Acta Numerica is a high-impact factor, prestigious annual publication containing invited surveys by leading researchers in numerical mathematics and scientific computing. The surveys present overviews of developments in their area and provide techniques and analyses. It is essential reading for all practitioners and researchers. This volume was originally published in 2005.

Acta Numerica surveys annually the most important developments in numerical mathematics and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important and timely developments in a manner accessible to the wider community of professionals with an interest in scientific computing. Acta Numerica volumes have proved to be a valuable tool not only for researchers and professionals wishing to develop their understanding of numerical techniques and algorithms and follow new developments, but also as an advanced teaching aid at colleges and universities. Many of the original articles have been used as the prime resource for graduate courses. This particular volume was originally published in 2002.

Acta Numerica surveys annually the most important developments in numerical mathematics and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important and timely developments in a manner accessible to the wider community of professionals with an interest in scientific computing. Acta Numerica volumes have proved to be a valuable tool not only for researchers and professionals wishing to develop their understanding of numerical techniques and algorithms and follow new developments, but also as an advanced teaching aid at colleges and universities. Many of the original articles have been used as the prime resource for graduate courses. This particular volume was originally published in 2003.

Acta Numerica is a high-impact factor, prestigious annual publication containing invited surveys by leading researchers in numerical mathematics and scientific computing. The surveys present overviews of developments in their area and provide techniques and analyses. It is essential reading for all practitioners and researchers. This volume was originally published in 2006.

Acta Numerica is a high-impact factor, prestigious annual publication containing invited surveys by leading researchers in numerical mathematics and scientific computing. The surveys present overviews of developments in their area and provide techniques and analyses. It is essential reading for practitioners and researchers. This volume was originally published in 2007.

'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

This is a completely up-to-date compendium of Fortran algorithms for numerical mathematics, including many sophisticated algorithms which are not available elsewhere. All have been extensively field-tested and cover methods for solving nonlinear equations, the method of Laguerre for solving algebraic equations, conjugating gradients for solving linear systems of equations, and the McKee algorithm for solving special systems of symmetric equations. The real, practical algorithms provided make the book indispensable for applied scientists working in all areas of research. The CD contains Fortran programs for the algorithms given in the text.

Advances in the field of signal processing, nonlinear dynamics, statistics, and optimization theory, combined with marked improvement in instrumenta tion and development of computers systems, have made it possible to apply the power of mathematics to the task of understanding the human brain. This verita ble revolution already has resulted in widespread availability of high resolution neuroimaging devices in clinical as well as research settings. Breakthroughs in functional imaging are not far behind. Mathematical tech niques developed for the study of complex nonlinear systems and chaos already are being used to explore the complex nonlinear dynamics of human brain phys iology. Global optimization is being applied to data mining expeditions in an effort to find knowledge in the vast amount of information being generated by neuroimaging and neurophysiological investigations. These breakthroughs in the ability to obtain, store and analyze large datasets offer, for the first time, exciting opportunities to explore the mechanisms underlying normal brain func tion as well as the affects of diseases such as epilepsy, sleep disorders, movement disorders, and cognitive disorders that affect millions of people every year. Ap plication of these powerful tools to the study of the human brain requires, by necessity, collaboration among scientists, engineers, neurobiologists and clini cians. Each discipline brings to the table unique knowledge, unique approaches to problem solving, and a unique language.

Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences. This introductory textbook fills a gap in the literature, offering a concise, integrated presentation of methods, applications, software tools, and hands-on projects. Included are numerous exercises, problems, and Mathematica/Matlab-based programming projects. The emphasis is on interdisciplinary applications to serve a broad audience of advanced undergraduate/graduate students with different backgrounds in applied mathematics, engineering, physics/geophysics. The work may also serve as a self-study reference for researchers and practitioners seeking a quick introduction to the subject for their research.

Acta Numerica is a high-impact factor, prestigious annual publication containing invited surveys by leading researchers in numerical mathematics and scientific computing. The surveys present overviews of developments in their area and provide techniques and analyses. It is essential reading for practitioners and researchers. It is essential reading for all practitioners and researchers.

The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.

This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide 'state of the art' techniques and analysis.

This book is a thoroughly revised result, updated to mid-1995, of the NATO Advanced Research Workshop on "Intelligent Learning Environments: the case of geometry", held in Grenoble, France, November 13-16, 1989. The main aim of the workshop was to foster exchanges among researchers who were concerned with the design of intelligent learning environments for geometry. The problem of student modelling was chosen as a central theme of the workshop, insofar as geometry cannot be reduced to procedural knowledge and because the significance of its complexity makes it of interest for intelligent tutoring system (ITS) development. The workshop centred around the following themes: modelling the knowledge domain, modelling student knowledge, design ing "didactic interaction", and learner control. This book contains revised versions of the papers presented at the workshop. All of the chapters that follow have been written by participants at the workshop. Each formed the basis for a scheduled presentation and discussion. Many are suggestive of research directions that will be carried out in the future. There are four main issues running through the papers presented in this book: * knowledge about geometry is not knowledge about the real world, and materialization of geometrical objects implies a reification of geometry which is amplified in the case of its implementation in a computer, since objects can be manipulated directly and relations are the results of actions (Laborde, Schumann). This aspect is well exemplified by research projects focusing on the design of geometric microworlds (Guin, Laborde).

This book constitutes the thoroughly refereed post workshop proceedings of the 10th International Workshop on Approximation and Online Algorithms, WAOA 2012, held in Ljubljana, Slovenia, in September 2012 as part of the ALGO 2012 conference event. The 22 revised full papers presented together with invited talk were carefully reviewed and selected from 60 submissions. The workshop covered areas such as geometric problems, online algorithms, scheduling, algorithmic game theory, and approximation algorithms.

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers. Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design.

The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.

The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

This collection is dedicated to the 70th jubilee of Yu. N. Savchenko, and presents experimental, theoretical, and numerical investigations written by an international group of well-known authors. The contributions solve very important problems of the high-speed hydrodynamics, such as supersonic motion in water, drag diminishing, dynamics and stability of supercavitating vehicles, water entry and hydrodynamic performances of hydrofoils, ventilated cavities after a disc and under the ship bottom.
The book is written for researches, scientists, engineers, and students interested in problems of hydromechanics."

This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.

This is a very lucid introduction to spectral methods emphasizing the mathematical aspects of the theory rather than the many applications in numerical analysis and the engineering sciences. The first part is a fairly complete introduction to Fourier series while the second emphasizes polynomial expansion methods like Chebyshev's. The author gives rigorous proofs of fundamental results related to one-dimensional advection and diffusions equations. The book addresses students as well as practitioners of numerical analysis.

The need for a rigorous mathematical theory for Differential-Algebraic Equations (DAEs) has its roots in the widespread applications of controlled dynamical systems, especially in mechanical and electrical engineering. Due to the strong relation to (ordinary) differential equations, the literature for DAEs mainly started out from introductory textbooks. As such, the present monograph is new in the sense that it comprises survey articles on various fields of DAEs, providing reviews, presentations of the current state of research and new concepts in - Controllability for linear DAEs - Port-Hamiltonian differential-algebraic systems - Robustness of DAEs - Solution concepts for DAEs - DAEs in circuit modeling. The results in the individual chapters are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available in from the author's Web site. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder-Mead search algorithm.