Series: Cambridge Library Collection - Mathematics
26 Paperback books (ISBN-13: 9781108003179)
Details
Page extent: 12657 pages
Size: 244 x 170 mm
Weight: 34 kg
Augustin-Louis, Baron Cauchy (1789*1857) was the pre-eminent French mathematician
of the nineteenth century. He began his career as a military engineer during
the Napoleonic Wars, but even then was publishing significant mathematical
papers, and was persuaded by Lagrange and Laplace to devote himself entirely
to mathematics. His greatest contributions are considered to be the Cours
dfanalyse de lfEcole Royale Polytechnique (1821), Resume des lecons sur
le calcul infinitesimal (1823) and Lecons sur les applications du calcul
infinitesimal a la geometrie (1826*8), and his pioneering work encompassed
a huge range of topics, most significantly real analysis, the theory of
functions of a complex variable, and theoretical mechanics.
Twenty-six volumes of his collected papers were published between 1882 and 1958. The first series (volumes 1-12) consists of
papers published by the Academie des Sciences de lfInstitut de France;
the second series (volumes 13-26) of papers published elsewhere.
Contents
The complete collection of Oeuvres completes.
1
Series: Cambridge Monographs on Applied and Computational Mathematics (No. 17)
Paperback (ISBN-13: 9780521131018)
Page extent: 348 pages
Size: 229 x 152 mm
Weight: 0.51 kg
Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book
gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial
basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of
scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of
partial differential equations. It then leads the reader from basic properties to the current state of research, addressing
all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient
implementation. Each chapter ends with a section giving information on the historical background and hints for further
reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it
can be used to support courses in computer-aided geometric design, and meshless methods for partial differential equations.
* A complete survey on multivariate scattered data approximation * Covers
theory behind, and implementation of, techniques * Contains complete proofs
of all theorems and covers several illustrating examples
1. Applications and motivations; 2. Hear spaces and multivariate polynomials; 3. Local polynomial reproduction; 4. Moving
least squares; 5. Auxiliary tools from analysis and measure theory; 6. Positive definite functions; 7. Completely monotine
functions; 8. Conditionally positive definite functions; 9. Compactly supported functions; 10. Native spaces; 11. Error
estimates for radial basis function interpolation; 12. Stability; 13. Optimal recovery; 14. Data structures; 15. Numerical
methods; 16. Generalised interpolation; 17. Interpolation on spheres and other manifolds.
Series: Encyclopedia of Mathematics and its Applications (No. 133)
Hardback (ISBN-13: 9780521761352)
155 b/w illus. 70 tables 240 exercises
Page extent: 700 pages
Size: 234 x 156 mm
Fundamental arithmetic operations support virtually all of the engineering,
scientific, and financial computations required for practical applications,
from cryptography, to financial planning, to rocket science. This comprehensive
reference provides researchers with the thorough understanding of number
representations that is a necessary foundation for designing efficient
arithmetic algorithms. Using the elementary foundations of radix number
systems as a basis for arithmetic, the authors develop and compare alternative
algorithms for the fundamental operations of addition, multiplication,
division, and square root with precisely defined roundings. Various finite
precision number systems are investigated, with the focus on comparative
analysis of practically efficient algorithms for closed arithmetic operations
over these systems. Each chapter begins with an introduction to its contents
and ends with bibliographic notes and an extensive bibliography. The book
may also be used for graduate teaching: problems and exercises are scattered
throughout the text and a solutions manual is available for instructors.
* Will appeal to any scientist wishing to understand the hardware used
for practical number crunching * Provides a solid theoretical foundation
for the subject of practical (finite precision) computation * A comprehensive
reference for
specialists and suitable for graduate teaching
Preface; 1. Radix polynomial representations; 2. Base and digit set conversion; 3. Addition; 4. Multiplication; 5. Division;
6. Square root; 7. Floating point number systems; 8. Modular arithmetic and residue number systems; 9. Rational arithmetic;
Author index; Index.
Cours specialises 16 (2009), 161 pages
Ces notes de cours constituent une introduction mathematique a l'etude de modeles probabilistes sur reseau, issus de la
physique statistique. A travers les exemples de la percolation et du modele d'Ising, nous abordons les phenomenes de
changements de phases et nous introduisons un certain nombre de techniques
classiques. Nous presentons egalement * c'est l'un des buts principaux
de ce cours * des resultats recents, dus a Stanislas Smirnov concernant
l'invariance conforme de ces deux modeles en dimension deux.
Mots-clefs : Physique statistique, mecanique statistique, probabilites, transitions de phases, percolation, modele d'Ising,
modele de Potts, invariance conforme
Abstract:
Ising model and percolation
These lecture notes provide a mathematical introduction to the study of random lattice-based models from statistical physics.
Via the study of percolation and of the Ising model, we introduce the notion of phase transitions and we describe some
classical techniques. One of the main goals of these notes is also to present recent results of Stanislav Smirnov concerning
the conformal invariance of these models in two-dimensional space.
Keywords: Statistical physics, statistical mecanics, probability theory, phase transitions, percolation, Ising model, Potts
model, conformal invariance
ISBN : 978-2-85629-276-1
ISBN: 978-0-470-18094-5
Hardcover
445 pages
April 2009
New Bayesian approach helps you solve tough problems in signal processing with ease
Signal processing is based on this fundamental concept*the extraction of critical information from noisy, uncertain data.
Most techniques rely on underlying Gaussian assumptions for a solution, but what happens when these assumptions are
erroneous* Bayesian techniques circumvent this limitation by offering a completely different approach that can easily
incorporate non-Gaussian and nonlinear processes along with all of the usual methods currently available.
This text enables readers to fully exploit the many advantages of the "Bayesian approach" to model-based signal processing.
It clearly demonstrates the features of this powerful approach compared to the pure statistical methods found in other texts.
Readers will discover how easily and effectively the Bayesian approach, coupled with the hierarchy of physics-based models
developed throughout, can be applied to signal processing problems that previously seemed unsolvable.
Bayesian Signal Processing features the latest generation of processors (particle filters) that have been enabled by the
advent of high-speed/high-throughput computers. The Bayesian approach is uniformly developed in this book's algorithms,
examples, applications, and case studies. Throughout this book, the emphasis
is on nonlinear/non-Gaussian problems; however, some classical techniques
(e.g. Kalman filters, unscented Kalman filters, Gaussian sums, grid-based
filters, et al) are
included to enable readers familiar with those methods to draw parallels between the two approaches.
Special features include:
Unified Bayesian treatment starting from the basics (Bayes's rule) to the more advanced (Monte Carlo sampling), evolving to
the next-generation techniques (sequential Monte Carlo sampling)
Incorporates "classical" Kalman filtering for linear, linearized, and nonlinear systems; "modern" unscented Kalman filters;
and the "next-generation" Bayesian particle filters
Examples illustrate how theory can be applied directly to a variety of processing problems
Case studies demonstrate how the Bayesian approach solves real-world problems in practice
MATLABR notes at the end of each chapter help readers solve complex problems
using readily available software commands and point out software packages
available
Problem sets test readers' knowledge and help them put their new skills into practice
The basic Bayesian approach is emphasized throughout this text in order to enable the processor to rethink the approach to
formulating and solving signal processing problems from the Bayesian perspective. This text brings readers from the classical
methods of model-based signal processing to the next generation of processors
that will clearly dominate the future of signal processing for years to
come. With its many illustrations demonstrating the applicability of the
Bayesian approach to real-world problems in signal processing, this text
is essential for all students, scientists, and engineers who investigate
and
apply signal processing to their everyday problems.
ISBN: 978-0-470-82454-2
Hardcover
320 pages
April 2010
Bayesian methods are a powerful tool in many areas of science and engineering, especially statistical physics, medical
sciences, electrical engineering, and information sciences. They are also ideal for civil engineering applications, given the
numerous types of modeling and parametric uncertainty in civil engineering problems. For example, earthquake ground motion
cannot be predetermined at the structural design stage. Complete wind pressure profiles are difficult to measure under
operating conditions. Material properties can be difficult to determine to a very precise level * especially concrete, rock,
and soil. For air quality prediction, it is difficult to measure the hourly/daily pollutants generated by cars and factories
within the area of concern. It is also difficult to obtain the updated air quality information of the surrounding cities.
Furthermore, the meteorological conditions of the day for prediction are also uncertain. These are just some of the civil
engineering examples to which Bayesian probabilistic methods are applicable.
Familiarizes readers with the latest developments in the field
Includes identification problems for both dynamic and static systems
Addresses challenging civil engineering problems such as modal/model updating
Presents methods applicable to mechanical and aerospace engineering
Gives engineers and engineering students a concrete sense of implementation
Covers real-world case studies in civil engineering and beyond, such as:
structural health monitoring
seismic attenuation
finite-element model updating
hydraulic jump
artificial neural network for damage detection
air quality prediction
Includes other insightful daily-life examples
Companion website with MATLAB code downloads for independent practice
Written by a leading expert in the use of Bayesian methods for civil engineering problems
This book is ideal for researchers and graduate students in civil and mechanical engineering or applied probability and
statistics. Practicing engineers interested in the application of statistical methods to solve engineering problems will also
find this to be a valuable text.