1.

Record Nr.

UNINA9910130965103321

Autore

Markley Nelson Groh <1940->

Titolo

Principles of differential equations / / Nelson G. Markley

Pubbl/distr/stampa

Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2004

©2004

ISBN

1-283-30628-X

9786613306289

1-118-03153-9

1-118-03328-0

Descrizione fisica

1 online resource (354 p.)

Collana

Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts

Disciplina

515.35

515/.35

Soggetti

Differential equations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Principles of Differential Equations; Contents; Preface; 1 Fundamental Theorems; 1.1 Preliminaries; 1.2 Existence; 1.3 Uniqueness; 1.4 Numerical Approximation; 1.5 Continuation; 1.6 Continuity in Initial Conditions; 2 Classical Themes; 2.1 Integrals; 2.2 The Qualitative Point of View; 2.3 Differential Inequalities; 3 Linear Differential Equations; 3.1 Elementary Properties; 3.2 Fundamental Matrix Solutions; 3.3 Higher Order Linear Differential Equations; 3.4 Complex Linear Differential Equations; 4 Constant Coefficients; 4.1 The Exponential of a Matrix; 4.2 Generalized Eigenspaces

4.3 Canonical Forms4.4 Higher Order Equations; 4.5 The Range of the Exponential Map; 5 Stability; 5.1 Stability at Fixed Points; 5.2 Stability and Constant Coefficients; 5.3 Stability and General Linear Systems; 5.4 Linear Systems with Periodic Coefficients; 6 The Poincaré Return Map; 6.1 Local Sections; 6.2 Planar Dynamics; 6.3 Recurrence; 7 Smooth Vector Fields; 7.1 Differentiate Functions; 7.2 Differentiation in Initial Conditions; 7.3 Linearization; 7.4 Hamiltonian Systems; 8 Hyperbolic Phenomenon; 8.1 Hyperbolic Linear Vector Fields; 8.2 Perturbed Hyperbolic Systems



8.3 The Contraction Mapping Principle8.4 Local Stable Manifolds; 9 Bifurcations; 9.1 The Implicit Function Theorem; 9.2 Persistence of Periodic Points; 9.3 Hopf Bifurcations; Bibliography; Index

Sommario/riassunto

An accessible, practical introduction to the principles of differential equations The field of differential equations is a keystone of scientific knowledge today, with broad applications in mathematics, engineering, physics, and other scientific fields. Encompassing both basic concepts and advanced results, Principles of Differential Equations is the definitive, hands-on introduction professionals and students need in order to gain a strong knowledge base applicable to the many different subfields of differential equations and dynamical systems. Nelson Markley includes essential background