Books in Brief

By DSWeb Manager
Nonlinear Science; Emergence and Dynamics of Coherent Structures, 2nd ed.,

Alwyn Scott, Oxford University Press (2003), price $69.50, ISBN: 0198528523.

Level: beginning/intermediate.

This text forms an excellent introduction to solitons and waves, reaction-diffusion systems, and lattice dynamics. The material is integrated very well with applications, with a particular focus on mathematical biology and neuroscience. The text is designed for a graduate-level course; the writing is clear, and the exercises are copious and informative.
Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems

Da-Quan Jiang, Min Qian, and Min-Ping Qian, Springer Lecture Notes in Mathematics 1833, (2004), price $59.95, ISBN: 3540206116.

Level: advanced.

This text covers nonequilibrium statistical physics from the perspective of dynamical systems theory, with a focus on entropy production. For diffusion processes on manifolds, there is a detailed connection between entropy production and rotation numbers. Axiom A systems are also treated in depth.

New Difference Schemes for Partial Differential Equations

Allaberen Ashyralyev and Pavel Sobolevskii, Birkhauser (2004), price $199.00, ISBN: 3764370548.

Level: advanced.

This monograph covers high-accuracy difference schemes for regular and singular perturbation boundary value problems in PDEs. Both Cauchy and boundary value problems are covered in detail. The text is quite `hard' in the sense of being liberal in its use of functional analysis.

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