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Chaos and Nonlinear Dynamics
This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.
Elements of Mathematical Ecology
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.
From Statistical Physics to Statistical Inference and Back
Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.
Classical Mechanics with Maxima
This book guides undergraduate students in the use of Maxima—a computer algebra system—in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook. When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using Maxima are easily transferred to other, proprietary software.
A Smooth and Discontinuous Oscillator
This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in...
The Conference on Computers in Physics Instruction
Computers are revolutionizing activities in all areas of life. Physics researchers, accustomed to being at the forefront of technology, have been deeply affected by the computer revolution. This effect has serious implications for what is taught and how it is taught in the physics classroom. This conference was organized to allow physics teachers and software developers in physics education to come together and see the state of the art in using computers to teach physics. The conference included 39 invited lectures and 122 contributed presentations. It introduced a number of innovations in the hope of increasing interactions and stimulating future contacts. This document contains the text of...
Einstein, Gödel & Co.
Ich habe das Institute for Advanced Study in Princeton zum erstenmal im Herbst 1983 besucht, als ich einen Zeitschriftenartikel recherchierte. Zuvor war mir nur der gute Ruf des Instituts bekannt; ich wußte wenig mehr, als daß Einstein und Gödel dort einen großen Teil ihres Lebens als Wissenschaftler gearbeitet hatten. Wie wohl auch anderen wissen schaftlich interessierten Laien hatten mir in meiner Jugend Bilder von Einsteins altem Arbeitszimmer im Institut, wie ich sie in Beschreibun gen seines Lebens und auch in Büchern über die Naturwissenschaft des zwanzigsten Jahrhunderts gesehen hatte, großen Eindruck gemach- berühmte Bilder, aufgenommen kurz nach seinem Tod im April 1955. Sie...
Computing with Mathematica
Computing with Mathematica, Second Edition is engaging and interactive. It is designed to teach readers how to use Mathematica efficiently for solving problems arising in fields such as mathematics, computer science, physics, and engineering. The text moves from simple to complex, often following a specific example on a number of different levels. This gradual increase in complexity allows readers to steadily build their competence without being overwhelmed. The Second Edition of this acclaimed book features: - Substantive real world examples - Challenging exercises, moving from simple to complex - A collection of interactive projects from a variety of applications "I really think this is an almost perfect text." -Stephen Brick, University of South Alabama - Substantive real world examples - Challenging exercises, moving from simple to complex examples
