Maximum and Minimum Principles

A Unified Approach with Applications
Erscheinungsjahr 2007
ISBN: 978-0-521-34876-8
Verlag: Cambridge University Press

Buch, Englisch, Band 1, 488 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 785 g

Reihe: Cambridge Texts in Applied Mathematics

In many problems of applied mathematics, science, engineering or economics, an energy expenditure or its analogue can be approximated by upper and lower bounds. This book provides a unified account of the theory required to establish such bounds, by expressing the governing conditions of the problem, and the bounds, in terms of a saddle functional and its gradients. There are several features, including a chapter on the Legendre dual transformation and some of its singularities. Many substantial examples and exercises are included, especially from the mechanics of fluids, elastic and plastic solids and from optimisation theory. The saddle functional viewpoint gives the book a wide scope. The treatment is straightforward, the only prerequisite being a basic knowledge of the calculus of variations. Part of the book is based on final-year undergraduate courses. This is developed into an account which will interest a wide range of students and professionals in applied mathematics, engineering, physics and operations research.

Autoren/Hrsg.

Sewell, M. J.

Crighton, C. G.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

Preface; 1. Saddle function problems; 2. Duality and Legendre transformations; 3. Upper and lower bounds via saddle functionals; 4. Extensions of the general approach; 5. Mechanics of solids and fluids; References; Index.