Edited by Yibin Fu, Raymond W. Ogden

Nonlinear Elasticity
Theory and Applications

London Mathematical Society Lecture Note Series series

Description

Nonlinear elasticity is concerned with nonlinear effects associated with deformations of elastic bodies subjected to external forces or temperature variations. It has important applications in many areas, including the aerospace and rubber industries, and biomechanics. This book, written by a group of leading researchers invited especially for the purpose, provides an up-to-date and concise account of the fundamentals of the theory of nonlinear elasticity and a comprehensive review of several major current research directions in
this important field. It combines the characteristics of coherence and detail found in freshness of research articles. The emphasis is placed firmly on coverage of modern topics and recent developments rather than on the very theoretical approach often found. The book will be an excellent reference source for both
beginners and specialists in engineering, applied mathematics and physics. It is also ideally suited for graduate courses.

Chapter Contents

Preface; 1. Elements of the theory of finite elasticity R. W. Ogden; 2. Hyperelastic Bell materials: retrospection, experiment, theory M. F. Beatty; 3. Universal results in finite elasticity G. Saccomandi; 4. Equilibrium solutions for compressible nonlinearly elastic materials C. O. Horgan; 5. Exact integrals and solutions for finite deformations of the incompressible Varga elastic materials J. M. Hill; 6. Shear Ph. Boulanger and M. Hayes; 7. Elastic membranes D. M. Haughton; 8. Elements of the theory of elastic surfaces D. J. Steigmann; 9. Singularity theory and nonlinear bifurcation analysis Y.-C. Chen; 10. Perturbation
methods and nonlinear stability analysis Y. B. Fu; 11. Nonlinear dispersive waves in a circular rod composed of a Mooney-Rivlin material H.-H. Dai; 12. Strain-energy functions with multiple local minima: modeling phase transformations using finite thermo-elasticity R. Abeyaratne, K. Bhattacharya and J. K. Knowles; 13.
Pseudo-elasticity and stress softening R. W. Ogden.

ISBN: 0-521-79695-4
Binding: Paperback
Pages: 536

Brian R. Hunt, Ronald L. Lipsman, Jonathan M. Rosenberg

A Guide to MATLAB
For Beginners and Experienced Users

Description

This book is a short, focused introduction to MATLAB, a comprehensive software system for mathematics and technical computing. It should be useful to both beginning and experienced users. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's
programming features, graphical capabilities, and desktop interface. It also includes an introduction to SIMULINK, a companion to MATLAB for system simulation. Written for MATLAB 6, this book can also be used with earlier (and later) versions of MATLAB. This book contains worked-out examples of applications of
MATLAB to interesting problems in mathematics, engineering, economics, and physics. In addition, it contains explicit instructions for using MATLAB's Microsoft Word interface to produce polished, integrated, interactive documents for reports, presentations, or on-line publishing. This book explains everything you need to know to
begin using MATLAB to do all these things and more. Intermediate and advanced users will find useful information here, especially if they are making the switch to MATLAB 6 from an earlier version.

Chapter Contents

Preface; 1. Getting started; 2. MATLAB basics; 3. Interacting with MATLAB; 4. Beyond the basics; 5.
MATLAB graphics; 6. M-Books; 7. MATLAB programming; 8. SIMULINK and GUIs; 9. Applications; 10. MATLAB and the internet; 11. Troubleshooting; Solutions to the practice sets; Glossary; Index.

ISBN: 0-521-00859-X
Binding: Paperback
ISBN: 0-521-80380-2
Binding: Hardcover
Pages: 330

David Williams

Weighing the Odds

Description

In this lively look at probability and statistics the author demonstrates to mathematics students the intrinsic interest of statistics and probability, and to statistics students that, though statistics involves more than mathematics, its language can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, for example,
genetics, filtering, the Black-Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches,
emphasising confidence intervals rather than hypothesis test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of linear regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUGS code is
provided for computational examples and simulations. Many exercises are included; hints or solutions are often provided.

Chapter Contents

Preface; 1. Introduction; 2. Events and probabilities; 3. Random variables, means and variances; 4. Conditioning and independence; 5. Generating functions and the central limit theorem; 6. Confidence intervals for 1-parameter models; 7. Conditional pdfs and multi-parameter Bayesian statistics; 8. Linear models, ANOVA etc; 9. Some further probability; 10. Quantum probability and quantum computing; Appendix A.
Some prerequisites and addenda; Appendix B. Discussion of some selected exercises; Appendix C. Tables; Appendix D. A small sample of the literature; Bibliography; Index.

ISBN: 0-521-00618-X
Binding: Paperback
ISBN: 0-521-80356-X
Binding: Hardcover
Pages: 560

Willem-Paul de Roever, Frank de Boer, Ulrich
Hanneman, Jozef Hooman, Yassine Lakhnech,
Mannes Poel, Job Zwiers

Concurrency Verification
An Introduction to State-based Methods

Cambridge Tracts in Theoretical Computer Science series

Description

This is a systematic and comprehensive introduction both to compositional proof methods for the state-based verification of concurrent programs, such as the assumption-commitment and rely-guarantee paradigms, and to noncompositional methods, whose presentation culminates in an exposition of the
communication-closed-layers (CCL) paradigm for verifying network protocols. Compositional concurrency verification methods reduce the verification of a concurrent program to the independent verification of its parts. If those parts are tightly-coupled, one additionally needs verification methods based on the causal order
between events. These are presented using CCL. The semantic approach followed here allows a systematic presentation of all these concepts in a unified framework which highlights essential concepts. The book is self-contained, guiding the reader from advanced undergraduate level to the state-of-the-art. Every method is illustrated by examples, and a picture gallery of some of the subject's key figures complements the text.

Chapter Contents

Preface; Part I. Introduction and Overview: 1. Introduction; Part II. The Inductive Assertion Method: 2. Floyd's inductive assertion method for transition diagrams; 3. The inductive assertion method for shared-variable concurrency; 4. The inductive assertion method for synchronous message passing; 5. Expressibility and relative
completeness; Part III. Compositional Proof Methods: 6. Introduction to compositional reasoning; 7. Compositional proof methods: synchronous message passing; 8. Compositional proof methods: shared-variable concurrency; Part IV. Hoare Logic: 9. A proof system for sequential programs using Hoare triples; 10. A Hoare logic for shared-variable concurrency; 11. A Hoare logic for synchronous message passing; Part V.
Layered Design: 12. Transformational design and Hoare logic; Bibliography; Glossary of symbols; Index.

ISBN: 0-521-80608-9
Binding: Hardback
Pages: 776

A. Neumaier

Introduction Numerical Mathematics

Description

Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive
methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific
programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.

Chapter Contents

1. The numerical evaluation of expressions; 2. Linear systems of equations; 3. Interpolation and numerical differentiation; 4. Numerical integration; 5. Univariate nonlinear equations; 6. Systems of nonlinear equations.

ISBN: 0-521-33610-4
Binding: Paperback
Pages: 365