(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, makin the book suitable for beggining graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as with fluid mechanics, elasticity, and electromagnetism.
Cambridge Texts in Applied Mathematics 24
2000 c. 475 pages
ISBN 0-521-63257-9 Hardback
ISBN 0-521-63450-4 Paperback
The growing impact of nonlinear science on biology and medicine is fundamentally changing our view of living organisms and disease processes. This book introduces the application to biomedicine of a broad range of concepts from nonlinear dynamics, such as self-organization, complexity, coherence, stochastic resonance, fractals, and chaos. Written by leading figures in the field, coverage details experimental and theoretical research, as well as the emerging technological possibilities such as nonlinear control techniques for treating pathological biodynamics, including heart arrhythmias and epilepsy. Self-Organized Biological Dynamics and Nonlinear Control will attract the interest of professionals and students from a wide range of disciplines, including physicists, chemists, biologists, sensory physiologists and medical researchers such as cardiologists, neurologists and biomedical engineers.
May 2000 442 pages
ISBN 0-521-62436-3 Hardback
This groundbreaking book describes the emerging field of theoretical immunology, in particular the use of mathematical models to describe the spread of infectious diseases within patients. It reveals fascinating insights into the dynamics of viral and other infections, and the interactions between infectious agents and immune responses. Structured around the examples of HIV/AIDS and hepatitis B, Nowak and May show how mathematical models can help researchers to understand the detailed dynamics of infection and the effects of antiviral therapy. Models are developed to describe the dynamics of drug resistance, immune responses, viral evolution and mutation, and to optimise the design of therapy and vaccines.
November 2000 250 pages
ISBN 0-19-850417-9 Paperback
ISBN 0-19-850418-7 Hardback
Hard Ball Systems and the Lorentz Gas are fundamental models arising in the theory of Hamiltonian dynamical systems. Moreover, in these models, some key laws of statistical physics can also be tested or even established by mathematically rigorous tools. The mathematical methods are most beautiful but sometimes quite involved. This collection of surveys written by leading researchers of the fields - mathematicians, physicists or mathematical physicists - treat both mathematically rigourous results, and evolving physical theories where the methods are analytic or computational. Some basic topics: hyperbolicity and ergodicity, correlation decay, Lyapunov exponents, Kolmogorov-Sinai entropy, entropy production, irreversibility. This collection is a unique introduction into the subject for graduate students, postdocs or researchers - in both mathematics and physics - who want to start working in the field.
Encyclopaedia of Mathematical Sciences, Vol. 101
2001, 400 pages.
ISBN 3-540-67620-1 Hardcover
This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time — two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler.
World Scientific Series on Nonlinear Science, Series A - Vol. 39
Jan 2001, 232 pages
ISBN 981-02-4404-5