This book (with free Online Edition) contains thorough study notes for AQA GCSE Extension Science - also known as GCSE Further Additional Science. It covers the final 'Extension' topics from GCSE Biology, Chemistry and Physics (Modules B3a, B3b, C3a, C3b, P3a, P3b). It's easy to read and revise from - everything's explained simply in CGP's student-friendly style. What's more, a free Online Edition of the whole book is included - perfect for revising on a PC, Mac or tablet device.
A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selected book exercises. See www.cambridge.org/economics/resources
Sharkovsky's Theorem, Li and Yorke's "period three implies chaos" result, and the (3x+1) conjecture are beautiful and deep results that demonstrate the rich periodic character of first-order, nonlinear difference equations. To date, however, we still know surprisingly little about higher-order nonlinear difference equations.