Böcker av James C. (University of Warwick) Robinson

This text covers key results in functional analysis that are essential for further study in analysis, the calculus of variations, dynamical systems, and the theory of partial differential equations. More than 200 fully-worked exercises and detailed proofs are given, making this ideal for upper undergraduate and beginning graduate courses.

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes many traditional elements of the subject. It gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems.

A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier-Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray-Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a graduate course of one or two semesters. It is also a useful resource for anyone working in mathematical fluid dynamics.

This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part of the book to the finite-dimensional global attractors that arise in certain infinite-dimensional dynamical systems, deducing practical consequences from the existence of such attractors: a version of the Takens time-delay embedding theorem valid in spatially extended systems, and a result on parametrisation by point values. This book will appeal to all researchers with an interest in dimension theory, particularly those working in dynamical systems.

A first introduction to ordinary differential and difference equations, accessible for mathematicians, scientists and engineers. All important and relevant approaches are covered, and many illustrative examples are included. MATLAB is used to generate graphical representations of solutions, for which code is supplied. Exercises and worked solutions are available for teachers.