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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.

  • Elliptic Problem Solvers

    • 1st Edition
    • Martin H. Schultz
    • English
    Elliptic Problem Solvers provides information pertinent to some aspects of the numerical solution of elliptic partial differential equations. This book presents the advances in developing elliptic problem solvers and analyzes their performance. Organized into 40 chapters, this book begins with an overview of the approximate solution of using a standard Galerkin method employing piecewise linear triangular finite elements. This text then defines the types of vector architecture and discusses the variation in performance that can occur on a vector processor as a function of algorithm and implementation. Other chapters consider the implementation of techniques for elliptical problems. This book discusses as well the six techniques for the solution of nonsymmetric linear systems arising from finite difference discretization of the convection-diffusion equation. The final chapter deals with the basic semiconductor device equations. This book is a valuable resource for electrical and computer engineers, scientists, computer programmers, pure mathematicians, and research workers.

  • Transformations

    Mathematical Approaches to Culture Change
    • 1st Edition
    • Colin Renfrew + 1 more
    • English
    Transformations: Mathematical Approaches to Culture Change focuses on the application of contemporary mathematical techniques to the study of culture change and formulates problems in archaeology, anthropology, and historiography in such a way that they are susceptible to treatment of a mathematical kind. Mathematical models, extending from the almost purely quantitative methods of physics to the purely verbal conceptual explanations, are described. Emphasis is placed on catastrophe theoretic models that exemplify the use of soft mathematics in situations in which the use of hard quantitative models is not possible. Comprised of 21 chapters, this book begins with an overview of the role of mathematics in theoretical archaeology, followed by a discussion on two general categories of mathematical methods that seem to be suitable for modeling cultural transformations: methods of dynamical systems theory and methods that give greater emphasis on discrete entities and the structural relations or patterns among them. Subsequent chapters deal with the use of mathematics in history; morphogenesis in biological and social systems; simulation of the growth of hierarchies; and logistic trends in Southwest population growth. A reconstruction of political units in the Valley of Mexico during the Toltec period is also presented. This monograph will be of interest to archaeologists, anthropologists, historians, biologists, sociologists, and mathematicians.

  • Vector and Operator Valued Measures and Applications

    • 1st Edition
    • Don H. Tucker + 1 more
    • English
    Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.

  • Programming in an Object-Oriented Environment

    • 1st Edition
    • Raimund K. Ege
    • English
    Programming in an Object-Oriented Environment provides an in-depth look at the concepts behind the technology of object-oriented programming. This book explains why object-oriented programming has the potential to vastly improve the productivity of programmers and how to apply this technology in a practical environment. Many programming examples are included, focusing on how different programming languages support the core of object-oriented concepts. C++ is used as the main sample language throughout this text. This monograph consists of two major parts. Part I provides an introduction to object-oriented concepts, their rationale and their implementation in programming languages. The object-oriented approach to programming in an object-oriented environment is discussed in Part II. This publication is intended for software professionals who are interested in learning the fundamental concepts of object-oriented programming and how to apply these concepts in a practical computer environment.

  • Sparse Matrix Computations

    • 1st Edition
    • James R. Bunch + 1 more
    • English
    Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.

  • Neural Networks for Perception

    Human and Machine Perception
    • 1st Edition
    • Harry Wechsler
    • English
    Neural Networks for Perception, Volume 1: Human and Machine Perception focuses on models for understanding human perception in terms of distributed computation and examples of PDP models for machine perception. This book addresses both theoretical and practical issues related to the feasibility of both explaining human perception and implementing machine perception in terms of neural network models. The book is organized into two parts. The first part focuses on human perception. Topics on network model of object recognition in human vision, the self-organization of functional architecture in the cerebral cortex, and the structure and interpretation of neuronal codes in the visual system are detailed under this part. Part two covers the relevance of neural networks for machine perception. Subjects considered under this section include the multi-dimensional linear lattice for Fourier and Gabor transforms, multiple- scale Gaussian filtering, and edge detection; aspects of invariant pattern and object recognition; and neural network for motion processing. Neuroscientists, computer scientists, engineers, and researchers in artificial intelligence will find the book useful.

  • Introduction to Numerical Computations

    • 2nd Edition
    • James S. Vandergraft
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Introduction to Numerical Computations, Second Edition introduces numerical algorithms as they are used in practice. This edition covers the usual topics contained in introductory numerical analysis textbooks that include all of the well-known and most frequently used algorithms for interpolation and approximation, numerical differentiation and integration, solution of linear systems and nonlinear equations, and solving ordinary differential equations. A complete discussion of computer arithmetic, problems that arise in the computer evaluation of functions, and cubic spline interpolation are also provided. This text likewise discusses the Newton formulas for interpolation and adaptive methods for integration. The level of this book is suitable for advanced undergraduate students and readers with elementary mathematical background.

  • High-Level Language Computer Architecture

    • 1st Edition
    • Yaohan Chu
    • English
    High-Level Language Computer Architecture offers a tutorial on high-level language computer architecture, including von Neumann architecture and syntax-oriented architecture as well as direct and indirect execution architecture. Design concepts of Japanese-language data processing systems are discussed, along with the architecture of stack machines and the SYMBOL computer system. The conceptual design of a direct high-level language processor is also described. Comprised of seven chapters, this book first presents a classification of high-level language computer architecture according to the proximity of the machine language and the programming language. This classification gives four types: von Neumann architecture, syntax-oriented architecture, indirect execution architecture, and direct execution architecture. In order to illustrate the possible evolution of computer architecture, design concepts of Japanese-language data processing systems are chosen as an example. Subsequent chapters focus on the syntax-oriented architecture; the historical SYMBOL computer system which makes use of an indirect execution architecture; and design concepts of direct-execution architecture for the ALGOL 60 language. The final chapter describes the architecture for the processor for an APL subset. This monograph will be of interest to specialists in electronics and computer science.

  • Calculus Using Mathematica

    • 1st Edition
    • K.D. Stroyan
    • English
    Calculus Using Mathematica is intended for college students taking a course in calculus. It teaches the basic skills of differentiation and integration and how to use Mathematica, a scientific software language, to perform very elaborate symbolic and numerical computations. This is a set composed of the core text, science and math projects, and computing software for symbolic manipulation and graphics generation. Topics covered in the core text include an introduction on how to get started with the program, the ideas of independent and dependent variables and parameters in the context of some down-to-earth applications, formulation of the main approximation of differential calculus, and discrete dynamical systems. The fundamental theory of integration, analytical vector geometry, and two dimensional linear dynamical systems are elaborated as well. This publication is intended for beginning college students.

  • Combinatorics on Words

    Progress and Perspectives
    • 1st Edition
    • Larry J. Cummings
    • English
    Combinatorics on Words: Progress and Perspectives covers the proceedings of an international meeting by the same title, held at the University of Waterloo, Canada on August 16-22, 1982. This meeting highlights the diverse aspects of combinatorics on words, including the Thue systems, topological dynamics, combinatorial group theory, combinatorics, number theory, and computer science. This book is organized into four parts encompassing 19 chapters. The first part describes the Thue systems with the Church-Rosser property. A Thue system will be called “Church-Rosser” if two strings are congruent with respect to that system if and only if they have a common descendant, that is, a string that can be obtained applying only rewriting rules that reduce length. The next part deals with the problems related to the encoding of codes and the overlapping of words in rational languages. This part also explores the features of polynomially bounded DOL systems yield codes. These topics are followed by discussions of some combinatorial properties of metrics over the free monoid and the burnside problem of semigroups of matrices. The last part considers the ambiguity types of formal grammars, finite languages, computational complexity of algebraic structures, and the Bracket-context tree functions. This book will be of value to mathematicians and advance undergraduate and graduate students.

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