Mathematics : Differential Equations

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from. interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to name. just a few, are ubiquitous dynamical concepts throughout the articles. more...

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The focus of this handbook is on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate, which makes it a useful addition to the arsenals of mathematicians, scientists, and engineers alike. more...

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Self-contained text, ideal for graduate students new to the area and researchers. more...

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Higher-Order Finite Element Methods provides an exhaustive survey of intrinsic techniques and practical implementation of higher-order finite element schemes. It addresses automatic hp-adaptivity in one- and two-spatial dimensions, and includes up-to-date references to ongoing research related to automatic hp-adaptivity in 3D. The authors' discussion of suitable data structures and efficient linear solvers provides an excellent introduction to key, often neglected aspects of this class of methods. Avoiding heavy mathematical jargon where possible, the book is written in a clear and comprehensive way for both applied mathematicians and engineers who are interested in finite elements. more...

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This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications held at the Ecole Normale Sup??rieure de Lyon, France, July 17-21, 2006. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modelling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly. The field is currently in interaction with a variety of scientific domains, including fluid dynamics, physics, electromagnetism, chemistry, biology, road and network traffic, and engineering. Many of these papers present new effective numerical methods and their application in various contexts. more...

Price: $139.00