Publication is planned for April 2003 | Hardback | 600 pages
11 line diagrams 3 tables | ISBN: 0-521-82267-X
This book provides a thorough introduction to the theory of
classical integrable systems, discussing the various approaches
to the subject and explaining their interrelations. The book
begins by introducing the central ideas of the theory of
integrable systems, based on Lax representations, loop groups and
Riemann surfaces. These ideas are then illustrated with detailed
studies of model systems. The connection between isomonodromic
deformation and integrability is discussed, and integrable field
theories are covered in detail. The KP, KdV and Toda hierarchies
are explained using the notion of Grassmannian, vertex operators
and pseudo-differential operators. A chapter is devoted to the
inverse scattering method and three complementary chapters cover
the necessary mathematical tools from symplectic geometry,
Riemann surfaces and Lie algebras. The book contains many worked
examples and is suitable for use as a textbook on graduate
courses. It also provides a comprehensive reference for
researchers already working in the field.
Contents
1. Introduction; 2. Integrable dynamical systems; 3. Synopsis of
integrable systems; 4. Algebraic methods; 5. Analytical methods;
6. The closed Toda chain; 7. The Calogero-Moser model; 8.
Isomonodromic deformations; 9. Grassmannian and integrable
hierarchies; 10. The KP hierarchy; 11. The KdV hierarchy; 12. The
Toda field Theories; 13. Classical inverse scattering method; 14.
Symplectic geometry; 15. Riemann surfaces; 16. Lie algebras.
Publication is planned for August 2003 | Hardback | 500 pages
10 line diagrams 138 exercises |
ISBN: 0-521-80686-0
Combinatorica, an extension to the popular computer algebra
system MathematicaR, is the most comprehensive software available
for teaching and research applications of discrete mathematics,
particularly combinatorics and graph theory. This book is the
definitive reference/user’s guide to Combinatorica, with
examples of all 450 Combinatorica functions in action, along with
the associated mathematical and algorithmic theory. The authors
cover classical and advanced topics on the most important
combinatorial objects: permutations, subsets, partitions, and
Young tableaux, as well as all important areas of graph theory:
graph construction operations, invariants, embeddings, and
algorithmic graph theory. In addition to being a research tool,
Combinatorica makes discrete mathematics accessible in new and
exciting ways to a wide variety of people, by encouraging
computational experimentation and visualization. The book
contains no formal proofs, but enough discussion to understand
and appreciate all the algorithms and theorems it contains.
Contents
1. Combinatorica: an explorer’s guide: 2. Permutations and
combinations; 3. Algebraic combinatorics; 4. Partitions,
compositions, and Young tableaux; 5. Graph representation; 6.
Generating graphs; 7. Properties of graphs; 8 Algorithmic graph
theory.
Publication is planned for April 2003 | Hardback | 250 pages
18 line diagrams | ISBN: 0-521-81828-1
Computational simulation of scientific phenomena
and engineering problems often depend on
solving linear systems with a large number
of unknowns. This book gives an insight into
the construction of iterative methods for
the solution of such systems and helps the
reader to select the best solver for given
classes of problems. The emphasis is on the
main ideas and how they have led to efficient
solvers such as CG, GMRES, and Bi-CGSTAB.
The book also explains the main concepts
behind the construction of preconditioners.
The reader is encouraged to build their own
experience by analysing numerous examples
that illustrate how best to exploit the methods.
The book also hints at many open problems
and as such it will appeal to established
researchers. There are many exercises that
motivate the material and help students to
understand the essential steps in the analysis
and construction of algorithms.
Contents
1. Introduction; 2. Mathematical preliminaries; 3. Basic
iteration methods; 4. Construction of approximate solutions; 5.
The conjugate gradients method; 6. GMRES and MINRES; 7. Bi-conjugate
gradients; 8. How serious is irregular convergence?; 9. BI-CGSTAB;
10. Solution of singular systems; 11. Solution of f(A)x = b with
Krylov subspace information; 12. Miscellaneous; 13.
Preconditioning
Publication is planned for May 2003 | Hardback | 224 pages |
ISBN: 0-521-82585-7
Probability theory has recently become more important as an area
of study and research. However, it is often the case that
graduate classes are quite small and students will need to learn
independently. This set of exercises can be used for classroom
teaching or independent study and will help students reach the
level where they can begin to tackle current research. The book
is based on the authors’ teaching at Paris, where probability
is extremely strong. There are outline answers to all the
problems, and numerous references to the literature.
Contents
1. Measure theory and probability; 2. Independence and
conditioning; 3. Gaussian variables; 4. Distributional
computations; 5. Convergence of random variables; 6. Random
processes.
Publication is planned for July 2003 | Hardback | 520 pages 50
tables 125 exercises 119 figures |
ISBN: 0-521-80689-5
Publication is planned for July 2003 | Paperback | 520 pages 50
tables 125 exercises 119 figures |
ISBN: 0-521-53441-0
This textbook presents in a unified manner the fundamentals of
both continuous and discrete versions of the Fourier and Laplace
transforms. These transforms play an important role in the
analysis of all kinds of physical phenomena. As a link between
the various applications of these transforms the authors use the
theory of signals and systems, as well as the theory of ordinary
and partial differential equations. The book is divided into four
major parts: periodic functions and Fourier series, non-periodic
functions and the Fourier integral, switched-on signals and the
Laplace transform, and finally the discrete versions of these
transforms, in particular the Discrete Fourier Transform together
with its fast implementation, and the z-transform. This textbook
is designed for self-study. It includes many worked examples,
together with more than 120 exercises, and will be of great value
to undergraduates and graduate students in applied mathematics,
electrical engineering, physics and computer science.
Contents
Preface; Introduction; 1. Signals and systems; 2. Mathematical
prerequisites; 3. Fourier series: definition and properties; 4.
The fundamental theorem of Fourier series; 5. Applications of
Fourier series; 6. Fourier integrals: definition and properties;
7. The fundamental theorem of the Fourier integral; 8.
Distributions; 9. The Fourier transform of distributions; 10.
Applications of the Fourier integral; 11. Complex functions; 12.
The Laplace transform: definition and properties; 13. Further
properties, distributions, and the fundamental theorem; 14.
Applications of the Laplace transform; 15. Sampling of continuous-time
signals; 16. The discrete Fourier transform; 17. The fast Fourier
transform; 18. The z-transform; 19. Applications of discrete
transforms.