Luigi Morino - Böcker

The symposium was organized with the intention of creating an opportunity for mathematicians and engineers working on nonlinear problems to communicate with each other and exchange experiences in the use of boundary integral methods. The spirit of the symposium is clearly reflected in the papers collected in the volume. Some mathematical issues of boundary integral methods for the solution of nonlinear problems are examined in depth. In addition, several applications to fluid and solid mechanics and heat transfer problems are presented. The reader is given a wide overview of the broad class of applications where boundary integral methods represent a very appealing tool for the analysis of nonlinear problems.

This book is to present a highly readable introduction to dynamical systems, namely initial-value problems of systems of differential equations (mathematics), and particle dynamics (mechanics). Linear algebra is extensively covered as a prerequisite.This is the stand-alone second volume of a book that covers an integrated approach to mathematics and mechanics from elementary to graduate level material of scientific curricula-the first of this breadth.A simple, intuitive approach is used throughout. In particular, gut-level proofs are preferred over abstract ones, even if not succinct and elegant. To make the volume simple to read and, at the same time, rigorous, additional material (clearly marked as optional) is provided. Overall, every statement is proven-the sentence “it may be shown that . . . ” is banned from this book.Continuum systems, such as strings, pipes, membranes, and beams, are briefly addressed as limiting cases of discrete ones, with applications to musical string-and wind-instruments.Advanced material includes: Jordan matrices, power spectral density with application to clean-air-turbulence response, and approximate solutions of nonlinear differential equations by multiple scales and normal form, with application to limit cycles and post-flutter analysis. For completeness, there is an introduction to the numerical integration of differential equations and other computational techniques, in particular optimization and its relationship with genetic algorithms, neural networks, and artificial intelligence.

This volume contains edited papers from IABEM-90, the 1990 Symposium of the Interna­ tional Association for Boundary Element Methods (IABEM). As stated in the By-Laws of the Association, the purposes of IABEM are: 1. to promote the international exchange of technical information related to the devel­ opment and application of boundary-integral equation (BIE) formulations and their numerical implementation to problems in engineering and science, commonly referred to as the boundary element method (BEM); 2. to promote research and development activities for the advancement of boundary­ integral equation methods and boundary element solution algorithms; 3. to foster closer personal relationships within the BEM community of researchers. The objectives of the Symposium, in line with those of the Association, was to provide a forum where the two "souls" of the Association, i. e. , (i) mathematical foundations and numerical aspects, and (ii) engineering applications could be integrated. We believe that the first aspect has been neglected in too many of the BEM Symposia held in the past, which, with a few exceptions (notably, the IUTAM Symposia on the subject) have emphasized the practical aspects of the method. As a consequence, we have tried to give a stronger emphasis to the more theoretical issues: this is attested for instance, by the fact that the two general lectures were given by Prof. Gaetano Fichera, of the University of Rome "La Sapienza," and Prof.

Guidelines that facilitate the reading of the book are presented.The interplay between mathematics and mechanics is presented within a historical context, to show that often mechanics stimulated mathematical developments - Newton comes to mind.