UK Nonlinear News, February 2000
(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
This introduction to nonlinear physics is designed and centered around Maple's ability to perform symbolic computations, plot, animate, and permit students to investigate various nonlinear models. Previously published in two separate volumes, this revised and updated edition now combines both the standard text and the lab files in one comprehensive volume. Included again is a floppy disk containing the Maple code and software. Besides expansions of the theoretical part, this second edition features many new and improved examples, Maple experiments and files, and all Maple code has been updated to Release V.
December 1999, Approximately 656 pp, 272 illustrations &
Hardcover. ISBN 0-8176-4119-X.
Chaos is introduced and incorporated as an intergral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter spave analysis are developed with ample exercises.
Semidefinite programming (SDP) has been one of the most exciting and active research areas in optimization during the 1990's. It has attracted researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity was spurred by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory.
The HANDBOOK OF SEMIDEFINITE PROGRAMMING offers an advanced and broad overview of the current state of the field, It contains nineteen chapters written by the leading experts on the subject. The chapters are organized in three parts: Theory, Algorithms, and Applications and Extensions.
February 25, xxvi+654 pages, hardcover
Special pre-publication price of US$100 may be obtained from http://orion.math.uwaterloo.ca/~hwolkowi/henry/book/fronthandbk.d/handbooksdp.html
(orders must be received by Friday, March 31, 2000)
Source: Henry Wolkowicz
Until recently much mathematical modelling has involved the assumption that physical systems are linear, or nearly so. This led to the construction of equations which, although relatively easy to solve, were unrealistic and meant that significant phenomena were overlooked. It has recently been discovered that nonlinear systems actually lead to the emergence of new structures which have their own properties, and which reflect reality much more closely. The discovery of these emergent structures is therefore of vital importance. Although written at an introductory level this book covers several important areas of nonlinear science, and places a strong emphasis on the applications to reality. It will serve as an important text and reference for graduate students and researchers alike.
Hardback (laminated boards),
UK Price: £39.95
Publication date: 11 March 1999
Oxford Applied and Engineering Mathematics
Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having linnks with the geometric theory of differential equations, numerical analysis, and linear algebra.
Several features make this book unique. The first is the systematic use of bordered matricx methods in the numerical computation and continuation of various bifurcations. The second is a detailed treatment of bialternate matrix products and their Jordan structure. Govaerts discusses their uses in the numerical methods for Hopf and related bifurcations. A third geature if a unified treatment of singularity theory with and without a distinguished bifurcation parameter, from a numerical point of view. Finally, numerical methods for symmetry-breaking bifurcations are discussed in detail, up to the fundamental cases covered by the equivariant branching lemma.
Anyone interested in computational methods for ODEs, PDEs, and bifurcation theory will find this volume a great addition to their library. This volume can be used as a text for graduate courses on numerical computation of bifurcations or numerical singularity theory. A basic knowledge of linear algebra, numerical linear algebra, calculus, and differential equations is required for full understanding of the material.
January 2000. Approximately 347 pages. Softcover.
This book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material on stability, Z-transforms, discrete control theory and asymptotic theory, continued fractions, and orthogonal polynominals. The presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students in mathematics, engineering science, and economics. Moreover, scientists and engineers who are interested in discrete mathematical models will find it a useful reference.
1999 448pp 64 illustrations Hardcover
Undergraduate Texts in Mathematics
The Institute for Mathematics and its Applications (IMA)
devoted its 1997-1998 program to Emerging Applications of
Dynamical Systems. Dynamical systems theory and related numerical
algorithms provide powerful tools for studying the solution
behavior of differential equations and mappings. In the past 25
years computational methods have been developed for calculating
fixed points, limit cycles, and bifurcation points. A remaining
challenge is to develop robust methods for calculating more
complicated objects, such as higher-codimension bifurcations of
fixed points, periodic orbits, and connecting orbits, as well as
the calcuation of invariant manifolds. Another challenge is to
extend the applicability of algorithms to the very large systems
that result from discretizing partial differential equations.
Even the calculation of steady states and their linear stability
can be prohibitively expensive for large systems (e.g. 10^3-10^6
equations) if attempted by simple direct methods.From the
Contents: Numerical bifurcation techniques for chemical
reactor problems.- Path-following of large bifurcation problems
with iterative methods.- On the bifurcation from continuous to
segmented chip formation in metal cutting.- Using dynamical
system tools in Matlab.- Formation and instabilities of coherent
structures in channel flows.- Applications of smooth orthogonal
factorizations of matrices.- Continuation of codimension-2
equilibrium bifurcations in CONTENT.February 2000, Approximately
496 pp 134 figs Hardcover
The IMA Volumes in Mathematics and its Applications Vol. 119
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Last Updated: 6th February 2000.