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Understanding Nonlinear Dynamics (Textbooks in Mathematical Sciences)by Daniel Kaplan
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.
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.
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.
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.
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