Publication is planned for Oct. 2003 | Hardback
| 240 pages |
ISBN: 0-521-80157-5
Cambridge Tracts in Mathematics vol.154
Finite arrangements of convex bodies were
intensively
investigated in the second half of the 20th
century. Connections
to many other subjects were made, including
crystallography, the
local theory of Banach spaces, and combinatorial
optimisation.
This book, the first one dedicated solely
to the subject,
provides an in-depth state-of-the-art discussion
of the theory of
finite packings and coverings by convex bodies.
It contains
various new results and arguments, besides
collecting those
scattered around in the literature, and provides
a comprehensive
treatment of problems whose interplay was
not clearly understood
before. In order to make the material more
accessible, each
chapter is essentially independent, and two-dimensional
and
higher-dimensional arrangements are discussed
separately.
Arrangements of congruent convex bodies in
Euclidean space are
discussed, and the density of finite packing
and covering by
balls in Euclidean, spherical and hyperbolic
spaces is considered.
Publication is planned for November 2003
| Paperback | 600
pages 102 line diagrams 3 half-tones 9 tables
81 exercises | ISBN:
0-521-52541-1
Hydrodynamic stability is of fundamental
importance in fluid
mechanics and is concerned with the problem
of transition from
laminar to turbulent flow. Drazin and Reid
emphasise throughout
the ideas involved, the physical mechanisms,
the methods used,
and the results obtained, and, wherever possible,
relate the
theory to both experimental and numerical
results. A distinctive
feature of the book is the large number of
problems it contains.
These problems not only provide exercises
for students but also
provide many additional results in a concise
form. This new
edition of this celebrated introduction differs
principally by
the inclusion of detailed solutions for those
exercises, and by
the addition of a Foreword by Professor J.
W. Miles.
Reviews
‘The work is undeniably of high scholarship,
consummate
accuracy and penetrating insight … All specialists
in stability
theory will be happy that two such authorities
have found the
time, and spared so few pains, to produce
a work of such
excellence.’ Nature
Contents
Foreword; Preface; 1. Introduction; 2. Thermal
instability; 3.
Centrifugal instability; 4. Parallel shear
flows; 5. Uniform
asymptotic approximations; 6. Additional
topics in linear
stability theory; 7. Nonlinear stability;
Appendix A. A class of
generalized Airy functions; Appendix B. Solutions
to the
problems; Bibliography; Motion picture index;
Subject index.
November 2003 | Hardback | 434 pages 115
exercises 168 figures
| ISBN: 0-521-82612-8
Advanced Dynamics is a broad and detailed
description of the
analytical tools of dynamics as used in mechanical
and aerospace
engineering. The strengths and weaknesses
of various approaches
are discussed, and particular emphasis is
placed on learning
through problem solving. The book begins
with a thorough review
of vectorial dynamics and goes on to cover
Lagrange’s and
Hamilton’s equations as well as less familiar
topics such as
impulse response, and differential forms
and integrability.
Techniques are described that provide a considerable
improvement
in computational efficiency over the standard
classical methods,
especially when applied to complex dynamical
systems. The
treatment of numerical analysis includes
discussions of numerical
stability and constraint stabilization. Many
worked examples and
homework problems are provided. The book
is intended for use on
graduate courses on dynamics, and will also
appeal to researchers
in mechanical and aerospace engineering.
Contents
1. Introduction to particle dynamics; 2.
Lagrange’s and
Hamilton’s equations; 3. Kinematics and
dynamics of a rigid
body; 4. Equations of motion: differential
approach; 5. Equations
of motion: integral approach; 6. Introduction
to numerical
methods; Appendix.
November 2003 | Hardback | 390 pages 100
line diagrams | ISBN:
0-521-82446-X
Association schemes are of interest to both
mathematicians and
statisticians and this book is written with
both audiences in
mind. For statisticians, it shows how to
construct designs for
experiments in blocks, how to compare such
designs, and how to
analyse data from them. The reader is only
assumed to know very
basic abstract algebra. For pure mathematicians,
it tells why
association schemes are important and develops
the theory to the
level of some recent research. This book
has arisen from a course
successfully taught by the author and as
such the material is
thoroughly class-tested. There are a great
number of examples and
exercises that will increase the book’s
appeal to both graduate
students and their instructors. It is ideal
for those coming
either from pure mathematics or statistics
backgrounds who wish
to bring their understanding of association
schemes up to the
current state of the art.
Contents
1. Association schemes; 2. The Bose-Mesner
algebra; 3. Combining
association schemes; 4. Incomplete-block
designs; 5. Partial
balance; 6. Families of partitions; 7. Designs
for structured
sets; 8. Groups; 9. Posets; 10. Subschemes,
quotients, duals and
products; 11. Association schemes on the
same set; 12. Where
next?; 13. History and references.