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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.

  • An Introduction to Analytic Geometry and Calculus

    • 1st Edition
    • A. C. Burdette
    • English
    An Introduction to Analytic Geometry and Calculus covers the basic concepts of analytic geometry and the elementary operations of calculus. This book is composed of 14 chapters and begins with an overview of the fundamental relations of the coordinate system. The next chapters deal with the fundamentals of straight line, nonlinear equations and graphs, functions and limits, and derivatives. These topics are followed by a discussion of some applications of previously covered mathematical subjects. This text also considers the fundamentals of the integrals, trigonometric functions, exponential and logarithm functions, and methods of integration. The final chapters look into the concepts of parametric equations, polar coordinates, and infinite series. This book will prove useful to mathematicians and undergraduate and graduate mathematics students.

  • Measure, Integration, and Functional Analysis

    • 1st Edition
    • Robert B. Ash
    • English
    Measure, Integration, and Functional Analysis deals with the mathematical concepts of measure, integration, and functional analysis. The fundamentals of measure and integration theory are discussed, along with the interplay between measure theory and topology. Comprised of four chapters, this book begins with an overview of the basic concepts of the theory of measure and integration as a prelude to the study of probability, harmonic analysis, linear space theory, and other areas of mathematics. The reader is then introduced to a variety of applications of the basic integration theory developed in the previous chapter, with particular reference to the Radon-Nikodym theorem. The third chapter is devoted to functional analysis, with emphasis on various structures that can be defined on vector spaces. The final chapter considers the connection between measure theory and topology and looks at a result that is a companion to the monotone class theorem, together with the Daniell integral and measures on topological spaces. The book concludes with an assessment of measures on uncountably infinite product spaces and the weak convergence of measures. This book is intended for mathematics majors, most likely seniors or beginning graduate students, and students of engineering and physics who use measure theory or functional analysis in their work.

  • The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

    • 1st Edition
    • A. K. Aziz
    • English
    The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.

  • Computer Arithmetic and Self-Validating Numerical Methods

    • 1st Edition
    • Christian Ullrich
    • English
    Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods,” held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.

  • Mathematical Models of Attitude Change

    Change in Single Attitudes and Cognitive Structure
    • 1st Edition
    • John E. Hunter + 2 more
    • Peter R. Monge
    • English
    Mathematical Models of Attitude Change, Volume 1: Change in Single Attitudes and Cognitive Structure presents the mathematical models that address the existing verbal attitude change theories, which are translated into families of mathematical models. This book discusses the two types of attitude change, namely, the attitude toward the object of the message and the attitude toward the source of the message. Organized into three parts encompassing 17 chapters, this volume begins with an overview of the mathematical models of attitude change that are derived from several theories. This text then explains the empirical work designed to test selected mathematical models of attitude change. Other chapters consider the predictions made by different models, including reinforcement, information processing, social judgment, balance, dissonance, and congruity. This book discusses as well the attitude-related variable, namely, belief and belief change. The final chapter deals with models of change in hierarchical organized attitudes using alternative theories of attitude change. This book is a valuable resource for psychologists.

  • 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.

  • Handbook of Neural Computing Applications

    • 1st Edition
    • Alianna J. Maren + 2 more
    • English
    Handbook of Neural Computing Applications is a collection of articles that deals with neural networks. Some papers review the biology of neural networks, their type and function (structure, dynamics, and learning) and compare a back-propagating perceptron with a Boltzmann machine, or a Hopfield network with a Brain-State-in-a-Box network. Other papers deal with specific neural network types, and also on selecting, configuring, and implementing neural networks. Other papers address specific applications including neurocontrol for the benefit of control engineers and for neural networks researchers. Other applications involve signal processing, spatio-temporal pattern recognition, medical diagnoses, fault diagnoses, robotics, business, data communications, data compression, and adaptive man-machine systems. One paper describes data compression and dimensionality reduction methods that have characteristics, such as high compression ratios to facilitate data storage, strong discrimination of novel data from baseline, rapid operation for software and hardware, as well as the ability to recognized loss of data during compression or reconstruction. The collection can prove helpful for programmers, computer engineers, computer technicians, and computer instructors dealing with many aspects of computers related to programming, hardware interface, networking, engineering or design.

  • Asymptotic Approximations of Integrals

    Computer Science and Scientific Computing
    • 1st Edition
    • R. Wong
    • Werner Rheinboldt + 1 more
    • English
    Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

  • Elementary Linear Algebra

    • 1st Edition
    • Richard O. Hill
    • English
    Elementary Linear Algebra reviews the elementary foundations of linear algebra in a student-oriented, highly readable way. The many examples and large number and variety of exercises in each section help the student learn and understand the material. The instructor is also given flexibility by allowing the presentation of a traditional introductory linear algebra course with varying emphasis on applications or numerical considerations. In addition, the instructor can tailor coverage of several topics. Comprised of six chapters, this book first discusses Gaussian elimination and the algebra of matrices. Applications are interspersed throughout, and the problem of solving AX = B, where A is square and invertible, is tackled. The reader is then introduced to vector spaces and subspaces, linear independences, and dimension, along with rank, determinants, and the concept of inner product spaces. The final chapter deals with various topics that highlight the interaction between linear algebra and all the other branches of mathematics, including function theory, analysis, and the singular value decomposition and generalized inverses. This monograph will be a useful resource for practitioners, instructors, and students taking elementary linear algebra.

  • Linear Integral Equations

    Theory and Technique
    • 1st Edition
    • Ram P. Kanwal
    • English
    Linear Integral Equations: Theory and Technique is an 11-chapter text that covers the theoretical and methodological aspects of linear integral equations. After a brief overview of the fundamentals of the equations, this book goes on dealing with specific integral equations with separable kernels and a method of successive approximations. The next chapters explore the properties of classical Fredholm theory and the applications of linear integral equations to ordinary and partial differential equations. These topics are followed by discussions of the symmetric kernels, singular integral equations, and the integral transform methods. The final chapters consider the applications of linear integral equations to mixed boundary value problems. These chapters also look into the integral equation perturbation methods. This book will be of value to undergraduate and graduate students in applied mathematics, theoretical mechanics, and mathematical physics.

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