A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it...

The aim of this book is to bring together classical and recent developments in the particular field of Newtonian flow at low Reynolds numbers. The methods are developed from first principles, alternative formulations are compared, a variety of configurations are addressed, the proper mathematical framework is discussed in the context of functional analysis and integral-equation-theory, and procedures of numerical solution in the context of the boundary element method are introduced. The text contains a fair amount of original material pertaining, in particular, to the properties and explicit...

By providing an introduction to nonlinear differential equations, Dr. Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincare-Bendixson theorem, the Hopf bifurcation and chaotic systems.

The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the fundamental dynamics of fluid motion. They are applied routinely to problems in engineering, geophysics, astrophysics, and atmospheric science. This book is an introductory physical and mathematical presentation of the Navier-Stokes equations, focusing on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion. The goal of the book is to present a mathematically rigorous investigation...

Viscous flow crops up in many real-life situations such as aerodynamics and lubrication, and because of its universality it is a paradigm for the application of mathematics to the real world. This book is a coherent account of the ways in which mathematics can both give insight into viscous flow and suggest analogies and implications for other branches of applied mathematics. The authors place particular emphasis on the unification brought about by the use of asymptotic analysis and scaling properties and the use of everyday observations from the real world (especially industry) to illustrate...

This book presents a thorough grounding in the techniques of modeling, and proceeds to explore a range of continuum models from an impressive array of disciplines, including biology, chemical engineering, fluid and solid mechanics, geophysics, medicine, and physics. It assumes only a basic mathematical grounding in calculus and analysis and will provide a wealth of examples for students of mathematics, engineering, and the range of applied sciences.

This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and...

A good working knowledge of symmetry methods is very valuable for those working with mathematical models. This book is a straightforward introduction to the subject for applied mathematicians, physicists, and engineers. The informal presentation uses many worked examples to illustrate the major symmetry methods. Written at a level suitable for postgraduates and advanced undergraduates, the text will enable readers to master the main techniques quickly and easily. The book contains some methods not previously published in a text, including those methods for obtaining discrete symmetries and...

A good working knowledge of symmetry methods is very valuable for those working with mathematical models. This book is a straightforward introduction to the subject for applied mathematicians, physicists, and engineers. The informal presentation uses many worked examples to illustrate the major symmetry methods. Written at a level suitable for postgraduates and advanced undergraduates, the text will enable readers to master the main techniques quickly and easily. The book contains some methods not previously published in a text, including those methods for obtaining discrete symmetries and...

Starting from dimensional analysis and physical similarity, G. Barenblatt describes the art of discovering scaling laws. He demonstrates the concepts of intermediate asymptotics and the renormalization group as natural consequences of self-similarity and shows how and when these tools can tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used independently by biologists, chemists, astronomers, engineers and geoscientists.