898719224 |

OCLC Number: | 693771742 |

Language Note: | English. |

Notes: | This SIAM edition is an unabridged, corrected republication of the edition published by Birkhäuser, Boston, Basel, Stuttgart, 1982. The original edition was published by John Wiley & Sons, New York, 1964"--Title page verso. |

Description: | 1 online resource (xvi, 612 pages) : illustrations. |

Contents: | Preliminaries -- Existence -- Differential inequalities and uniqueness -- Linear differential equations -- Dependence on initial conditions and parameters -- Total and partial differential equations -- The Poincaré-Bendixson theory -- Plane stationary points -- Invariant manifolds and linearizations -- Perturbed linear systems -- Linear second order equations -- Use of implicity function and fixed point theorems -- Dichotomies for solutions of linear equations -- Miscellany on monotomy. |

Series Title: | Classics in applied mathematics, 38. |

Responsibility: | Philip Hartman. |

### Abstract:

Ordinary Differential Equations covers the fundamentals of the theory of ordinary differential equations (ODEs), including an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition to these results, the text illustrates techniques involving simple topological arguments, fixed point theorems, and basic facts of functional analysis. Unlike many texts, which supply only the standard simplified theorems, this book presents the basic theory of ODEs in a general way. This SIAM reissue of the 1982 second edition covers invariant manifolds, perturbations, and dichotomies, making the text relevant to current studies of geometrical theory of differential equations and dynamical systems. In particular, Ordinary Differential Equations includes the proof of the Hartman-Grobman theorem on the equivalence of a nonlinear to a linear flow in the neighborhood of a hyperbolic stationary point, as well as theorems on smooth equivalences, the smoothness of invariant manifolds, and the reduction of problems on ODEs to those on "maps" (Poincaré). Audience: readers should have knowledge of matrix theory and the ability to deal with functions of real variables.

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