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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.

  • Representation Theory of Finite Groups

    • 1st Edition
    • Martin Burrow
    • English
    Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.

  • Applied Time Series Analysis II

    Proceedings of the Second Applied Time Series Symposium Held in Tulsa, Oklahoma, March 3-5, 1980
    • 1st Edition
    • David F. Findley
    • English
    Applied Time Series Analysis II contains the proceedings of the Second Applied Time Series Symposium Held in Tulsa, Oklahoma, on March 3-5, 1980. The symposium provided a forum for discussing significant advances in time series analysis and signal processing. Effective alternatives to the familiar least-square and maximum likelihood procedures are described, along with maximum likelihood procedures for modeling irregularly sampled series and for classifying non-stationary series. Comprised of 22 chapters, this volume begins with an introduction to the multidimensional filtering theory and presents specific case histories related to the multidimensional recursive filter stability problem; the least squares inverse problem; realization of filters; and spectral estimation. The unique properties of the three-dimensional wave equation are also considered. Subsequent chapters focus on high-resolution spectral estimators; time series analysis of geophysical inverse scattering problems; minimum entropy deconvolution; and fitting of a continuous time autoregression to discrete data. This monograph will appeal to students and practitioners in the fields of mathematics and statistics, electrical and electronics engineering, and information and computer sciences.

  • Elementary Topology

    A Combinatorial and Algebraic Approach
    • 1st Edition
    • Donald W. Blackett
    • English
    Elementary Topology: A Combinatorial and Algebraic Approach focuses on the application of algebraic methods to topological concepts and theorems. The publication first elaborates on some examples of surfaces and their classifications. Discussions focus on combinatorial invariants of a surface, combinatorial equivalence, surfaces and their equations, topological surfaces, coordinates on a sphere and torus, and properties of the sphere and torus. The text then examines complex conics and covering surfaces and mappings into the sphere, including applications of the winding number in complex analysis, mappings into the plane, winding number of a plane curve, covering surfaces, and complex conies. The book examines vector fields, network topology, and three-dimensional topology. Topics include topological products and fiber bundles, manifolds of configurations, paths, circuits, and trees, vector fields and hydrodynamics, vector fields on a sphere, and vector fields and differential equations. The publication is highly recommended for sophomores, juniors, and seniors who have completed a year of calculus.

  • Elements of Differentiable Dynamics and Bifurcation Theory

    • 1st Edition
    • David Ruelle
    • English
    Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.

  • Dynamic Programming and Its Applications

    Proceedings of the International Conference on Dynamic Programming and Its Applications, University of British Columbia, Vancouver, British Columbia, Canada, April 14-16, 1977
    • 1st Edition
    • Martin L. Puterman
    • English
    Dynamic Programming and Its Applications provides information pertinent to the theory and application of dynamic programming. This book presents the development and future directions for dynamic programming. Organized into four parts encompassing 23 chapters, this book begins with an overview of recurrence conditions for countable state Markov decision problems, which ensure that the optimal average reward exists and satisfies the functional equation of dynamic programming. This text then provides an extensive analysis of the theory of successive approximation for Markov decision problems. Other chapters consider the computational methods for deterministic, finite horizon problems, and present a unified and insightful presentation of several foundational questions. This book discusses as well the relationship between policy iteration and Newton's method. The final chapter deals with the main factors severely limiting the application of dynamic programming in practice. This book is a valuable resource for growth theorists, economists, biologists, mathematicians, and applied management scientists.

  • Computers and the Cybernetic Society

    • 2nd Edition
    • Michael A. Arbib
    • English
    Computers and the Cybernetic Society, Second Edition examines the impact of computers on the cybernetic society and covers topics such as expert systems, management applications, and office automation. The idea of a computer program is considered, along with data banks and the movement and storage of information. Advances in computer technology are also discussed. Comprised of nine chapters, this book begins with an assessment of the interaction between computer developments and social pressures. The interplay between the exciting possibilities of computer networking and the social implications of computer technology is highlighted by focusing on planning networks and public information networks. The next two chapters provide a basic understanding of computers and programming by describing key concepts such as computer graphics, networks, microcomputers, and program design. The next five chapters give a comprehensive overview of the impact of computers on the cybernetic society. The final chapter explains how hardware works and describes the circuitry that computers use to execute a program at the level of machine-language instructions. This monograph is intended for both students and instructors in the fields of computer science and cybernetics.

  • Vector Analysis and Cartesian Tensors

    • 2nd Edition
    • D. E. Bourne + 1 more
    • English
    Vector Analysis and Cartesian Tensors, Second Edition focuses on the processes, methodologies, and approaches involved in vector analysis and Cartesian tensors, including volume integrals, coordinates, curves, and vector functions. The publication first elaborates on rectangular Cartesian coordinates and rotation of axes, scalar and vector algebra, and differential geometry of curves. Discussions focus on differentiation rules, vector functions and their geometrical representation, scalar and vector products, multiplication of a vector by a scalar, and angles between lines through the origin. The text then elaborates on scalar and vector fields and line, surface, and volume integrals, including surface, volume, and repeated integrals, general orthogonal curvilinear coordinates, and vector components in orthogonal curvilinear coordinates. The manuscript ponders on representation theorems for isotropic tensor functions, Cartesian tensors, applications in potential theory, and integral theorems. Topics include geometrical and physical significance of divergence and curl, Poisson's equation in vector form, isotropic scalar functions of symmetrical second order tensors, and diagonalization of second-order symmetrical tensors. The publication is a valuable reference for mathematicians and researchers interested in vector analysis and Cartesian tensors.

  • Introduction to Asymptotics and Special Functions

    • 1st Edition
    • F. W. J. Olver
    • English
    Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.

  • The Mathematica® Programmer

    • 1st Edition
    • Roman E. Maeder
    • English
    The Mathematica Programmer covers the fundamental programming paradigms and applications of programming languages. This book is organized into two parts encompassing 10 chapters. Part 1 begins with an overview of the programming paradigms. This part also treats abstract data types, polymorphism and message passing, object-oriented programming, and relational databases. Part 2 looks into the practical aspects of programming languages, including in lists and power series, fractal curves, and minimal surfaces. This book will prove useful to mathematicians and computer scientists.

  • Handbook of VLSI Chip Design and Expert Systems

    • 1st Edition
    • A. F. Schwarz
    • English
    Handbook of VLSI Chip Design and Expert Systems provides information pertinent to the fundamental aspects of expert systems, which provides a knowledge-based approach to problem solving. This book discusses the use of expert systems in every possible subtask of VLSI chip design as well as in the interrelations between the subtasks. Organized into nine chapters, this book begins with an overview of design automation, which can be identified as Computer-Aided Design of Circuits and Systems (CADCAS). This text then presents the progress in artificial intelligence, with emphasis on expert systems. Other chapters consider the impact of design automation, which exploits the basic capabilities of computers to perform complex calculations and to handle huge amounts of data with a high speed and accuracy. This book discusses as well the characterization of microprocessors. The final chapter deals with interactive I/O devices. This book is a valuable resource for system design experts, circuit analysts and designers, logic designers, device engineers, technologists, and application-specific designers.

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