Overview

The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science.

Full Product Details

Author:   John L. Troutman
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2nd ed. 1996
Dimensions:   Width: 15.50cm , Height: 2.60cm , Length: 23.50cm
Weight:   1.880kg
ISBN:  

9780387945118

ISBN 10:   0387945113
Pages:   462
Publication Date:   01 December 1995
Audience:   College/higher education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

0 Review of Optimization in ?d.- Problems.- One Basic Theory.- 1 Standard Optimization Problems.- 2 Linear Spaces and Gâteaux Variations.- 3 Minimization of Convex Functions.- 4 The Lemmas of Lagrange and Du Bois-Reymond.- 5 Local Extrema in Normed Linear Spaces.- 6 The Euler-Lagrange Equations.- Two Advanced Topics.- 7 Piecewise C1 Extremal Functions.- 8 Variational Principles in Mechanics.- 9 Sufficient Conditions for a Minimum.- Three Optimal Control.- 10 Control Problems and Sufficiency Considerations.- 11 Necessary Conditions for Optimality.- A.1. The Intermediate and Mean Value Theorems.- A.2. The Fundamental Theorem of Calculus.- A.3. Partial Integrals: Leibniz’ Formula.- A.4. An Open Mapping Theorem.- A.5. Families of Solutions to a System of Differential Equations.- A.6. The Rayleigh Ratio.- Historical References.- Answers to Selected Problems.

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