(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
Dynamical Models in Biology presents readers with a concise introduction to the field of modern mathematical biology. Modeling techniques are applied to dynamical phenomena such as populations, genetics, epidemics, evolution, immunology, morphogenesis, and predator-prey relations. Differential equations are primarily used and there is an emphasis on the stability of biological structures.
May 2001, 200pp
Since its first appearance as a set of lectures notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references.
Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz's global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems.
After more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text.
Courant Lectures Notes, Volume 6
May 2001, approximately 160 pages, softcover
Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thoughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.
Published 30 July 2001, 464 pages, soft- and hardcover
This substantially expanded and updated version of the classic 1980 book by the late Akira Okubo traces the developments that have flowed from the original work, building on detailed notes he left for revision. The first edition was a comprehensive treatment of the use of diffusion models in ecology that integrated rigorous mathematical theory and substantive applications. Enormous in scope, covering a wide range of topics and including models of spread, critical patch size, and grouping, it has remained one of the most popular books in mathematical biology and has stimulated extensive research in the two decades since its publication. In this volume friends and disciples of Okubo incorporate a wide range of results from their own fields that build upon the framework he first established.
2001, approximately 448 pages, 134 illustrations, hardcover
Interdisciplinary Applied Mathematics, Volume 14.
Mathematical models and methods are increasingly important in medicine and the life sciences, and this book provides an introduction to a broad range of problems in this area. Each chapter is graded in difficulty, so a reading of the first parts of each provides an elementary introduction to the proceses and their models. Materials in greater depth on the same topics come later. Exercises and some solutions are given to test the reader on important parts of the text or to lead the reader to the discovery of interesting extensions of the material.
For this new edition the text has been updated throughout, computer projects have been added at the ends of many chapters, and appendices providing mathematical background have been included.
2001, approximately 350 pages, 71 illustrations, hardcover
Texts in Applied Mathematics, Volume 10
Develops the modern theory of both regular and chaotic nonlinear oscillations. Among the up-to-date topics are synchronizzation and chaotization of self-oscillatory systems and the influence of weak random vibrations on the modification of the characteristics and behaviour of nonlinear systems.
2001. Approximately 400pp. Hardcover
Foundations of Engineering Mathematics
This monograph addresses the systematic representation of the new methods of analysis developed by the authors recenetly as applied to nonlinear mechanical systems. Specific features of dynamic processes of these systems are studied. Special attention is given to an analysis of different resonant phenomena taking unusual and diverse forms. These methods are applied to the analysis of mechanical systems designed for the generation and tranformation of intensive processing of an impuslive nature. These are machines for rock fragmentation, impact processing, and shock testing machines, plus many other types.
Foundations of Engineering Mathematics
This is a reprint of M.C. Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area.
Readershia: Graduate students in mathematics.
Advanced Series in Nonlinear Dynamics Volume 17.