Differential Equations: Theory and Applications

2. 2010 Auflage 2009
ISBN: 978-1-4419-1162-9
Verlag: Springer

Buch, Englisch, 626 Seiten, Book w. online files / update, Format (B × H): 166 mm x 241 mm, Gewicht: 1083 g

This book was written as a comprehensive introduction to the theory of ordinary di?erential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. H- torically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in mat- matics, thematerial is organized sothatthebookcan alsobeusedin awider setting within today’s modern university and society (see “Ways to Use the Book” below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can bene?t from using this text. Working professionals in any of these ?elds should be able to pro?t too by study of this text. An important, but optional component of the book (based on the - structor’s or reader’s preferences) is its computer material. The book is one of the few graduate di?erential equations texts that use the computer to enhance the concepts and theory normally taught to ?rst- and second-year graduate students in mathematics. I have made every attempt to blend - gether the traditional theoretical material on di?erential equations and the new, exciting techniques a?orded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab. The electronic material for mastering and enjoying the computer component of this book is on Springer’s website.

Zielgruppe

Graduate

Autoren/Hrsg.

Betounes, David

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

Techniques, Concepts and Examples.- Existence and Uniqueness: The Flow Map.- Linear Systems.- Linearization #x0026; Transformation.- Stability Theory.- Integrable Systems.- Newtonian Mechanics.- Hamiltonian Systems.- Elementary Analysis.- Lipschitz Maps and Linearization.- Linear Algebra.- Electronic Contents.