Publication is planned for May 2004 | Hardback
| 224 pages |
ISBN: 0-521-64121-7
Harmonic mappings in the plane are univalent
complex-valued
harmonic functions of a complex variable.
Conformal mappings are
a special case where the real and imaginary
parts are conjugate
harmonic functions, satisfying the Cauchy-Riemann
equations.
Harmonic mappings were studied classically
by differential
geometers because they provide isothermal
(or conformal)
parameters for minimal surfaces. More recently
they have been
actively investigated by complex analysts
as generalizations of
univalent analytic functions, or conformal
mappings. Many
classical results of geometric function theory
extend to harmonic
mappings, but basic questions remain unresolved.
This book is the
first comprehensive account of the theory
of planar harmonic
mappings, treating both the generalizations
of univalent analytic
functions and the connections with minimal
surfaces. Essentially
self-contained, the book contains background
material in complex
analysis and a full development of the classical
theory of
minimal surfaces, including the Weierstrass-Enneper
representation. It is designed to introduce
non-specialists to a
beautiful area of complex analysis and geometry.
Contents
1. Preliminaries; 2. Local properties of
harmonic mappings; 3.
Harmonic mappings onto convex regions; 4.
Harmonic self-mappings
of the disk; 5. Harmonic univalent functions;
6. Extremal
problems; 7. Mapping problems; 8. Additional
topics; 9. Minimal
surfaces; 10. Curvature of minimal surfaces;
Appendix; References.
April 2004 | Hardback | 228 pages | ISBN:
0-521-81151-1
April 2004 | Paperback | 228 pages | ISBN:
0-521-01012-8
A First Course in Combinatorial Optimization
is a text for a one-semester
introductory graduate-level course for students
of operations
research, mathematics, and computer science.
It is a self-contained
treatment of the subject, requiring only
some mathematical
maturity. Topics include: linear and integer
programming,
polytopes, matroids and matroid optimization,
shortest paths, and
network flows. Central to the exposition
is the polyhedral
viewpoint, which is the key principle underlying
the successful
integer-programming approach to combinatorial-optimization
problems. Another key unifying topic is matroids.
The author does
not dwell on data structures and implementation
details,
preferring to focus on the key mathematical
ideas that lead to
useful models and algorithms. Problems and
exercises are included
throughout as well as references for further
study.
Contents
Introduction; 0. Polytopes and linear programming;
1. Matroids
and the greedy algorithm; 2. Minimum-weight
dipaths; 3. Matroid
intersection; 4. Matching; 5. Flows and cuts;
6. Cutting planes;
7. Branch-&-bound; 8. Optimizing submodular
functions;
Appendix.
April 2004 | Hardback | 240 pages 39 line
diagrams 3 tables 46
exercises | ISBN: 0-521-83091-5
This textbook fills a gap in the existing
literature on general
relativity by providing the advanced student
with practical tools
for the computation of many physically interesting
quantities.
The context is provided by the mathematical
theory of black
holes, one of the most elegant, successful,
and relevant
applications of general relativity. Among
the topics discussed
are congruences of timelike and null geodesics,
the embedding of
spacelike, timelike, and null hypersurfaces
in spacetime, and the
Lagrangian and Hamiltonian formulations of
general relativity.
Although the book is self-contained, it is
not meant to serve as
an introduction to general relativity. Instead,
it is meant to
help the reader acquire advanced skills and
become a competent
researcher in relativity and gravitational
physics. The primary
readership consists of graduate students
in gravitational physics.
It will also be a useful reference for more
seasoned researchers
working in this field.
Contents
Preface; Notation and conventions; 1. Fundamentals;
2. Geodesic
congruences; 3. Hypersurfaces; 4. Langrangian
and Hamiltonian
formulation of general relativity; 5. Black
holes; Bibliography;
Index.