Synopses & Reviews
UNDERSTANDING NONLINEAR DYNAMICS is based on an undergraduate course taught for many years to students in the biological sciences. The text provides a clear and accessible development of many concepts from contemporary dynamics, including stability and multistability, cellular automata and excitable media, fractals, cycles, and chaos. A chapter on time-series analysis builds on this foundation to provide an introduction to techniques for extracting information about dynamics from data. The text will be useful for courses offered in the life sciences or other applied science programs, or as a supplement to emphasize the application of subjects presented in mathematics or physics courses. Extensive examples are derived from the experimental literature, and numerous exercise sets can be used in teaching basic mathematical concepts and their applications. Concrete applications of the mathematics are illustrated in such areas as biochemistry, neurophysiology, cardiology, and ecology. The text also provides an entry point for researchers not familiar with mathematics but interested in applications of nonlinear dynamics to the life sciences.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors."
This book presents the main concepts and applications of nonlinear dynamics at an elementary level. The book is based on a one-semester undergraduate course that has been given since 1975 at McGill University and has been constantly updated to keep up with current developments. Based on the authors' successful course for undergraduate students in the biological sciences, the primer presents the main concepts of non-linear dynamics at a level requiring only one year of calculus. This text will appeal to courses being offered in both mathematics and biology. Topics include finite difference equations, the concept of chaos, networks, cellular automata, on- and two-dimensional differential equations, the dynamics of non-linear equations, and linear stability analysis. Examples are all from the biological sciences, exercises are included in each chapter, and basic mathematical reviews are included in an appendix.
Based on an undergraduate course in the biological sciences, this book presents the main concepts of non-linear dynamics at a level requiring only one year of calculus. Covers finite difference equations, the concept of chaos, cellular automata, and more.
Includes bibliographical references (p. -408) and index.
Table of Contents
Preface.- About the Authors.- Finite-Difference Equations.- Boolean Networks and Cellular Automata.- Self-Similarity and Fractal Geometry.- One-Dimensional Differential Equations.- Two-Dimensional Differential Equations.- Time-Series Analysis.- Appendix A: A Multi-Functional Appendix.- Appendix B: A Note on Computer Notation.- Solutions to Selected Exercises.- Bibliography.- Index.