Maximum and Minimum Principles: A Unified Approach with Applications

Maximum and Minimum Principles: A Unified Approach with Applications

ISBN-10:
0521348765
ISBN-13:
9780521348768
Pub. Date:
05/28/2007
Publisher:
Cambridge University Press

Paperback

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Overview

Maximum and Minimum Principles: A Unified Approach with Applications

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.

Product Details

ISBN-13: 9780521348768
Publisher: Cambridge University Press
Publication date: 05/28/2007
Series: Cambridge Texts in Applied Mathematics Series , #1
Pages: 488
Product dimensions: 5.98(w) x 8.98(h) x 1.10(d)

Table of Contents

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.

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