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Elsevier

Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Mathematica by Example

    • 3rd Edition
    • Martha L. Abell + 1 more
    • English
    This third edition of Mathematica by Example is completely compatible with recent Mathematica versions. Highly readable and informative, this volume is geared toward the beginning Mathematica user, and focuses on the most often used features of this powerful tool. The book covers popular applications of mathematics within different areas including calculus, linear algebra, ordinary differential equations, and partial differential equations.

  • Geometric Computations with Interval and New Robust Methods

    Applications in Computer Graphics, GIS and Computational Geometry
    • 1st Edition
    • H Ratschek + 1 more
    • English
    This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes them rounding error free.

  • Encyclopedia of General Topology

    • 1st Edition
    • K.P. Hart + 2 more
    • English
    This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.Key features:• More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms

  • Foundations of Complex Analysis in Non Locally Convex Spaces

    Function Theory without Convexity Condition
    • 1st Edition
    • Volume 193
    • A. Bayoumi
    • English
    All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field.Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and non linear cases, in function theory.Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material.The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem.Each chapter contains illustrative examples to help the student and researcher to enhance his knowledge of theory of functions.The new concept of Quasi-differentiabil... introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces. In fact it is different but much stronger than the Frechet one.The book is intended not only for Post-Graduate (M.Sc.& Ph.D.) students and researchers in Complex and Functional Analysis, but for all Scientists in various disciplines whom need nonlinear or non-convex analysis and holomorphy methods without convexity conditions to model and solve problems.bull; The book contains new generalized versions of:i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in real and complex cases, Hahn-Banach Theorems, Bolzano Theorem, Krein-Milman Theorem, Mean value Theorem for Definite Integral, and many others.ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's. bull; The book contains some applications in Operations research and non convex analysis as a consequence of the new concept p-Extreme points given by the author.bull; The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in F-spaces without convexity conditions. bull; The book contains a general new concept of differentiability stronger than the Frechet one. This implies a new Differentiable Calculus called Quasi-differential (or Bayoumi differential) Calculus. It is due to the author's discovery in 1995.bull; The book contains the theory of polynomials and Banach Stienhaus theorem in non convex spaces.

  • Solutions Manual for Elementary Linear Algebra

    • 3rd Edition
    • Stephen Andrilli + 1 more
    • English
    Selected solutions to problems.

  • Intelligent Systems for Information Processing: From Representation to Applications

    • 1st Edition
    • B. Bouchon-Meunier + 2 more
    • English
    Intelligent systems are required to enhance the capacities being made available to us by the internet and other computer based technologies. The theory necessary to help providing solutions to difficult problems in the construction of intelligent systems are discussed. In particular, attention is paid to situations in which the available information and data may be imprecise, uncertain, incomplete or of a linguistic nature. Various methodologies to manage such information are discussed. Among these are the probabilistic, possibilistic, fuzzy, logical, evidential and network-based frameworks.One purpose of the book is not to consider these methodologies separately, but rather to consider how they can be used cooperatively to better represent the multiplicity of modes of information. Topics in the book include representation of imperfect knowledge, fundamental issues in uncertainty, reasoning, information retrieval, learning and mining, as well as various applications.Key Features:• Tools for construction of intelligent systems• Contributions by world leading experts• Fundamental issues and applications• New technologies for web searching• Methods for modeling uncertain information• Future directions in web technologies• Transversal to methods and domains

  • Handbook of Mathematical Formulas and Integrals

    • 3rd Edition
    • Alan Jeffrey
    • English
    The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated sixth edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important reference works. The Third Edition has new chapters covering solutions of elliptic, parabolic and hyperbolic equations and qualitative properties of the heat and Laplace equation.

  • Recent Advances and Trends in Nonparametric Statistics

    • 1st Edition
    • M.G. Akritas + 1 more
    • English
    The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium.Key features:• algorithic approaches• wavelets and nonlinear smoothers• graphical methods and data mining• biostatistics and bioinformatics• bagging and boosting• support vector machines• resampling methods

  • Elementary Linear Algebra

    • 3rd Edition
    • Stephen Andrilli + 1 more
    • English
    The transition to upper-level math courses is often difficult because of the shift in emphasis from computation (in calculus) to abstraction and proof (in junior/senior courses). This book provides guidance with the reading and writing of short proofs, and incorporates a gradual increase in abstraction as the chapters progress. This helps students prepare to meet the challenges of future courses such as abstract algebra and elementary analysis.

  • Differential Equations, Dynamical Systems, and an Introduction to Chaos

    • 2nd Edition
    • Morris W. Hirsch + 2 more
    • English
    Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems. The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems. This book will be particularly useful to advanced students and practitioners in higher mathematics.

  • Many-Dimensional Modal Logics: Theory and Applications

    • 1st Edition
    • Volume 148
    • A. Kurucz + 3 more
    • English
    Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.Key Features:• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science• Written by internationally leading researchers in the field of pure and applied logic• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science• Numerous open problems for further research• Well illustrated with pictures and tables

  • Handbook of Algebra

    • 1st Edition
    • Volume 3
    • English

  • On Growth, Form and Computers

    • 1st Edition
    • Sanjeev Kumar + 1 more
    • English
    Conceived for both computer scientists and biologists alike, this collection of 22 essays highlights the important new role that computers play in developmental biology research. Essays show how through computer modeling, researchers gain further insight into developmental processes. Featured essays also cover their use in designing computer algorithms to tackle computer science problems in areas like neural network design, robot control, evolvable hardware, and more. Peter Bentley, noted for his prolific research on evolutionary computation, and Sanjeev Kumar head up a respected team to guide readers through these very complex and fascinating disciplines.

  • Mathematics for Multimedia

    • 1st Edition
    • Mladen Victor Wickerhauser
    • English
    Mathematics for Multimedia explains the mathematics behind multimedia applications such as compression, signal processing, and image/video processing. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills. More specifically, it focuses on when and why modern robust methods provide more accurate results. The topics are 'gems' chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication. The course Mathematics for Multimedia has been offered biennially at Washington University since 1997. It has proved popular with students from sophomores to beginning graduate students who seek an innovative course of rigorous contemporary mathematics with practical applications. For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student, there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. The book also describes and illustrates easy-to-use software for applying cutting-edge techniques. This book is aimed at a wide audience, including computer science and multimedia students and professors as well as those interested in employing mathematics in multimedia design and implementation.

  • Beyond Wavelets

    • 1st Edition
    • Volume 10
    • Grant Welland
    • English
    "Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago byMorlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering.Classica... wavelets have provided effective and efficient mathematical tools for time-frequency analysis which enhances and replaces the Fourier approach.However, with the current advances in science and technology, there is an immediate need to extend wavelet mathematical tools as well. "Beyond Wavelets" presents a list of ideas and mathematicalfoundati... for such extensions, including: continuous and digital ridgelets, brushlets, steerable wavelet packets, contourlets, eno-wavelets, spline-wavelet frames, and quasi-affine wavelets. Wavelet subband algorithms are extended to pyramidal directional and nonuniform filter banks. In addition, this volume includes amethod for tomographic reconstruction using a mechanical image model and a statistical study for independent adaptive signal representation.Inves... already familiar with wavelet methods from areas such as engineering, statistics, and mathematics will benefit by owning this volume.

  • Mathematical Models of Hysteresis and their Applications

    Second Edition
    • 1st Edition
    • Isaak D. Mayergoyz
    • English
    This new edition has been significantly revised and updated to reflect advances in the field since the publication of the first edition, such as the systematic experimental testing of Preisach models of hysteresis. The author has, however, retained the two most salient features of the original, the emphasis on the universal nature of mathematical models of hysteresis and their applicability to the description of hysteresis phenomena in various areas of science, technology and economics and its accessibility to a broad audience of researchers, engineers, and students.

  • Introductory Statistics for Engineering Experimentation

    • 1st Edition
    • Peter R. Nelson + 2 more
    • English
    The Accreditation Board for Engineering and Technology (ABET) introduced a criterion starting with their 1992-1993 site visits that "Students must demonstrate a knowledge of the application of statistics to engineering problems." Since most engineering curricula are filled with requirements in their own discipline, they generally do not have time for a traditional two semesters of probability and statistics. Attempts to condense that material into a single semester often results in so much time being spent on probability that the statistics useful for designing and analyzing engineering/scientif... experiments is never covered. In developing a one-semester course whose purpose was to introduce engineering/scientif... students to the most useful statistical methods, this book was created to satisfy those needs.

  • Advances in Computers

    Highly Dependable Software
    • 1st Edition
    • Volume 58
    • Marvin Zelkowitz
    • English
    Since 1960, Advances in Computers has chronicled the constantly shifting theories and methods of Information Technology which greatly shapes our lives today. Highly Dependable Software is the 58th volume in this Series. The seven chapters describe various approaches towards dependability: software development measurability, transformation oriented programming, Bounded Model Checking, GUI testing, history and lessons from software inspections, impact and problems related to errors in software, the evolution of the various security policies. This book would be an invaluable addition to any university course in computer technology, and an excellent reference tool for industrial practitioners.

  • Advances in Computers

    • 1st Edition
    • Volume 59
    • Marvin Zelkowitz
    • English
    Since 1960, Advances in Computers has chronicled the constantly shifting theories and methods of Information Technology which greatly shapes our lives today. This volume, the 59th in the series, presents two general themes. The first 4 papers discuss tool use in developing software - how groups work together to produce a product, and why the very industries that need them often do NOT adopt such tools. The fifth paper addresses a current hardware issue - cache coherence. As we build faster machines, a way to increase performance is to have multiple CPUs working on solving the same problem. This requires two or more CPUs to address the same memory at the same time. The cache coherence problem is how to allow both machines to access the same memory without "stepping on each others toes" so that memory gets lost or corrupted.

  • Numerical Methods for Fluids, Part 3

    • 1st Edition
    • Volume 9
    • P.G. Ciarlet
    • English

  • Measure Theory and Integration

    • 2nd Edition
    • G De Barra
    • English
    This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension and for which detailed solutions are provided.

  • Calculations for Molecular Biology and Biotechnology

    A Guide to Mathematics in the Laboratory
    • 1st Edition
    • Frank H. Stephenson
    • English
    Calculations in Molecular Biology and Biotechnology: A Guide to Mathematics in the Laboratory is the first comprehensive guide devoted exclusively to calculations encountered in the genetic engineering laboratory. Mathematics, as a vital component of the successful design and interpretation of basic research, is used daily in laboratory work. This guide, written for students, technicians, and scientists, provides example calculations for the most frequently confronted problems encountered in gene discovery and analysis. The text and sample calculations are written in an easy-to-follow format. It is the perfect laboratory companion for anyone working in DNA manipulation and analysis.

  • Non-Self-Adjoint Boundary Eigenvalue Problems

    • 1st Edition
    • Volume 192
    • R. Mennicken + 1 more
    • English
    This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalentto a first order system, the main techniques are developed for systems. Asymptotic fundamentalsystems are derived for a large class of systems of differential equations. Together with boundaryconditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.The contour integral method and estimates of the resolvent are used to prove expansion theorems.For Stone regular problems, not all functions are expandable, and again relatively easy verifiableconditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such asthe Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.Key features:• Expansion Theorems for Ordinary Differential Equations• Discusses Applications to Problems from Physics and Engineering• Thorough Investigation of Asymptotic Fundamental Matrices and Systems• Provides a Comprehensive Treatment• Uses the Contour Integral Method• Represents the Problems as Bounded Operators• Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions

  • Sobolev Spaces

    • 2nd Edition
    • Volume 140
    • Robert A. Adams + 1 more
    • English
    Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences. This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.

  • Digital Arithmetic

    • 1st Edition
    • MiloÅ¡ D. Ercegovac + 1 more
    • English
    Digital arithmetic plays an important role in the design of general-purpose digital processors and of embedded systems for signal processing, graphics, and communications. In spite of a mature body of knowledge in digital arithmetic, each new generation of processors or digital systems creates new arithmetic design problems. Designers, researchers, and graduate students will find solid solutions to these problems in this comprehensive, state-of-the-art exposition of digital arithmetic.Ercegovac and Lang, two of the field's leading experts, deliver a unified treatment of digital arithmetic, tying underlying theory to design practice in a technology-independe... manner. They consistently use an algorithmic approach in defining arithmetic operations, illustrate concepts with examples of designs at the logic level, and discuss cost/performance characteristics throughout. Students and practicing designers alike will find Digital Arithmetic a definitive reference and a consistent teaching tool for developing a deep understanding of the "arithmetic style" of algorithms and designs.

  • Advances in Computers

    Information Repositories
    • 1st Edition
    • Volume 57
    • Marvin Zelkowitz
    • English
    Advances in Computers remains at the forefront in presenting the new developments in the ever-changing field of information technology. Since 1960, Advances in Computers has chronicled the constantly shifting theories and methods of this technology that greatly shape our lives today. Information Repositories focuses on the use of large data repositories to store and retrieve information. This series is an invaluable addition to any university course in computer technology, as well as finding itself at home on the bookshelf of industrial practitioners.

  • Mathematical Modelling

    A Way of Life - ICTMA 11
    • 1st Edition
    • S J Lamon + 2 more
    • English
    Mathematical modelling is often spoken of as a way of life, referring to habits of mind and to dependence on the power of mathematics to describe, explain, predict and control real phenomena. This book aims to encourage teachers to provide opportunities for students to model a variety of real phenomena appropriately matched to students’ mathematical backgrounds and interests from early stages of mathematical education. Habits, misconceptions, and mindsets about mathematics can present obstacles to university students’ acceptance of a ‘‘models-and-modelli... perspective’’ at this stage of mathematics education. Without prior experience in building, interpreting and applying mathematical models, many students may never come to view and regard modelling as a way of life. The book records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003.

  • Special Volume: Foundations of Computational Mathematics

    • 1st Edition
    • Volume 11
    • Phillipe G. Ciarlet
    • English
    From geometric integration and its applications, and linear programming and condition numbers under the real number computational model, to chaos in finite difference schemes, these essays explore the foundational issues of computational mathematics.

  • Perturbation Theory for Matrix Equations

    • 1st Edition
    • Volume 9
    • M. Konstantinov + 3 more
    • English
    The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis.In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds.Key features:• The first book in this field• Can be used by a variety of specialists• Material is self-contained• Results can be used in the development of reliable computational algorithms• A large number of examples and graphical illustrations are given• Written by prominent specialists in the field

  • Handbook of the Geometry of Banach Spaces

    • 1st Edition
    • Volume 2
    • English

  • Mathematical Modelling in Education and Culture

    ICTMA 10
    • 1st Edition
    • Q-X Ye + 3 more
    • English
    The mathematical modelling movement in mathematics education at school and university level has been influencing curricula for about 25 years. Lecturers will find material to enhance their teaching and extracurricular activities and educators will find innovative ideas to inform their course design and focus their research, while students will find interesting problems to explore.

  • Numerical Analysis of Wavelet Methods

    • 1st Edition
    • Volume 32
    • A. Cohen
    • English
    Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are: 1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions. 2. Full treatment of the theoretical foundations that are crucial for the analysis of wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory. 3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.

  • Parallel Computational Fluid Dynamics 2002

    New Frontiers and Multi-Disciplinary Applications
    • 1st Edition
    • K. Matsuno + 4 more
    • English
    This volume is proceedings of the international conference of the Parallel Computational Fluid Dynamics 2002. In the volume, up-to-date information about numerical simulations of flows using parallel computers is given by leading researchers in this field. Special topics are "Grid Computing" and "Earth Simulator". Grid computing is now the most exciting topic in computer science. An invited paper on grid computing is presented in the volume. The Earth-Simulator is now the fastest computer in the world. Papers on flow-simulations using the Earth-Simulator are also included, as well as a thirty-two page special tutorial article on numerical optimization.

  • Statistics and Probability for Engineering Applications

    • 1st Edition
    • William DeCoursey
    • English
    Statistics and Probability for Engineering Applications provides a complete discussion of all the major topics typically covered in a college engineering statistics course. This textbook minimizes the derivations and mathematical theory, focusing instead on the information and techniques most needed and used in engineering applications. It is filled with practical techniques directly applicable on the job. Written by an experienced industry engineer and statistics professor, this book makes learning statistical methods easier for today's student. This book can be read sequentially like a normal textbook, but it is designed to be used as a handbook, pointing the reader to the topics and sections pertinent to a particular type of statistical problem. Each new concept is clearly and briefly described, whenever possible by relating it to previous topics. Then the student is given carefully chosen examples to deepen understanding of the basic ideas and how they are applied in engineering. The examples and case studies are taken from real-world engineering problems and use real data. A number of practice problems are provided for each section, with answers in the back for selected problems. This book will appeal to engineers in the entire engineering spectrum (electronics/electri... mechanical, chemical, and civil engineering); engineering students and students taking computer science/computer engineering graduate courses; scientists needing to use applied statistical methods; and engineering technicians and technologists.

  • C<INF>o</INF>-Semigroups and Applications

    • 1st Edition
    • Volume 191
    • Ioan I. Vrabie
    • English
    The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-l... methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book.The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.

  • Discrete Optimization

    The State of the Art
    • 1st Edition
    • Volume 11
    • E. Boros + 1 more
    • English
    One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world.This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc.Key features:• state of the art surveys• comprehensiveness• prominent authors• theoretical, computational and applied aspects.This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3

  • Stochastic Processes: Modeling and Simulation

    • 1st Edition
    • Volume 21
    • D N Shanbhag
    • English
    This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.

  • Finite Element Method

    A Practical Course
    • 1st Edition
    • G.R. Liu + 1 more
    • English
    The Finite Element Method (FEM) has become an indispensable technology for the modelling and simulation of engineering systems. Written for engineers and students alike, the aim of the book is to provide the necessary theories and techniques of the FEM for readers to be able to use a commercial FEM package to solve primarily linear problems in mechanical and civil engineering with the main focus on structural mechanics and heat transfer.Fundamental theories are introduced in a straightforward way, and state-of-the-art techniques for designing and analyzing engineering systems, including microstructural systems are explained in detail. Case studies are used to demonstrate these theories, methods, techniques and practical applications, and numerous diagrams and tables are used throughout.The case studies and examples use the commercial software package ABAQUS, but the techniques explained are equally applicable for readers using other applications including NASTRAN, ANSYS, MARC, etc.

  • Progress in Optice

    • 1st Edition
    • Brian Evans
    • English

  • Quantum Mechanics in Hilbert Space

    • 1st Edition
    • Volume 41
    • English

  • Basic Structured Grid Generation

    With an introduction to unstructured grid generation
    • 1st Edition
    • M Farrashkhalvat + 1 more
    • English
    Finite element, finite volume and finite difference methods use grids to solve the numerous differential equations that arise in the modelling of physical systems in engineering. Structured grid generation forms an integral part of the solution of these procedures. Basic Structured Grid Generation provides the necessary mathematical foundation required for the successful generation of boundary-conforming grids and will be an important resource for postgraduate and practising engineers.The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids. The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front techniques.

  • Statistical Methods

    • 2nd Edition
    • Rudolf J. Freund + 1 more
    • English
    This broad text provides a complete overview of most standard statistical methods, including multiple regression, analysis of variance, experimental design, and sampling techniques. Assuming a background of only two years of high school algebra, this book teaches intelligent data analysis and covers the principles of good data collection.

  • Networks and Graphs

    Techniques and Computational Methods
    • 1st Edition
    • D K Smith
    • English
    Dr Smith here presents essential mathematical and computational ideas of network optimisation for senior undergraduate and postgraduate students in mathematics, computer science and operational research. He shows how algorithms can be used for finding optimal paths and flows, identifying trees in networks, and optimal matching. Later chapters discuss postman and salesperson tours, and demonstrate how many network problems are related to the ‘‘minimal-cost feasible-flow’’ problem. Techniques are presented both informally and with mathematical rigour and aspects of computation, especially of complexity, have been included. Numerous examples and diagrams illustrate the techniques and applications. The book also includes problem exercises with tutorial hints.

  • Applying Contemporary Statistical Techniques

    • 1st Edition
    • Rand R. Wilcox
    • English
    Applying Contemporary Statistical Techniques explains why traditional statistical methods are often inadequate or outdated when applied to modern problems. Wilcox demonstrates how new and more powerful techniques address these problems far more effectively, making these modern robust methods understandable, practical, and easily accessible.

  • An Introduction to Probability and Statistical Inference

    • 1st Edition
    • George G. Roussas
    • English
    Roussas introduces readers with no prior knowledge in probability or statistics, to a thinking process to guide them toward the best solution to a posed question or situation. An Introduction to Probability and Statistical Inference provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. "The text is wonderfully written and has the mostcomprehensive range of exercise problems that I have ever seen." — Tapas K. Das, University of South Florida"The exposition is great; a mixture between conversational tones and formal mathematics; the appropriate combination for a math text at [this] level. In my examination I could find no instance where I could improve the book." — H. Pat Goeters, Auburn, University, Alabama

  • Statistics with Maple

    • 1st Edition
    • John A. Rafter + 2 more
    • English
    Statistics with Maple is a practical guide for engineers, statisticians, business professionals and others who use the Maple software package and who wish to use it to produce numerical summaries, make graphical displays, and perform statistical inference. The book and software package is unique in its focus on using Maple for statistical methodology.This tutorial and reference manual assumes that readers have a basic knowledge of statistics and a familiarity with Maple.

  • Handbook of Complex Analysis

    • 1st Edition
    • Reiner Kuhnau
    • English
    Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers.

  • Scientific and Engineering Computations for the 21st Century - Methodologies and Applications

    Proceedings of the 15th Toyota Conference
    • 1st Edition
    • M. Mori + 1 more
    • English
    The 20th century saw tremendous achievements and progress in science and technology. Undoubtedly, computers and computer-related technologies acted as one of vital catalysts for accelerating this progress in the latter half of the century. The contributions of mathematical sciences have been equallyprofound, and the synergy between mathematics and computer science has played akey role in accelerating the progress of both fields as well as scienceand engineering.Mathemat... sciences will undoubtedly continue to play this vital role in thisnew century. In particular, mathematical modeling and numerical simulation will continue to be among the essential methodologies for solving massive and complex problems that arise in science, engineering and manufacturing. Underpinning this all from a sound, theoretical perspective will be numerical algorithms. In recognition of this observation, this volume focuses on the following specific topics.(1) Fundamental numerical algorithms(2) Applications of numerical algorithms(3) Emerging technologies.The articles included in this issue by experts on advanced scientific and engineering computations from numerous countries elucidate state-of-the-art achievements in these three topics from various angles and suggest the future directions. Although we cannot hope to cover all the aspects in scientific and engineering computations, we hope that the articles will interest, inform and inspire members of the science and engineering community.

  • Stochastic Dynamics. Modeling Solute Transport in Porous Media

    • 1st Edition
    • Volume 44
    • Don Kulasiri + 1 more
    • English
    Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas are explained in an intuitive manner wherever possible with out compromising rigor.The solute transport problem in porous media saturated with water had been used as a natural setting to discuss the approaches based on stochastic dynamics. The work is also motivated by the need to have more sophisticated mathematical and computational frameworks to model the variability one encounters in natural and industrial systems. This book presents the ideas, models and computational solutions pertaining to a single problem: stochastic flow of contaminant transport in the saturated porous media such as that we find in underground aquifers. In attempting to solve this problem using stochastic concepts, different ideas and new concepts have been explored, and mathematical and computational frameworks have been developed in the process. Some of these concepts, arguments and mathematical and computational constructs are discussed in an intuititve manner in this book.

  • Rules of Thumb for Chemical Engineers

    • 3rd Edition
    • Stephen M Hall
    • English
    The most complete guide of its kind, this is the standard handbook for chemical and process engineers. All new material on fluid flow, long pipe, fractionators, separators and accumulators, cooling towers, gas treating, blending, troubleshooting field cases, gas solubility, and density of irregular solids. This substantial addition of material will also include conversion tables and a new appendix, "Shortcut Equipment Design Methods."This convenient volume helps solve field engineering problems with its hundreds of common sense techniques, shortcuts, and calculations. Here, in a compact, easy-to-use format, are practical tips, handy formulas, correlations, curves, charts, tables, and shortcut methods that will save engineers valuable time and effort. Hundreds of common sense techniques and calculations help users quickly and accurately solve day-to-day design, operations, and equipment problems.

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