Overview

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this text provides a comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A sequential canonical dual transformation method for solving nonlinear problems is developed heuristically and illustrated by use of examples as well as extensive applications of nonlinear systems. This includes differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With coherent exposition, the work fills a large gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. An appendix provides some necessary background from elementary functional analysis. The book should be a useful resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the ideas of optimization and variational methods are employed.

Full Product Details

Author:   David Yang Gao
Publisher:   Springer
Imprint:   Springer
Edition:   2000 ed.
Volume:   39
Dimensions:   Width: 15.60cm , Height: 2.60cm , Length: 23.40cm
Weight:   1.860kg
ISBN:  

9780792361459

ISBN 10:   0792361458
Pages:   454
Publication Date:   31 January 2000
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

I Symmetry in Convex Systems.- 1. Mono-Duality in Static Systems.- 2. Bi-Duality in Dynamical Systems.- II Symmetry Breaking: Triality Theory in Nonconvex Systems.- 3. Tri-Duality in Nonconvex Systems.- 4. Multi-Duality and Classifications of General Systems.- III Duality in Canonical Systems.- 5. Duality in Geometrically Linear Systems.- 6. Duality in Finite Deformation Systems.- 7. Applications, Open Problems and Concluding Remarks.- Appendices.- A—Duality in Linear Analysis.- A.1 Linear spaces and duality.- A.2 Bilinear Forms and Inner Product Spaces.- A.3 Linear functionals and Dual spaces.- B—Linear Operators and Adjointness.- B.1 Linear Operators.- B.2 Adjoint Operators.- B.3 Duality Relations for Range and Nullspace.- C—Nonlinear Operators.- C.1 Operators on Finite-Dimensional Spaces.- C.2 Monotone and Pseudo-Monotone Operators on Banach Spaces.- C.3 Potential Operators and Duality Mappings.- References.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions