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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.

  • Topological Spaces

    • 1st Edition
    • H. J. Kowalsky
    • English
    Topological Spaces focuses on the applications of the theory of topological spaces to the different branches of mathematics. The book first offers information on elementary principles, topological spaces, and compactness and connectedness. Discussions focus on locally compact spaces, local connectedness, fundamental concepts and their reformulations, lattice of topologies, axioms of separation, fundamental concepts of set theory, and ordered sets and lattices. The manuscript then ponders on mappings and extensions and characterization of topological spaces, including completely regular spaces, transference of topologies, Wallman compactification, and embeddings. The publication takes a look at metric and uniform spaces and applications of topological groups. Topics include the Stone-Weierstrass Approximation Theorem, extensions and completions of topological groups, topological rings and fields, extension and completion of uniform spaces, uniform continuity and uniform convergence, metric spaces, and metritization. The text is a valuable reference for mathematicians and researchers interested in the study of topological spaces.

  • Advanced Calculus with Linear Analysis

    • 1st Edition
    • Joseph R. Lee
    • English
    Advanced Calculus with Linear Analysis provides information pertinent to the fundamental aspects of advanced calculus from the point of view of linear spaces. This book covers a variety of topics, including function spaces, infinite series, real number system, sequence spaces, power series, partial differentiation, uniform continuity, and the class of measurable sets. Organized into nine chapters, this book begins with an overview of the concept of a single-valued function, consisting of a rule, a domain, and a range. This text then describes an infinite sequence as an ordered set of elements that can be put into a one-to-one correspondence with the positive integers. Other chapters consider a normed linear space, which is complete if and only if every Cauchy sequence converges to an element in the space. This book discusses as well the convergence of an infinite series, which is determined by the convergence of the infinite sequence of partial sums. This book is a valuable resource for students.

  • An Introduction to Numerical Mathematics

    • 1st Edition
    • Eduard L. Stiefel
    • English
    An Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear programming, linear and nonlinear algebra, polynomials, numerical differentiation, and approximations. Organized into seven chapters, this book begins with an overview of the solution of linear problems wherein numerical mathematics provides very effective algorithms consisting of finitely many computational steps. This text then examines the method for the direct solution of a definite problem. Other chapters consider the determination of frequencies in freely oscillating mechanical or electrical systems. This book discusses as well eigenvalue problems for oscillatory systems of finitely many degrees of freedom, which can be reduced to algebraic equations. The final chapter deals with the approximate representation of a function f(x) given by I-values as in the form of a table. This book is a valuable resource for physicists, mathematicians, theoreticians, engineers, and research workers.

  • Complex Numbers in Geometry

    • 1st Edition
    • I. M. Yaglom
    • Henry Booker + 2 more
    • English
    Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the Lobachevskii plane; dual numbers as oriented lines of a plane; most general complex numbers; and double, hypercomplex, and dual numbers. The text then takes a look at circular transformations and circular geometry, including ordinary circular transformations, axial circular transformations of the Lobachevskii plane, circular transformations of the Lobachevskii plane, axial circular transformations, and ordinary circular transformations. The manuscript is intended for pupils in high schools and students in the mathematics departments of universities and teachers' colleges. The publication is also useful in the work of mathematical societies and teachers of mathematics in junior high and high schools.

  • Distributions and the Boundary Values of Analytic Functions

    • 1st Edition
    • E. J. Beltrami + 1 more
    • English
    Distributions and the Boundary Values of Analytic Functions focuses on the tools and techniques of distribution theory and the distributional boundary behavior of analytic functions and their applications. The publication first offers information on distributions, including spaces of testing functions, distributions of finite order, convolution and regularization, and testing functions of rapid decay and distributions of slow growth. The text then examines Laplace transform, as well as Laplace transforms of distributions with arbitrary support. The manuscript ponders on distributional boundary values of analytic functions, including causal and passive operators, analytic continuation and uniqueness, boundary value theorems and generalized Hilbert transforms, and representation theorems for half-plane holomorphic functions with S' boundary behavior. The publication is a valuable source of data for researchers interested in distributions and the boundary values of analytic functions.

  • Theoretical Numerical Analysis

    • 1st Edition
    • Burton Wendroff
    • English
    Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.

  • L. E. J. Brouwer Collected Works

    Geometry, Analysis, Topology and Mechanics
    • 1st Edition
    • Hans Freudenthal
    • English
    L. E. J. Brouwer Collected Works, Volume 2: Geometry, Analysis, Topology, and Mechanics focuses on the contributions and principles of Brouwer on geometry, topology, analysis, and mechanics, including non-Euclidean spaces, integrals, and surfaces. The publication first ponders on non-Euclidean spaces and integral theorems, lie groups, and plane transition theorem. Discussions focus on remarks on multiple integrals, force field of the non-Euclidean spaces with negative curvature, difference quotients and differential quotients, characterization of the Euclidean and non-Euclidean motion groups, and continuous one-one transformations of surfaces in themselves. The book also takes a look at vector fields on surfaces and new methods in topology, including continuous vector distributions on surfaces and orthogonal trajectories of the orbits of a one parameter plane projective group. The book then ponders on mechanics and topology of surfaces, as well as the motion of a particle on the bottom of a rotating vessel under the influence of gravitational force. The publication is a valuable reference for researchers interested in geometry, topology, analysis, and mechanics.

  • Statistical Methods

    • 1st Edition
    • Stefan Szulc
    • English
    Statistical Methods provides a discussion of the principles of the organization and technique of research, with emphasis on its application to the problems in social statistics. This book discusses branch statistics, which aims to develop practical ways of collecting and processing numerical data and to adapt general statistical methods to the objectives in a given field. Organized into five parts encompassing 22 chapters, this book begins with an overview of how to organize the collection of such information on individual units, primarily as accomplished by government agencies. This text then examines the other types of statistical series such as geographical, time, and structural series. Other chapters consider several types of relative numbers and analyze some related problems in greater detail. This book discusses as well the methods of analysis of interdependence between the characteristics deals with these methods. The final chapter deals with cases in which partial research is either an incorrect form of pseudo-sampling survey. This book is a valuable resource for economists.

  • Nonlinear Systems and Applications

    An International Conference
    • 1st Edition
    • V. Lakshmikantham
    • English
    Nonlinear Systems and Applications: An International Conference contains the proceedings of an International Conference on Nonlinear Systems and Applications held at the University of Texas at Arlington, on July 19-23, 1976. The conference provided a forum for reviewing advances in nonlinear systems and their applications and tackled a wide array of topics ranging from abstract evolution equations and nonlinear semigroups to controllability and reachability. Various methods used in solving equations are also discussed, including approximation techniques for delay systems. Most of the applications are in the area of the life sciences. Comprised of 59 chapters, this book begins with a discussion on monotonically convergent upper and lower bounds for classes of conflicting populations, followed by an analysis of constrained problems. The reader is then introduced to approximation techniques for delay systems in biological models; differential inequalities for Liapunov functions; and stability or chaos in discrete epidemic models. Subsequent chapters deal with nonlinear boundary value problems for elliptic systems; bounds for solutions of reaction-diffusion equations; monotonicity and measurability; and periodic solutions of some integral equations from the theory of epidemics. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.

  • Uncertainty in Artificial Intelligence

    Proceedings of the Eighth Conference (1992), July 17–19, 1992, Eighth Conference on Uncertainty in Artificial Intelligence, Stanford University
    • 1st Edition
    • Didier J. Dubois + 2 more
    • English
    Uncertainty in Artificial Intelligence: Proceedings of the Eighth Conference (1992) covers the papers presented at the Eighth Conference on Uncertainty in Artificial Intelligence, held at Stanford University on July 17-19, 1992. The book focuses on the processes, methodologies, technologies, and approaches involved in artificial intelligence. The selection first offers information on Relative Evidential Support (RES), modal logics for qualitative possibility and beliefs, and optimizing causal orderings for generating DAGs from data. Discussions focus on reversal, swap, and unclique operators, modal representation of possibility, and beliefs and conditionals. The text then examines structural controllability and observability in influence diagrams, lattice-based graded logic, and dynamic network models for forecasting. The manuscript takes a look at reformulating inference problems through selective conditioning, entropy and belief networks, parallelizing probabilistic inference, and a symbolic approach to reasoning with linguistic quantifiers. The text also ponders on sidestepping the triangulation problem in Bayesian net computations; exploring localization in Bayesian networks for large expert systems; and expressing relational and temporal knowledge in visual probabilistic networks. The selection is a valuable reference for researchers interested in artificial intelligence.

  • Protecting Information on Local Area Networks

    • 1st Edition
    • James A Schweitzer
    • English
    Protecting Information on Local Area Networks presents the various types of networks and explains why they are being expanded at such a rapid pace. This book considers how management can gain control of the valuable network-services information resources generally available. Organized into three parts encompassing seven chapters, this book begins with an overview of the various networks and their operations. This text then discusses the appropriate management actions to ensure some control over the use of networks and the business information resource. Other chapters consider the management rationale for network information security and explain the development of a company information network security policy. This book discusses as well security or network-connected personal computers. The final chapter deals with a number of major vulnerabilities of information when communicated or processed on network-connected personal computers. This book is a valuable resource for research scientists, technical security specialists, information systems specialists, and systems administrators.

  • Modern Dimension Theory

    • 1st Edition
    • Jun-Iti Nagata
    • N. G. De Bruijn + 2 more
    • English
    Bibliotheca Mathematica, Volume 6: Modern Dimension Theory provides a brief account of dimension theory as it has been developed since 1941, including the principal results of the classical theory for separable metric spaces. This book discusses the decomposition theorem, Baire's zero-dimensional spaces, dimension of separable metric spaces, and characterization of dimension by a sequence of coverings. The imbedding of countable-dimensiona... spaces, sum theorem for strong inductive dimension, and cohomology group of a topological space are also elaborated. This text likewise covers the uniformly zero-dimensional mappings, theorems in euclidean space, transfinite inductive dimension, and dimension of non-metrizable spaces. This volume is recommended to students and specialists researching on dimension theory.

  • Theory of Differential Equations

    • 1st Edition
    • I. M. Gel'fand + 1 more
    • English
    Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations. This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cauchy problem, systems that are Petrovski?-correct, and generalized eigenfunctions of self-adjoint operators are also reviewed. This text likewise covers the differentiation of functionals of strongly and weakly bounded variation. This volume is beneficial to students and researchers interested in the theory of differential equations.

  • Computer Arithmetic in Theory and Practice

    • 1st Edition
    • Ulrich W. Kulisch + 1 more
    • Werner Rheinboldt
    • English
    Computer Arithmetic in Theory and Practice deals with computer arithmetic and the various implementations of the entire arithmetic package on diverse processors, including microprocessors. It illustrates the importance of theoretical development in the sound implementation of arithmetic on computers, and argues that such an implementation requires the establishment of various isomorphisms between different definitions of arithmetic operations. Comprised of seven chapters, this volume begins with an introduction to the theory of computer arithmetic by giving an axiomatic characterization of the essential properties of sets and subsets; complete lattices and complete subnets; screens and roundings; and arithmetic operations. The discussion then turns to the concepts of a ringoid and a vectoid as well as those of ordered or weakly ordered ringoids and vectoids; interval arithmetic; and floating-point arithmetic. The operations in interval spaces are defined by means of semimorphisms. The final chapter shows how to embed the five basic data types (integer, real, complex, real interval, and complex interval) together with the arithmetic operations that are defined for all of these types into existing higher programming languages. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.

  • Gait Analysis

    An Introduction
    • 1st Edition
    • Michael W. Whittle
    • English
    Gait Analysis: An Introduction focuses on the systematic study of human walking and its contributions in the medical management of diseases affecting the locomotor system. The book first covers normal gait and pathological gait. Discussions focus on common pathologies affecting gait, amputee gait, walking aids, particular gait abnormalities, gait in the elderly and the young, moments of force, energy consumption, gait cycle, muscular activity during gait, and optimization of energy usage. The manuscript then elaborates on the methods of gait analysis, including visual gait analysis, general gait parameters, timing the gait cycle, direct motion measurement systems, electrogoniometers, electromyography, accelerometers, gyroscopes, and force platforms. The publication tackles the applications of gait analysis, as well as clinical gait and scientific gait analysis, normal ranges for gait parameters, conversions between measurement units, and computer program for general gait parameters. The manuscript is a valuable source of data for students of physical therapy, bioengineering, orthopedics, rheumatology, neurology, and rehabilitation.

  • The Handbook of Artificial Intelligence

    Volume 2
    • 1st Edition
    • Avron Barr + 1 more
    • English
    The Handbook of Artificial Intelligence, Volume II focuses on the improvements in artificial intelligence (AI) and its increasing applications, including programming languages, intelligent CAI systems, and the employment of AI in medicine, science, and education. The book first elaborates on programming languages for AI research and applications-oriente... AI research. Discussions cover scientific applications, teiresias, applications in chemistry, dependencies and assumptions, AI programming-language features, and LISP. The manuscript then examines applications-oriente... AI research in medicine and education, including ICAI systems design, intelligent CAI systems, medical systems, and other applications of AI to education. The manuscript explores automatic programming, as well as the methods of program specification, basic approaches, and automatic programming systems. The book is a valuable source of data for computer science experts and researchers interested in conducting further research in artificial intelligence.

  • Nonlinear Phenomena in Mathematical Sciences

    Proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, Held at the University of Texas at Arlington, Arlington, Texas, June 16–20, 1980
    • 1st Edition
    • V. Lakshmikantham
    • English
    Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences. In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques. This book will be helpful to students, practitioners, and researchers in the field of mathematics.

  • Teaching Machines and Programming

    • 1st Edition
    • K. Austwick
    • English
    Teaching Machines and Programming covers the significant developments in teaching machines and automated teaching, as well as the major theoretical issues and attributes involved in these procedures. After a brief introduction to teaching machine procedures, this six-chapter text goes on summarizing the industrial and military applications of teaching machines. The succeeding chapters consider the underlying theory, function, and schema of the adaptive teaching system, which are related to recognizable teaching functions performed by a human tutor. The last chapters discuss the development and features of linear programs and their application as new teaching aid. These chapters also look into some practical problems arising in programming for schools. This book will prove useful to computer programmers, school administrators, teachers, and students.

  • Linear Algebra

    • 1st Edition
    • R. R. Stoll + 1 more
    • English
    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understanding some of the examples and exercises. This book sets itself apart from other similar textbooks through its dedication to the principle that, whenever possible, definitions and theorems should be stated in a form which is independent of the notion of the dimension of a vector space. A second feature of this book which is worthy of mention is the early introduction of inner product spaces and the associated metric concepts. Students soon feel at ease with this class of spaces because they share so many properties with physical space when equipped with a rectangular coordinate system. Finally, the book includes a chapter concerned with several applications to other fields of the theory that have been developed.

  • Theoretical Aspects of Reasoning About Knowledge

    Proceedings of the Fifth Conference (TARK 1994)
    • 1st Edition
    • Ronald Fagin
    • English
    Theoretical Aspects of Reasoning About Knowledge contains the proceedings of the Fifth Conference on Theoretical Aspects of Reasoning About Knowledge (TARK 1994) held in Pacific Grove, California, on March 13-16, 1994. The conference provided a forum for discussing the theoretical aspects of reasoning about knowledge and tackled topics ranging from the logic of iterated belief revision and backwards forward induction to information acquisition from multi-agent resources, infinitely epistemic logic, and coherent belief revision in games. Comprised of 23 chapters, this book begins with a review of situation calculus and a solution to the frame problem, along with the use of a regression method for reasoning about the effect of actions. A novel programming language for high-level robotic control is described, along with a knowledge-based framework for belief change. Subsequent chapters deal with consistent belief reasoning in the presence of inconsistency; an epistemic logic of situations; an axiomatic approach to the logical omniscience problem; and an epistemic proof system for parallel processes. Inductive learning, knowledge asymmetries, and convention are also examined. This monograph will be of interest to both students and practitioners in the fields of artificial intelligence and computer science.

  • Discrete Computational Structures

    • 1st Edition
    • Robert R. Korfhage
    • Werner Rheinboldt
    • English
    Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasizes combinatorics and probability. Examples show different techniques of the general process of enumerating objects. Combinatorics cover permutations, enumerators for combinations, Stirling numbers, cycle classes of permutations, partitions, and compositions. The book cites as example the interplay between discrete mathematics and computing using a system of distinct representatives (SDR) problem. The problem, originating from group theory, graph theory, and set theory can be worked out by the student with a network model involving computers to generate and analyze different scenarios. The book is intended for sophomore or junior level, corresponding to the course B3, "Introduction to Discrete Structures," in the ACM Curriculum 68, as well as for mathematicians or professors of computer engineering and advanced mathematics.

  • Elements of Probability Theory

    • 1st Edition
    • L. Z. Rumshiskii
    • English
    Elements of Probability Theory presents the methods of the theory of probability. This book is divided into seven chapters that discuss the general rule for the multiplication of probabilities, the fundamental properties of the subject matter, and the classical definition of probability. The introductory chapters deal with the functions of random variables; continuous random variables; numerical characteristics of probability distributions; center of the probability distribution of a random variable; definition of the law of large numbers; stability of the sample mean and the method of moments; and Chebyshev’s theorem. The next chapters consider the limit theorem of de Moivre-Laplace and the solution of two fundamental problems in the theory of errors. The discussion then shifts to the best linear approximation to the regression function. The concluding chapters look into the central limit theorem of Lyapunov and the significance of the value of the coefficient of correlation. The book can provide useful information to the statisticians, students, and researchers.

  • Nonlinear Partial Differential Equations

    A Symposium on Methods of Solution
    • 1st Edition
    • W. F. Ames
    • English
    Nonlinear Partial Differential Equations: A Symposium on Methods of Solution is a collection of papers presented at the seminar on methods of solution for nonlinear partial differential equations, held at the University of Delaware, Newark, Delaware on December 27-29, 1965. The sessions are divided into four Symposia: Analytic Methods, Approximate Methods, Numerical Methods, and Applications. Separating 19 lectures into chapters, this book starts with a presentation of the methods of similarity analysis, particularly considering the merits, advantages and disadvantages of the methods. The subsequent chapters describe the fundamental ideas behind the methods for the solution of partial differential equation derived from the theory of dynamic programming and from finite systems of ordinary differential equations. These topics are followed by reviews of the principles to the lubrication approximation and compressible boundary-layer flow computation. The discussion then shifts to several applications of nonlinear partial differential equations, including in electrical problems, two-phase flow, hydrodynamics, and heat transfer. The remaining chapters cover other solution methods for partial differential equations, such as the synergetic approach. This book will prove useful to applied mathematicians, physicists, and engineers.

  • The Political Economy of U.S. Tariffs

    An Empirical Analysis
    • 1st Edition
    • Réal P. Lavergne
    • Karl Shell
    • English
    The Political Economy of U.S. Tariffs: An Empirical Analysis provides information pertinent to the political economy of trade barriers. This book discusses the cross-sectional regression analysis across industries to understand why some industries have been more privileged than others. Organized into seven chapters, this book begins with an overview of the structure of protection and identifies the primary actors or principles that condition the formation of trade policy more generally. This text then evaluates the institutional and theoretical reasons why political leverage should not be expected to play a significant role in explaining tariffs. Other chapters consider the notion that the structure of protection at any point in time represents some sort of equilibrium. This book discusses as well the distinction between nominal and effective tariffs. The final chapter deals with individual regressors and groups of regressors. This book is a valuable resource for economists and specialists in quantitative analysis.

  • Computer Programming and Computer Systems

    • 1st Edition
    • Anthony Hassitt
    • Anthony Ralston
    • English
    Computer Programming and Computer Systems imparts a “reading knowledge” of computer systems. This book describes the aspects of machine-language programming, monitor systems, computer hardware, and advanced programming that every thorough programmer should be acquainted with. This text discusses the automatic electronic digital computers, symbolic language, Reverse Polish Notation, and Fortran into assembly language. The routine for reading blocked tapes, dimension statements in subroutines, general-purpose input routine, and efficient use of memory are also elaborated. This publication is intended as an introduction to modern programming practices for professional programmers, but is also valuable to research workers in science, engineering, academic, and industrial fields who are using computers.

  • Distributed Computer Systems

    Theory and Practice
    • 1st Edition
    • H. S. M. Zedan
    • English
    Distributed Computer Systems: Theory and Practice is a collection of papers dealing with the design and implementation of operating systems, including distributed systems, such as the amoeba system, argus, Andrew, and grapevine. One paper discusses the concepts and notations for concurrent programming, particularly language notation used in computer programming, synchronization methods, and also compares three classes of languages. Another paper explains load balancing or load redistribution to improve system performance, namely, static balancing and adaptive load balancing. For program efficiency, the user can choose from various debugging approaches to locate or fix errors without significantly disturbing the program behavior. Examples of debuggers pertain to the ada language and the occam programming language. Another paper describes the architecture of a real-time distributed database system used for computer network management, monitoring integration, as well as administration and control of both local area or wide area communications networks. The book can prove helpful to programmers, computer engineers, computer technicians, and computer instructors dealing with many aspects of computers, such as programming, hardware interface, networking, engineering or design.

  • A Course of Higher Mathematics

    Integration and Functional Analysis, Volume 5
    • 1st Edition
    • V. I. Smirnov
    • A. J. Lohwater
    • English
    A Course of Higher Mathematics, Volume V focuses on the theory of integration and elements of functional analysis. This book is organized into five chapters. Chapter I discusses the theory of the classical Stieltjes integral and space C of continuous functions, while Chapter II deals with the foundations of the metric theory of functions of a real variable and Lebesgue-Stieltjes integral. The theory of completely additive set functions and case of the one-dimensional Hellinger integral are analyzed in Chapter III. Chapter IV contains an exposition of the foundations of the general theory of metric and normed spaces. The general theory of Hilbert space is covered in Chapter V. This volume is suitable for engineers, physicists, and students of pure mathematics.

  • A First Course in Linear Algebra

    • 1st Edition
    • Daniel Zelinsky
    • Samuel S. Saslaw
    • English
    A First Course in Linear Algebra provides an introduction to the algebra and geometry of vectors, matrices, and linear transformations. This book is designed as a background for second-year courses in calculus of several variables and differential equations where the theory of linear differential equations parallels that of linear algebraic equations. The topics discussed include the multiplication of vectors by scalars, vectors in n-space, planes and lines, and composites of linear mappings. The symmetric matrices and mappings, quadratic forms, change of coordinates, and effect of change of basis on matrices of linear functions are also described. This text likewise considers the computation of determinants, diagonalizable transformations, computation of eigenvalues and eigenvectors, and principal axis theorem. This publication is suitable for college students taking a course in linear algebra.

  • Axiomatic Projective Geometry

    • 2nd Edition
    • A. Heyting
    • N. G. De Bruijn + 2 more
    • English
    Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume V: Axiomatic Projective Geometry, Second Edition focuses on the principles, operations, and theorems in axiomatic projective geometry, including set theory, incidence propositions, collineations, axioms, and coordinates. The publication first elaborates on the axiomatic method, notions from set theory and algebra, analytic projective geometry, and incidence propositions and coordinates in the plane. Discussions focus on ternary fields attached to a given projective plane, homogeneous coordinates, ternary field and axiom system, projectivities between lines, Desargues' proposition, and collineations. The book takes a look at incidence propositions and coordinates in space. Topics include coordinates of a point, equation of a plane, geometry over a given division ring, trivial axioms and propositions, sixteen points proposition, and homogeneous coordinates. The text examines the fundamental proposition of projective geometry and order, including cyclic order of the projective line, order and coordinates, geometry over an ordered ternary field, cyclically ordered sets, and fundamental proposition. The manuscript is a valuable source of data for mathematicians and researchers interested in axiomatic projective geometry.

  • Calculus and Its Applications

    • 1st Edition
    • P. Mainardi + 1 more
    • English
    Calculus and its Applications provides information pertinent to the applications of calculus. This book presents the trapping technique in defining geometrical and physical entities that are usually regarded as limits of sums. Organized into 20 chapters, this book begins with an overview of the notion of average speed that seems to appear first as a qualitative concept. This text then presents the concepts of external and internal parameters to increase the appreciation of parametric functions. Other chapters consider separable differential equations with more detail than usual with their suitability in describing physical laws. This book discusses as well the study of variable quantities whose magnitude is determined by the magnitudes of several other variables. The final chapter deals with a homogeneous differential equation and auxiliary equations consisting imaginary roots. This book is a valuable resource for mathematicians and students. Readers whose interests span a variety of fields will also find this book useful.

  • Euclidean and Affine Transformations

    Geometric Transformations
    • 1st Edition
    • P. S. Modenov + 1 more
    • Henry Booker + 2 more
    • English
    Geometric Transformations, Volume 1: Euclidean and Affine Transformations focuses on the study of coordinates, trigonometry, transformations, and linear equations. The publication first takes a look at orthogonal transformations, including orthogonal transformations of the first and second kinds; representations of orthogonal transformations as the products of fundamental orthogonal transformations; and representation of an orthogonal transformation of space as a product of fundamental orthogonal transformations. The text then examines similarity and affine transformations. Topics include properties of affine mappings, Darboux's lemma and its consequences, affine transformations in coordinates, homothetic transformations, similarity transformations of the plane in coordinates, and similarity mapping. The book takes a look at the representation of a similarity transformation as the product of a homothetic transformation and an orthogonal transformation; application of affine transformations to the investigation of properties of the ellipse; and representation of any affine transformation as a product of affine transformations of the simplest types. The manuscript is a valuable reference for high school teachers and readers interested in the Euclidean and affine transformations.

  • Microcomputer Design and Applications

    • 1st Edition
    • Samuel C. Lee
    • English
    Microcomputer Design and Applications provides information pertinent to the fundamental aspects of microcomputer design and applications. This book presents a design approach for multiple-processor computers. Organized into two parts encompassing 16 chapters, this book begins with an overview of a number system and supporting computational algorithms, which is especially useful for microcomputer control and digital signal processing. This text then presents an integrated technical and management-based method for developing microprocessor software. Other chapters consider file structures for a small-scale database system designed for microprocessor implementation and present the formulation of file structures for a typical microprocessor/flopp... disk system. This book discusses as well the proposed solution to specify a high-level, machine-oriented, structured programming language suitable for general microprocessors and to implement a portable compiler for this language. The final chapter deals with a distributed processing system for non-invasive cardiac surveillance. This book is a valuable resource for engineers and computer scientists.

  • Applied Nonlinear Analysis

    Proceedings of an International Conference on Applied Nonlinear Analysis, Held at the University of Texas at Arlington, Arlington, Texas, April 20–22, 1978
    • 1st Edition
    • V. Lakshmikantham
    • English
    Applied Nonlinear Analysis contains the proceedings of an International Conference on Applied Nonlinear Analysis, held at the University of Texas at Arlington, on April 20-22, 1978. The papers explore advances in applied nonlinear analysis, with emphasis on reaction-diffusion equations; optimization theory; constructive techniques in numerical analysis; and applications to physical and life sciences. In the area of reaction-diffusion equations, the discussions focus on nonlinear oscillations; rotating spiral waves; stability and asymptotic behavior; discrete-time models in population genetics; and predator-prey systems. In optimization theory, the following topics are considered: inverse and ill-posed problems with application to geophysics; conjugate gradients; and quasi-Newton methods with applications to large-scale optimization; sequential conjugate gradient-restoration algorithm for optimal control problems with non-differentiable constraints; differential geometric methods in nonlinear programming; and equilibria in policy formation games with random voting. In the area of constructive techniques in numerical analysis, numerical and approximate solutions of boundary value problems for ordinary and partial differential equations are examined, along with finite element analysis and constructive techniques for accretive and monotone operators. In addition, the book explores turbulent fluid flows; stability problems for Hopf bifurcation; product integral representation of Volterra equations with delay; weak solutions of variational problems, nonlinear integration on measures; and fixed point theory. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.

  • Young Tableaux in Combinatorics, Invariant Theory, and Algebra

    An Anthology of Recent Work
    • 1st Edition
    • Joseph P.S. Kung
    • English
    Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians. Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardso... rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory. This volume will be helpful to students and practitioners of algebra.

  • Proceedings of the Third International Conference on Data and Knowledge Bases

    Improving Usability and Responsiveness
    • 1st Edition
    • C. Beeri + 2 more
    • English
    Proceedings of the Third International Conference on Data and Knowledge Bases: Improving Usability and Responsiveness compiles papers presented at the Third International Conference on Data and Knowledge Bases held in Jerusalem, Israel on June 28-30, 1988. This book discusses the management system for graph-like documents, selection of processing strategies for different recursive queries, and supporting concurrent access to facts in logic programs. The design considerations for a Prolog database engine, experience with the domain algebra, and two level transaction management in a multiprocessor database machine are also described. This publication likewise covers the non-deterministic choice in Datalog and locally balanced compact Trie Hashing. This compilation is a good source for researchers and specialists of disciplines related to computer science.

  • Computer Organization and Design

    The Hardware / Software Interface
    • 1st Edition
    • John L. Hennessy + 1 more
    • English
    Computer Organization and Design: The Hardware/Software Interface presents the interaction between hardware and software at a variety of levels, which offers a framework for understanding the fundamentals of computing. This book focuses on the concepts that are the basis for computers. Organized into nine chapters, this book begins with an overview of the computer revolution. This text then explains the concepts and algorithms used in modern computer arithmetic. Other chapters consider the abstractions and concepts in memory hierarchies by starting with the simplest possible cache. This book discusses as well the complete data path and control for a processor. The final chapter deals with the exploitation of parallel machines. This book is a valuable resource for students in computer science and engineering. Readers with backgrounds in assembly language and logic design who want to learn how to design a computer or understand how a system works will also find this book useful.

  • General Topology and Its Relations to Modern Analysis and Algebra 2

    Proceedings of the Second Prague Topological Symposium, 1966
    • 1st Edition
    • Z. Frolík + 2 more
    • English
    General Topology and Its Relations to Modern Analysis and Algebra II is comprised of papers presented at the Second Symposium on General Topology and its Relations to Modern Analysis and Algebra, held in Prague in September 1966. The book contains expositions and lectures that discuss various subject matters in the field of General Topology. The topics considered include the algebraic structure for a topology; the projection spectrum and its limit space; some special methods of homeomorphism theory in infinite-dimensional topology; types of ultrafilters on countable sets; the compactness operator in general topology; and the algebraic generalization of the topological theorems of Bolzano and Weierstrass. This publication will be found useful by all specialists in the field of Topology and mathematicians interested in General Topology.

  • Multi-Objective Programming in the USSR

    • 1st Edition
    • Elliot R. Lieberman
    • Gerald J. Lieberman + 1 more
    • English
    Statistical Modeling and Decision Science: Multi-Objective Programming in the USSR provides information pertinent to multi-objective programming that has emerged as an increasingly active area of research in the fields of applied mathematics, operations research, and decision and management science. This book traces and analyzes the development of Soviet multi-objective programming. Organized into 24 chapters, this book begins with an overview of the research institutes most actively involved in multi-objective programming research. This text then presents an analytical framework for grouping and classifying the diverse Soviet methods. Other chapters consider the methods and then evaluated according to the significance and soundness of its basic approach and its kinship to other methods. This book discusses as well some significant Soviet theoretical research and several distinctive approaches proposed by Soviet researchers for comparing the effectiveness of alternative interactive multi-objective programming method. The final chapter deals with distinctive Soviet tendencies in multi-objective research. This book is a valuable resource for economists.

  • Differential and Riemannian Geometry

    • 1st Edition
    • Detlef Laugwitz
    • English
    Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces. The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry. The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations. The book is a valuable reference for researchers interested in differential and Riemannian geometry.

  • Essentials of Elementary School Mathematics

    • 1st Edition
    • Max D. Larsen + 1 more
    • English
    Essentials of Elementary School Mathematics is an introductory text on the essentials of mathematics taught in elementary schools. It presents a systematic development of the mathematics of arithmetic. A primary objective is to give students a background sufficient to understand and answer at an appropriate level the various quite penetrating questions asked by young students. Some examples and exercises are concerned primarily with pedagogical aspects of arithmetic. Comprised of 14 chapters, this book begins with an overview of the language of mathematics, focusing on concepts such as the conjunction (and); negation (not); disjunction (or); and conditional (if...then...). The discussion then turns to the theory of sets; the concept of binary operations; and recognition and identification of properties of various relations. The next section deals with the number systems of arithmetic: whole numbers, integers, rational numbers, and real numbers. Number theory and clock arithmetic are also examined, along with counting techniques and probability. The final section is devoted to motion geometry and analytic geometry. This monograph should be of interest to students and teachers of mathematicians at the elementary level.

  • A Second Course in Calculus

    • 1st Edition
    • Harley Flanders + 2 more
    • English
    This text, designed for a second year calculus course, can follow any standard first year course in one-variable calculus. Its purpose is to cover the material most useful at this level, to maintain a balance between theory and practice, and to develop techniques and problem solving skills. The topics fall into several categories: Infinite series and integrals Chapter 1 covers convergence and divergence of series and integrals. It ?ontains proofs of basic convergence tests, relations between series and Integrals, and manipulation with geometric, exponential, and related series. Chapter 2 covers approximation of functions by Taylor polynomials, with emphasis on numerical approximations and estimates of remainders. Chapt~r 3 deals with power series, including intervals of convergence, expanSIOns of functions, and uniform convergence. It features calculations with s~ries by algebraic operations, substitution, and term-by-term differentiation and integration. Vector methods Vector algebra is introduced in Chapter 4 and applied to solid analytic geometry. The calculus of one-variable vector functions and its applications to space curves and particle mechanics comprise Chapter 5. Linear algebra Chapter 7 contains a practical introduction to linear algebra in two and three dimensions. We do not attempt a complete treatment of foundations, but rather limit ourselves to thoRe topics that have immediate application to calculus. The main topics are linear transformations in R2 and R3, their matrix representations, manipulation with matrices, linear systems, quadratic forms, and quadric surfaces. Differential calculus of several variables Chapter 6 contains preliminary material on sets in the plane and space, and the definition and basic properties of continuous functions. This is followed by partial derivatives with applications to maxima and minima. Chapter 8 continues with a careful treatment of differentiability and applications to tangent planes, gradients, directional derivatives, and differentials. Here ideas from linear algebra are used judiciously. Chapter 9 covers higher xii Preface order partial derivatives, Taylor polynomials, and second derivative tests for extrema. Multiple integrals In Chapters 10 and 11 we treat double and triple integrals intuitively, with emphasis on iteration, geometric and physical applications, and coordinate changes. In Chapter 12 we develop the theory of the Riemann integral starting with step functions. We continue with Jacobians and the change of variable formula, surface area, and Green's Theorem. Differential equations Chapter 13 contains an elementary treatment of first order equations, with emphasis on linear equations, approximate solutions, and applications. Chapter 14 covers second order linear equations and first order linear systems, including matrix series solutions. These chapters can be taken up any time after Chapter 7. Complex analysis The final chapter moves quickly through basic complex algebra to complex power series, shortcuts using' the complex exponential function, and applications to integration and differential equations. Features The key points of one-variable calculus are reviewed briefly as needed. Optional topics are scattered throughout, for example Stirling's Formula, characteristic roots and vectors, Lagrange multipliers, and Simpson's Rule for double integrals. Numerous worked examples teach practical skills and demonstrate the utility of the theory. We emphaRize Rimple line drawingR that a student can learn to do himself.

  • A Treatise on Trigonometric Series

    Volume 1
    • 1st Edition
    • N. K. Bary
    • English
    A Treatise on Trigonometric Series, Volume 1 deals comprehensively with the classical theory of Fourier series. This book presents the investigation of best approximations of functions by trigonometric polynomials. Organized into six chapters, this volume begins with an overview of the fundamental concepts and theorems in the theory of trigonometric series, which play a significant role in mathematics and in many of its applications. This text then explores the properties of the Fourier coefficient function and estimates the rate at which its Fourier coefficients tend to zero. Other chapters consider some tests for the convergence of a Fourier series at a given point. This book discusses as well the conditions under which the series does converge uniformly. The final chapter deals with adjustment of a summable function outside a given perfect set. This book is a valuable resource for advanced students and research workers. Mathematicians will also find this book useful.

  • Projective Transformations

    Geometric Transformations
    • 1st Edition
    • P. S. Modenov + 1 more
    • Henry Booker + 2 more
    • English
    Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserv... transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

  • Computer Programming

    A Mixed Language Approach
    • 3rd Edition
    • Marvin L. Stein + 1 more
    • English
    Computer Programming: A Mixed Language Approach describes computer programming from a mixed language perspective. More specifically, it examines how to make effective use of the hardware and software aspects of the total system using the mixed languages that are a composite of the absolute machine languages and the more facile problem-oriented languages. In addition to the absolute machine language required by the computer "hardware" and the problem-oriented language provided by the "software" of symbolic assembly programs and compilers, a third kind of programming language is considered, namely, the symbolic machine language. Comprised of nine chapters, this book illustrates mixed language programming using Fortran and the Fortran Symbolic Assembly Program. The discussion begins by describing a modern digital computer and introducing the general theory of number systems. Subsequent chapters focus on the way in which computing machines are organized to perform their functions; how a computer executes the sequence of instructions and performs a given calculation, a process known as coding; and non-arithmetic instructions used on computers. Subroutines, input-output, and assembly of complete programs are also explored. The final chapter is devoted to Fortran and programs written completely in Fortran, as well as executive programs and programs in mixed languages. This monograph is intended for both professional programmers-to-be and non-professionals in computer programming.

  • Functional Analysis and Numerical Mathematics

    • 1st Edition
    • Lothar Collatz
    • English
    Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixed-point theorem for a general iterative method in pseudometric spaces; special cases of the fixed-point theorem and change of operator; iterative methods for differential and integral equations; and systems of equations and difference methods. The manuscript takes a look at monotonicity, inequalities, and other topics, including monotone operators, applications of Schauder's theorem, matrices and boundary value problems of monotone kind, discrete Chebyshev approximation and exchange methods, and approximation of functions. The publication is a valuable source of data for mathematicians and researchers interested in functional analysis and numerical mathematics.

  • Conceptual Information Processing

    • 1st Edition
    • Roger C. Schank
    • English
    Fundamental Studies in Computer Science, 3: Conceptual Information Processing discusses a theory of natural language and implementation of that theory on a computer, focusing basically on an Artificial Intelligence approach to linguistics. This book aims to write computer programs that could understand and generate sentences, which is intended as a first step towards the long range goal of a computer that can communicate with people in natural language. The topics covered include computational linguistics, conceptual dependency theory, history of the analyzer, representation in memory, and structure of BABEL. This publication is a good reference for researchers and specialists working in the field of computer science.

  • French's Index of Differential Diagnosis

    • 11th Edition
    • F. Dudley Hart
    • English
    French's Index of Differential Diagnosis, 11th Edition focuses on treatise on the application of differential diagnosis to all the main signs and symptoms of diseases. The book covers surgery, gynecology, ophthalmology, dermatology, and neurology. The manuscript first ponders on anemia, angioma, antisocial behavior, anxiety, ascites, ataxia, abnormal blood pressure, bradycardia, foulness of breath, and pain in breast. The book then discusses confabulation, cramps, cyanosis, cystinuria, delusions, dementia, diarrhea, diplopia, depression, erythema, and inflammation of eye. The publication takes a look at indigestion, impotence, insomnia, jaundice, keloid, marasmus, muscular atrophy, nasal obstruction, nausea, nasal discharge, swelling of neck, obesity, palpitations, and pelvic swelling. The manuscript also reviews loss of weight, vertigo, vomiting, defects of vision, vaginal discharge, vaginal swelling, sore throat, pain in tongue, trismus, grinding of teeth during sleep, and snoring. The book is a vital reference for researchers wanting to study differential diagnosis.

  • Contributions to Statistics

    • 1st Edition
    • P. C. Mahalanobis
    • C. R. Rao
    • English
    Contributions to Statistics focuses on the processes, methodologies, and approaches involved in statistics. The book is presented to Professor P. C. Mahalanobis on the occasion of his 70th birthday. The selection first offers information on the recovery of ancillary information and combinatorial properties of partially balanced designs and association schemes. Discussions focus on combinatorial applications of the algebra of association matrices, sample size analogy, association matrices and the algebra of association schemes, and conceptual statistical experiments. The book then examines lattice sampling by means of Lahiri's sampling scheme; contributions of interpenetrating networks of samples; and apparently unconnected problems encountered in sampling work. The publication takes a look at screening processes, place of the design of experiments in the logic of scientific inference, and rarefaction. Topics include mathematical probability, scientific experience, combinatorial progress, gains and losses, criterion and scores, simple drug screening process, and screening of crop varieties. The manuscript then reviews the estimation and interpretation of gross differences and the simple response variance; partially balanced asymmetrical factorial designs; and approximation of distributions of sums of independent summands by infinitely divisible distributions. The selection is a dependable reference for statisticians and researchers interested in the processes, methodologies, and approaches employed in statistics.

  • A Course of Higher Mathematics

    Adiwes International Series in Mathematics, Volume 4
    • 1st Edition
    • V. I. Smirnov
    • A. J. Lohwater
    • English
    A Course of Higher Mathematics, Volume IV provides information pertinent to the theory of the differential equations of mathematical physics. This book discusses the application of mathematics to the analysis and elucidation of physical problems. Organized into four chapters, this volume begins with an overview of the theory of integral equations and of the calculus of variations which together play a significant role in the discussion of the boundary value problems of mathematical physics. This text then examines the basic theory of partial differential equations and of systems of equations in which characteristics play a key role. Other chapters consider the theory of first order equations. This book discusses as well some concrete problems that indicate the aims and ideas of the calculus of variations. The final chapter deals with the boundary value problems of mathematical physics. This book is a valuable resource for mathematicians and readers who are embarking on the study of functional analysis.

  • Curves and Surfaces

    • 1st Edition
    • Pierre-Jean Laurent + 2 more
    • English
    Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Other chapters consider a nonparametric technique for estimating under random censorship the amplitude of a change point in change point hazard models. This book discusses as well the algorithm for ray tracing rational parametric surfaces based on inversion and implicitization. The final chapter deals with the results concerning the norm of the interpolation operator and error estimates for a square domain. This book is a valuable resource for mathematicians.

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