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Validated Numerics
A comprehensive, self-contained primer on validated numerics This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into accou...
An Introduction to Dynamical Systems
This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course. The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where pe...
Colonial Virginians and Their Maryland Relatives
This copiously documented volume sheds new light on one of the earliest families to settle in Virginia, that of Captain William Tucker of London, and on a number of allied families whose progenitors figured in the early history of the Virginia and Maryland colonies.
Validated Numerics
""Validated Numerics" contains introductory material on interval arithmetic and rigorous computations that is easily accessible to students with little background in mathematics and computer programming. I am not aware of any other book like it. The exercises and computer labs make it ideal for the classroom, and the references offer a good starting point for readers trying to gain deeper knowledge in this area."--Zbigniew Galias, AGH University of Science and Technology, Krakw -- "A significant contribution, particularly since there are not many texts in this area. "Validated Numerics" will be read by those interested in interval arithmetic, numerical analysis, and ways to make computer simulations more robust and less susceptible to errors. It is well written and well organized."--A. J. Meir, Auburn University.
The Archaeology of Political Spaces
This book, consisting of 12 contributions, amalgamates the most recent results from archaeological research in the Upper Mesopotamian piedmont. Under the growing influence of expanding territorial states which had become established during the 2nd millennium BC, this region experienced a substantial change in social and political life during that time. The discussion is centered around settlement shapes, developments in the material culture, as well as written documents that attest to this change. In summary, this book emphasizes the significant roll of archaeological research in the reconstruction of models concerning the formation and transformation of political space in the ancient world.
Robust Chaos and Its Applications
Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.
Nonlinear Dynamics and Chaos
The goal of this third edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering is the same as previous editions: to provide a good foundation - and a joyful experience - for anyone who’d like to learn about nonlinear dynamics and chaos from an applied perspective. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals,...
Topology and Dynamics of Chaos
The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,
Intelligent Computing Based on Chaos
Chaos is a fascinating phenomenon that has been observed in nature, laboratory, and has been applied in various real-world applications. Chaotic systems are deterministic with no random elements involved yet their behavior appears to be random. Obser- tions of chaotic behavior in nature include weather and climate, the dynamics of sat- lites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, to mention only a few examples. Chaos has been observed in the laboratory in a number of systems such as electrical circuits, lasers, chemical reactions, fluid dynamics, mechanical systems, and magneto-mechanical devices. Chaotic behavior has ...
