Jordan Canonical Form: Application to Differential Equations (Synthesis Lectures on Mathematics & Statistics, 2)

Weintraub, Steven H.

ISBN 10: 1598298046 / ISBN 13: 9781598298048

Verlag: Morgan and Claypool Publishers, 2008

Beschreibung

Good.

Bestandsnummer des Verkäufers ERICA82915982980463

Bibliografische Details

• Titel: Jordan Canonical Form: Application to Differential Equations (Synthesis Lectures on Mathematics & Statistics, 2)
• Verlag: Morgan and Claypool Publishers
• Erscheinungsjahr: 2008
• Sprache: Englisch
• ISBN-10: 1598298046
• ISBN-13: 9781598298048
• Einband: paperback
• Zustand: Good
• Buchtyp: book

Über diesen Titel

Inhaltsangabe

Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. In this book we develop JCF and show how to apply it to solving systems of differential equations. We first develop JCF, including the concepts involved in it—eigenvalues, eigenvectors, and chains of generalized eigenvectors. We begin with the diagonalizable case and then proceed to the general case, but we do not present a complete proof. Indeed, our interest here is not in JCF per se, but in one of its important applications. We devote the bulk of our attention in this book to showing how to apply JCF to solve systems of constant-coefficient first order differential equations, where it is a very effective tool. We cover all situations—homogeneous and inhomogeneous systems; real and complex eigenvalues. We also treat the closely related topic of the matrix exponential. Our discussion is mostly confined to the 2-by-2 and 3-by-3 cases, and we present a wealth of examples that illustrate all the possibilities in these cases (and of course, exercises for the reader). Table of Contents: Jordan Canonical Form / Solving Systems of Linear Differential Equations / Background Results: Bases, Coordinates, and Matrices / Properties of the Complex Exponential