Publication is planned for June 2003 | Paperback
| 664 pages
160 line diagrams 350 exercises | ISBN: 0-521-53429-1
Complex variables provide powerful methods
for attacking problems
that can be very difficult to solve in any
other way, and it is
the aim of this book to provide a thorough
grounding in these
methods and their application. Part I of
this text provides an
introduction to the subject, including analytic
functions,
integration, series, and residue calculus
and also includes
transform methods, ODEs in the complex plane,
and numerical
methods. Part II contains conformal mappings,
asymptotic
expansions, and the study of Riemann?Hilbert
problems. The
authors provide an extensive array of applications,
illustrative
examples and homework exercises. This new
edition has been
improved throughout and is ideal for use
in undergraduate and
introductory graduate level courses in complex
variables.
Reviews
‘… an excellent text, and one of the most
complete and well-written
books on complex variables I have seen …
The index is nicely
composed, complete, and accurate … useful
as a reference … I
highly recommend it to anyone interested
in the subject and have
placed it prominently upon my reference bookshelf.’
Duwayne
Anderson, Optics and Photonics News
‘… an excellent text, and one of the most
complete and well-written
books on complex variables I have seen …
I highly recommend it
to anyone interested in the subject…’.
Optics and Photonics
News
Contents
Part I: 1. Complex numbers and elementary
functions; 2. Analytic
functions and integration; 3. Sequences,
series and singularities
of complex functions; 4. Residue calculus
and applications of
contour integration; Part II: 5. Conformal
mapping and
applications; 6. Asymptotic evaluation of
integrals; 7.
Riemann?Hilbert problems; Index.
Publication is planned for November 2003
| Hardback | 318
pages 75 line diagrams | ISBN: 0-521-82758-2
The study of algorithmic graph theory and
structured families of
graphs is an important branch of discrete
mathematics. It finds
numerous applications, from data transmission
through networks to
efficiently scheduling aircraft and crews,
as well as
contributing to breakthroughs in genetic
analysis and studies of
the brain. Especially important have been
the theory and
applications of new intersection graph models
such as
generalizations of permutation graphs and
interval graphs. One of
these is the study of tolerance graphs and
tolerance orders. This
book contains the first thorough study of
tolerance graphs and
related topics, indeed the authors have included
proofs of major
results previously unpublished in book form.
It will act as a
springboard for researchers, and especially
graduate students, to
pursue new directions of investigation. With
many examples and
exercises it is also suitable for use as
the text for a graduate
course in graph theory.
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Contents
1. Introduction; 2. Early work on tolerance
graphs; 3. Trees,
cotrees and bipartite graphs; 4. Interval
probe graphs; 5.
Bitolerance graphs and ordered sets; 6. Unit
and 50% tolerance
graphs; 7. Comparability and invariance results;
8. Bounded
bitolerance recognition; 9. Algorithms on
tolerance graphs; 10.
The hierarchy of bitolerance orders; 11.
Tolerance models on
trees; 12. Phi-tolerance models; 13. Directed
tolerance graphs;
14. Open questions and further directions.
Publication is planned for October 2003 |
Paperback | 250
pages | ISBN: 0-521-53437-2
In recent years there have been important
and far reaching
developments in the study of nonlinear waves
and a class of
nonlinear wave equations which arise frequently
in applications.
The wide interest in this field comes from
the understanding of
special waves called 壮olitons・and the associated
development
of a method of solution to a class of nonlinear
wave equations
termed the inverse scattering transform (IST).
Before these
developments, very little was known about
the solutions to such
壮oliton equations・ The IST technique applies
to both
continuous and discrete nonlinear Schringer
equations of
scalar and vector type. Also included is
the IST for the Toda
lattice and nonlinear ladder network, which
are well-known
discrete systems. This book presents the
detailed mathematical
analysis of the scattering theory; soliton
solutions are obtained
and soliton interactions, both scalar and
vector, are analyzed.
Much of the material is not available in
the previously-published
literature.
Publication is planned for October 2003 |
Hardback | 225 pages
40 line diagrams | ISBN: 0-521-82679-9
Publication is planned for October 2003 |
Paperback | 225 pages
40 line diagrams | ISBN: 0-521-53410-0
Niels Lauritzen’s approach to teaching abstract
algebra is
based on an extensive use of examples, applications
and exercises.
As the title suggests the philosophy is to
develop an abstract
subject on concrete and more easily comprehensible
foundations.
The book is based on extensive teaching experience
at Aarhus and
the author’s clarity and attention to detail
will be
appreciated as an aid to curricula the world
over. The book
contains novel applications, for example
RSA encoding. It also
features a treatment of Grobner bases at
an undergraduate level.
This is the first time that this important
subject has been made
accessible at this level.
Publication is planned for January 2004 |
Paperback | 654
pages 120 line diagrams | ISBN: 0-521-53927-7
This book provides a working knowledge of
those parts of exterior
differential forms, differential geometry,
algebraic and
differential topology, Lie groups, vector
bundles and Chern forms
that are essential for a deeper understanding
of both classical
and modern physics and engineering. Included
are discussions of
analytical and fluid dynamics, electromagnetism
(in flat and
curved space), thermodynamics, the deformation
tensors of
elasticity, soap films, special and general
relativity, the Dirac
operator and spinors, and gauge fields, including
Yang-Mills, the
Aharonov-Bohm effect, Berry phase, and instanton
winding numbers,
quarks, and quark model for mesons. Before
discussing abstract
notions of differential geometry, geometric
intuition is
developed through a rather extensive introduction
to the study of
surfaces in ordinary space; consequently,
the book should be of
interest also to mathematics students. Ideal
for graduate and
advanced undergraduate students of physics,
engineering and
mathematics as a course text or for self
study.
Contents
Preface; Part I. Manifolds, Tensors and Exterior
Forms: 1.
Manifolds and vector fields; 2. Tensors and
exterior forms; 3.
Integration of differential forms; 4. The
Lie derivative; 5. The
Poincare lemma and potentials; 6. Holonomic
and non-holonomic
constraints; Part II. Geometry and Topology:
7. R3 and Minkowski
space; 8. The geometry of surfaces in R3;
9. Covariant
differentiation and curvature; 10. Geodesics;
11. Relativity,
tensors, and curvature; 12. Curvature and
topology: Synge’s
theorem; 13. Betti numbers and de Rham’s
theorem; 14. Harmonic
forms; Part III. Lie Groups, Bundles and
Chern Forms: 15. Lie
groups; 16. Vector bundles in geometry and
physics; 17. Fiber
bundles, Gauss-Bonnet, and topological quantization;
18.
Connections and associated bundles; 19. The
Dirac equation; 20.
Yang-Mills fields; 21. Betti numbers and
covering spaces; 22.
Chern forms and homotopy groups; Appendix
A. Forms in continuum
mechanics; Appendix B. Harmonic chains and
Kirchhoff’s circuit
laws; Appendix C. Symmetries, quarks, and
meson masses; Appendix
D. Representations and hyperelastic bodies;
Appendix E: Orbits
and Morse-Bott theory in compact Lie groups.