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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.

  • Locking Performance in Centralized Databases

    • 1st Edition
    • Y.C. Tay
    • W. Rheinboldt + 1 more
    • English
    Perspectives in Computing: Locking Performance in Centralized Databases reports some results from a project whose aim was the development of a performance model for concurrency control algorithms. This book proposes a model that is powerful enough to help users understand, compare, and control the performance of the algorithms. Organized into four chapters, this book begins with an overview of the model in its simplest form. This text then explains locking, which uses a combination of blocking and restarts to achieve correctness. Other chapters test the model and the method of analysis by comparing the model's predictions to simulation results wherein the prediction and simulations indicate that restarts can cause thrashing. This book discusses as well the formula for throughput and for the restart rate. The final chapter deals with the adaptation of the model to timestamping and distributed algorithms. This book is a valuable resource for mathematicians and research workers.

  • Statistical Inference and Related Topics

    Proceedings of the Summer Research Institute on Statistical Inference for Stochastic Processes, Bloomington, Indiana, July 31 – August 9, 1975
    • 1st Edition
    • Madan Lal Puri
    • English
    Statistical Inference and Related Topics, Volume 2 presents the proceedings of the Summer Research Institute on Statistical Inference for Stochastic Processes, held in Bloomingdale, Indiana on July 31 to August 9, 1975. This book focuses on the theory of statistical inference for stochastic processes. Organized into 15 chapters, this volume begins with an overview of the case of continuous distributions with one real parameter. This text then reviews some results for multidimensional empirical processes and Brownian sheets when they are indexed by families of sets. Other chapters consider a class of cubic spline estimators of probability density functions over a finite interval. This book discusses as well the method to construct nonelimination type sequential procedures to select a subset containing all the superior populations. The final chapter deals with Markov sequences, which are among the most interesting available for study with a rich theory and varied applications. This book is a valuable resource for graduate students and research workers.

  • Numerical Algebra

    • 1st Edition
    • John Todd
    • Ch. Blanc + 2 more
    • English
    Basic Numerical Mathematics, Volume II: Numerical Algebra focuses on numerical algebra, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The existence of an orthogonal matrix which diagonalizes a real symmetric matrix is highlighted, and partitioned or block matrices are discussed, along with induced norms and inversion problems. Comprised of 12 chapters, this volume begins with an overview of the manipulation of vectors and matrices, followed by an analysis of induced norms. The reader is then introduced to the direct solution of the inversion problem, first in the context of theoretical arithmetic (that is, when round-off is disregarded) and second in the context of practical computation. Various methods of handling the characteristic value problems are also considered, together with several iterative methods for the solution of a system of linear equations. Two applications are described: the solution of a two-point boundary value problem and the solution of least squares curve fitting. The book concludes with an account of the singular value decomposition and pseudo-inverses. This monograph will be of interest to mathematicians and students of mathematics.

  • Frontiers of Pattern Recognition

    The Proceedings of the International Conference on Frontiers of Pattern Recognition
    • 1st Edition
    • Satosi Watanabe
    • English
    Frontiers of Pattern Recognition contains the proceedings of the International Conference on Frontiers of Pattern Recognition which took place on January 18-20, 1971, at the University of Hawaii, Honolulu. The compendium consists of 30 papers from authorities from eleven different countries, which describe the frontiers of pattern recognition as viewed from diverse viewpoints. Topics discussed include some techniques for recognizing structures in pictures, grammatical inference, syntactic pattern recognition and stochastic languages, and pattern cognition and the organization of information. Also covered are subjects on human face recognition, cluster analysis, and learning algorithms of pattern recognition in non-stationary conditions. Computer scientists, mathematicians, statisticians, linguists, and psychologists will find the book informative.

  • Control Theory of Systems Governed by Partial Differential Equations

    • 1st Edition
    • A.K. Aziz + 2 more
    • English
    Control Theory of Systems Governed by Partial Differential Equations covers the proceedings of the 1976 Conference by the same title, held at the Naval Surface Weapons Center, Silver Spring, Maryland. The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type. This chapter also explores the control of free surfaces and the geometrical control variables. The last chapter provides a summary of the features and applications of the numerical approximation of problems of optimal control. This book will prove useful to mathematicians, engineers, and researchers.

  • Analytic Computational Complexity

    • 1st Edition
    • J.F. Traub
    • English
    Analytic Computational Complexity contains the proceedings of the Symposium on Analytic Computational Complexity held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7-8, 1975. The symposium provided a forum for assessing progress made in analytic computational complexity and covered topics ranging from strict lower and upper bounds on iterative computational complexity to numerical stability of iterations for solution of nonlinear equations and large linear systems. Comprised of 14 chapters, this book begins with an introduction to analytic computational complexity before turning to proof techniques used in analytic complexity. Subsequent chapters focus on the complexity of obtaining starting points for solving operator equations by Newton's method; maximal order of multipoint iterations using n evaluations; the use of integrals in the solution of nonlinear equations in N dimensions; and the complexity of differential equations. Algebraic constructions in an analytic setting are also discussed, along with the computational complexity of approximation operators. This monograph will be of interest to students and practitioners in the fields of applied mathematics and computer science.

  • 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.

  • Introduction to Probability Models

    • 5th Edition
    • Sheldon M. Ross
    • English
    Introduction to Probability Models, Fifth Edition focuses on different probability models of natural phenomena. This edition includes additional material in Chapters 5 and 10, such as examples relating to analyzing algorithms, minimizing highway encounters, collecting coupons, and tracking the AIDS virus. The arbitrage theorem and its relationship to the duality theorem of linear program are also covered, as well as how the arbitrage theorem leads to the Black-Scholes option pricing formula. Other topics include the Bernoulli random variable, Chapman-Kolmogorov equations, and properties of the exponential distribution. The continuous-time Markov chains, single-server exponential queueing system, variations on Brownian motion; and variance reduction by conditioning are also elaborated. This book is a good reference for students and researchers conducting work on probability models.

  • Mathematical Techniques of Applied Probability

    Discrete Time Models: Basic Theory
    • 1st Edition
    • Jeffrey J. Hunter
    • J. William Schmidt
    • English
    Mathematical Techniques of Applied Probability, Volume 1: Discrete Time Models: Basic Theory provides information pertinent to the basic theory of discrete time models. This book introduces the tools of generating functions and matrix theory to facilitate a detailed study of such models. Organized into five chapters, this volume begins with an overview of the elementary theory of probability for discrete random variables. This text then reviews the concepts of convergence, absolute convergence, uniform convergence, continuity, differentiation, and integration. Other chapters consider the occurrence of general patterns of successes and failures in Bernoulli trials. This book discusses as well the matrix theory, which is used in the study of stochastic processes, particularly in the analysis of the behavior of Markov chains. The final chapter deals with the properties of a special class of discrete time chains. This book is a valuable resource for students and teachers.

  • Discriminant Analysis and Applications

    • 1st Edition
    • T. Cacoullos
    • English
    Discriminant Analysis and Applications comprises the proceedings of the NATO Advanced Study Institute on Discriminant Analysis and Applications held in Kifissia, Athens, Greece in June 1972. The book presents the theory and applications of Discriminant analysis, one of the most important areas of multivariate statistical analysis. This volume contains chapters that cover the historical development of discriminant analysis methods; logistic and quasi-linear discrimination; and distance functions. Medical and biological applications, and computer graphical analysis and graphical techniques for multidimensional data are likewise discussed. Statisticians, mathematicians, and biomathematicians will find the book very interesting.

  • Waves on Fluid Interfaces

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 18–20, 1982
    • 1st Edition
    • Richard E. Meyer
    • English
    Mathematics Research Center Symposium: Waves on Fluid Interfaces covers the proceedings of a symposium conducted by the Mathematics Research Center of the University of Wisconsin-Madison on October 18-20, 1982. The book focuses on nonlinear instabilities of classical interfaces, physical structure of real interfaces, and the challenges these reactions pose to the understanding of fluids. The selection first elaborates on finite-amplitude interfacial waves, instability of finite-amplitude interfacial waves, and finite-amplitude water waves with surface tension. Discussions focus on reformulation as an integro-differential equation, perturbation solutions, results for interfacial waves with current jump, wave of zero height, weakly nonlinear waves, and numerical methods. The text then takes a look at generalized vortex methods for free-surface flows; a review of solution methods for viscous flow in the presence of deformable boundaries; and existence criteria for fluid interfaces in the absence of gravity. The book ponders on the endothelial interface between tissue and blood, moving contact line, rupture of thin liquid films, film waves, and interfacial instabilities caused by air flow over a thin liquid layer. Topics include stability analysis of liquid film, interpretation of film instabilities, simple film, linear stability theory, inadequacy of the usual hydrodynamic model, and marcomolecule transport across the artery wall. The selection is a valuable source of data for researchers interested in the reactions of waves on fluid interfaces.

  • Applications of Number Theory to Numerical Analysis

    • 1st Edition
    • S. K. Zaremba
    • English
    Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.

  • Introduction to Parallel Programming

    • 1st Edition
    • Steven Brawer
    • English
    Introduction to Parallel Programming focuses on the techniques, processes, methodologies, and approaches involved in parallel programming. The book first offers information on Fortran, hardware and operating system models, and processes, shared memory, and simple parallel programs. Discussions focus on processes and processors, joining processes, shared memory, time-sharing with multiple processors, hardware, loops, passing arguments in function/subroutine calls, program structure, and arithmetic expressions. The text then elaborates on basic parallel programming techniques, barriers and race conditions, and nested loops. The manuscript takes a look at overcoming data dependencies, scheduling summary, linear recurrence relations, and performance tuning. Topics include parallel programming and the structure of programs, effect of the number of processes on overhead, loop splitting, indirect scheduling, block scheduling and forward dependency, and induction variable. The publication is a valuable reference for researchers interested in parallel programming.

  • Introduction to Discrete Linear Controls

    Theory and Application
    • 1st Edition
    • Albert B. Bishop
    • J. William Schmidt
    • English
    Introduction to Discrete Linear Controls: Theory and Applications focuses on the design, analysis, and operation of discrete-time decision processes. The publication first offers information on systems theory and discrete linear control systems, discrete control-system models, and the calculus of finite differences. Discussions focus on the calculus of finite differences and linear difference equations, summations, control of cylinder diameter, generalized discrete process controller with sampling, difference equations, control theory, and system models. The text then examines classical solution of linear difference equations with constant, inverse transformation, and measures and environmental effects of system performance. The manuscript takes a look at parameter selection in first-order systems considering sampling and instrumentation errors, second-order systems, and system instability, including responses of the generalized second-order process controller; criterion for stability of discrete linear systems; and proportional-plus-di... control. The publication is a valuable source of information for engineers, operations researchers, and systems analysts.

  • Iterative Solution of Nonlinear Equations in Several Variables

    • 1st Edition
    • J. M. Ortega + 1 more
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution. This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods. This publication is a good reference for specialists and readers with an extensive functional analysis background.

  • Group Theory and Its Applications

    Volume III
    • 1st Edition
    • Ernest M. Loebl
    • English
    Group Theory and its Applications, Volume III covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with an introduction to Wedderburn’s theory to establish the structure of semisimple algebras, algebras of quantum mechanical interest, and group algebras. The succeeding chapter deals with Dynkin’s theory for the embedding of semisimple complex Lie algebras in semisimple complex Lie algebras. These topics are followed by a review of the Frobenius algebra theory, its centrum, its irreducible, invariant subalgebras, and its matric basis. The discussion then shifts to the concepts and application of the Heisenberg-Weyl ring to quantum mechanics. Other chapters explore some well-known results about canonical transformations and their unitary representations; the Bargmann Hilbert spaces; the concept of complex phase space; and the concept of quantization as an eigenvalue problem. The final chapter looks into a theoretical approach to elementary particle interactions based on two-variable expansions of reaction amplitudes. This chapter also demonstrates the use of invariance properties of space-time and momentum space to write down and exploit expansions provided by the representation theory of the Lorentz group for relativistic particles, or the Galilei group for nonrelativistic ones. This book will prove useful to mathematicians, engineers, physicists, and advance students.

  • Nonlinear Evolution Equations

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 17–19, 1977
    • 1st Edition
    • Michael G. Crandall
    • English
    Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on October 17-19, 1977. This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm’s method. The next chapters examine the theoretical and practical aspects of Boltzmann, Navier-Stokes, and evolution equations. These topics are followed by discussions of the practical applications of Trotter’s product formula for some nonlinear semigroups and the finite time blow-up in nonlinear problems. The closing chapters deal with a Hamiltonian approach to the K-dV and other equations, along with a variational method for finding periodic solutions of differential equations. This book will prove useful to mathematicians and engineers.

  • Probabilistic Analysis and Related Topics

    Volume 1
    • 1st Edition
    • A. T. Bharucha-Reid
    • English
    Probabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator theory, measure theory, and numerical analysis. The selection first offers information on stochastic partial differential equations in turbulence related problems and estimation and stochastic control for linear infinite-dimensional systems. Discussions focus on deterministic quadratic cost-control problem; partial differential equations in stochastic wave propagation; and theory of stochastic partial differential equations. The text then examines random integrodifferential equations, including small perturbations, existence and uniqueness of solutions, stochastic properties of solution processes, and vibration string. The manuscript ponders on equivalence and singularity of Gaussian measures and applications and stochastic Riemannian geometry. Concerns include semilocal properties, Brownian motion, reproducing kernel Hilbert spaces and Gaussian processes, equivalence and singularity of Gaussian processes, and general problem of equivalence and singularity. The selection is a vital source of information for mathematicians and researchers interested in the general theory of random functions.

  • Science, Computers, and the Information Onslaught

    A Collection of Essays
    • 1st Edition
    • Donald M. Kerr + 2 more
    • English
    Science, Computers, and the Information Onslaught: A Collection of Essays covers the proceedings of the 1981 meeting on “Science and the Information Onslaught”, held at Los Alamos, New Mexico. This book is organized into five parts encompassing 19 chapters. The first part deals with the problems of measurement and the uses of information in decisions concerning national security. This part also emphasizes the dependence of survival on technological progress. The next part examines the foundations of information theory, the interaction between psychological concepts and the mathematical theories of automata, and the major problems in robotics. These topics are followed by discussions of the efforts to codify languages in formal grammatical systems and the past misuse of irrelevantly detailed information in decision making, specifically the use and misuse of information in government decisions about technological projects. The remaining parts consider the project of enhancing human abilities by the insertion of silicon chips in the body. These parts also assess the implications of a microelectronic technology capable of producing chips bearing millions of logically active circuit elements. Accounts of cryptanalytic successes in World War II are also included. This book will be of value to mathematicians, physicists, linguistics, and computer scientists.

  • Random Polynomials

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • A. T. Bharucha-Reid + 1 more
    • Z. W. Brinbaum + 1 more
    • English
    Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Random Polynomials focuses on a comprehensive treatment of random algebraic, orthogonal, and trigonometric polynomials. The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials. The text then elaborates on the number and expected number of real zeros of random algebraic polynomials; number and expected number of real zeros of other random polynomials; and variance of the number of real zeros of random algebraic polynomials. Topics include the expected number of real zeros of random orthogonal polynomials and the number and expected number of real zeros of trigonometric polynomials. The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials. The publication is a dependable reference for probabilists, statisticians, physicists, engineers, and economists.

  • Metric Affine Geometry

    • 1st Edition
    • Ernst Snapper + 1 more
    • English
    Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.

  • Applied Fuzzy Systems

    • 1st Edition
    • Toshiro Terano + 2 more
    • English
    Applied Fuzzy Systems provides information pertinent to the fundamental aspects of fuzzy systems theory and its application. This book discusses the development of high-level artificial intelligence and information processing systems, as well as the realization of fuzzy computers. Organized into six chapters, this book begins with an overview of the fundamental problems addressed by fuzzy systems. This text then reviews standard computer logic or two-valued Boolean algebra. Other chapters consider bus scheduling, evaluation of structural reliability, applications of schema systems for decision-making, and processing of natural-language information and systems for medical diagnosis as examples of fuzzy expert systems. This book discusses as well a practical fuzzy expert system for durability evaluations of reinforced concrete slabs for bridges, along with an example of application. The final chapter deals with the important parts of the construction of fuzzy computers, their architecture, and the outlook for the future. This book is a valuable resource for engineers, mathematicians, technicians, and research workers.

  • Studies in Topology

    • 1st Edition
    • Nick M. Stavrakas + 1 more
    • English
    Studies in Topology is a compendium of papers dealing with a broad portion of the topological spectrum, such as in shape theory and in infinite dimensional topology. One paper discusses an approach to proper shape theory modeled on the "ANR-systems" of Mardesic-Segal, on the "mutations" of Fox, or on the "shapings" of Mardesic. Some papers discuss homotopy and cohomology groups in shape theory, the structure of superspace, on o-semimetrizable spaces, as well as connected sets that have one or more disconnection properties. One paper examines "weak" compactness, considered as either a strengthening of absolute closure or a weakening of relative compactness (subject to entire topological spaces or to subspaces of larger spaces). To construct spaces that have only weak properties, the investigator can use the various productivity theorems of Scarborough and Stone, Saks and Stephenson, Frolik, Booth, and Hechler. Another paper analyzes the relationship between "normal Moore space conjecture" and productivity of normality in Moore spaces. The compendium is suitable for mathematicians, physicists, engineers, and other professionals involved in topology, set theory, linear spaces, or cartography.

  • Numerical Methods for Partial Differential Equations

    • 2nd Edition
    • William F. Ames
    • Werner Rheinboldt + 1 more
    • English
    Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.

  • Stochastic Analysis

    Liber Amicorum for Moshe Zakai
    • 1st Edition
    • Eddy Mayer-Wolf + 2 more
    • English
    Stochastic Analysis: Liber Amicorum for Moshe Zakai focuses on stochastic differential equations, nonlinear filtering, two-parameter martingales, Wiener space analysis, and related topics. The selection first ponders on conformally invariant and reflection positive random fields in two dimensions; real time architectures for the Zakai equation and applications; and quadratic approximation by linear systems controlled from partial observations. Discussions focus on predicted miss, review of basic sequential detection problems, multigrid algorithms for the Zakai equation, invariant test functions and regularity, and reflection positivity. The text then takes a look at a model of stochastic differential equation in Hubert spaces applicable to Navier Stokes equation in dimension 2; wavelets as attractors of random dynamical systems; and Markov properties for certain random fields. The publication examines the anatomy of a low-noise jump filter, nonlinear filtering with small observation noise, and closed form characteristic functions for certain random variables related to Brownian motion. Topics include derivation of characteristic functions for the examples, proof of the theorem, sequential quadratic variation test, asymptotic optimal filters, mean decision time, and asymptotic optimal filters. The selection is a valuable reference for researchers interested in stochastic analysis.

  • 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.

  • Algebraic Analysis

    Papers Dedicated to Professor Mikio Sato on the Occasion of His Sixtieth Birthday
    • 1st Edition
    • Masaki Kashiwara + 1 more
    • English
    Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion of his 60th Birthday, Volume II is a collection of research papers on algebraic analysis and related topics in honor to Professor Mikio Sato’s 60th birthday. This volume is divided into 29 chapters and starts with research works concerning the fundamentals of KP equations, strings, Schottky problem, and the applications of transformation theory for nonlinear integrable systems to linear prediction problems and isospectral deformations,. The subsequent chapters contain papers on the approach to nonlinear integrable systems, the Hodge numbers, the stochastic different equation for the multi-dimensional weakly stationary process, and a method of harmonic analysis on semisimple symmetric spaces. These topics are followed by studies on the quantization of extended vortices, moduli space for Fuchsian groups, microfunctions for boundary value problems, and the issues of multi-dimensional integrable systems. The remaining chapters explore the practical aspects of pseudodifferential operators in hyperfunction theory, the elliptic solitons, and Carlson’s theorem for holomorphic functions. This book will prove useful to mathematicians and advance mathematics students.

  • Multivariable Calculus, Linear Algebra, and Differential Equations

    • 2nd Edition
    • Stanley I. Grossman
    • English
    Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in "n" variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus.

  • The Architecture of Supercomputers

    Titan, a Case Study
    • 1st Edition
    • Daniel P. Siewiorek + 1 more
    • English
    The Architecture of Supercomputers: Titan, A Case Study describes the architecture of the first member of an entirely new computing class, the graphic supercomputing workstation known as Titan. This book is divided into seven chapters. Chapter 1 provides an overview of the Titan architecture, including the motivation, organization, and processes that created it. A survey of all the techniques to speed up computation is presented in Chapter 2. Chapter 3 reviews the issue of particular benchmarks and measures, while Chapter 4 analyzes a model of a concurrency hierarchy extending from the register set to the entire operating system. The architecture of Titan graphics supercomputer and its implementation are considered in Chapter 5. Chapter 6 examines the performance of Titan in terms of the various information flow data rates. The last chapter is devoted to the actual performance on benchmark kernels and how the architecture and implementation affect performance. This publication is recommended for architects and engineers designing processors and systems.

  • 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.

  • Graphical Representation of Multivariate Data

    • 1st Edition
    • Peter C. C. Wang
    • English
    Graphical Representation of Multivariate Data is a collection of papers that explores and expands the use of graphical methods to represent multivariate data. One paper explains the application of the graphical representation of k-dimensional data technique as a statistical tool to analyze Soviet foreign policy. The technique encompasses data files, data modifications, and transformations of Soviet foreign policy in 25 countries from 1964 to 1975. The Faces methodology (a representation of multidimensional data developed by Herman Chernoff) analyzes ten sets of these data. Another paper describes the Faces techniques, Andrew's sine curves, Anderson's metroglyphs, which are then compared to Facial representations. Examples show the application of Chernoff Faces at the Los Alamos Scientific Laboratory. The paper considers the technique's main drawback—subjectivit... a positive feature that can be overcome. Another paper agrees that computer-generated faces are a good representations to induce actions on tasks based on multivariate metrical data, The paper also acknowledges that the stereotyping of faces can be useful when making a display. One paper investigates the responsiveness to facial and verbal cues using the Syracuse person perception tool as a measuring tool. The collection is suitable for investigators, professors, or students in mathematics, computer science, or engineering courses. It will also be very helpful for researchers involved in graphical display of multivariate data from a wide range of different fields such as statistics, economics, regional planning, clinical research, social/political science, psychiatric studies, international relations, international trade, and arms transfer.

  • Picture Languages

    Formal Models for Picture Recognition
    • 1st Edition
    • Azriel Rosenfeld
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Picture Languages: Formal Models for Picture Recognition treats pictorial pattern recognition from the formal standpoint of automata theory. This book emphasizes the capabilities and relative efficiencies of two types of automata—array automata and cellular array automata, with respect to various array recognition tasks. The array automata are simple processors that perform sequences of operations on arrays, while the cellular array automata are arrays of processors that operate on pictures in a highly parallel fashion, one processor per picture element. This compilation also reviews a collection of results on two-dimensional sequential and parallel array acceptors. Some of the analogous one-dimensional results and array grammars and their relation to acceptors are likewise covered in this text. This publication is suitable for researchers, professionals, and specialists interested in pattern recognition and automata theory.

  • 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.

  • Multivariable Calculus with Linear Algebra and Series

    • 1st Edition
    • William F. Trench + 1 more
    • English
    Multivariable Calculus with Linear Algebra and Series presents a modern, but not extreme, treatment of linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples. Comprised of seven chapters, this book begins with an introduction to linear equations and matrices, including determinants. The next chapter deals with vector spaces and linear transformations, along with eigenvalues and eigenvectors. The discussion then turns to vector analysis and analytic geometry in R3; curves and surfaces; the differential calculus of real-valued functions of n variables; and vector-valued functions as ordered m-tuples of real-valued functions. Integration (line, surface, and multiple integrals) is also considered, together with Green's and Stokes's theorems and the divergence theorem. The final chapter is devoted to infinite sequences, infinite series, and power series in one variable. This monograph is intended for students majoring in science, engineering, or mathematics.

  • Analytic Geometry

    • 1st Edition
    • A. C. Burdette
    • English
    Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus. This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes. This book will prove useful to undergraduate trigonometric students.

  • Methods of Numerical Integration

    • 2nd Edition
    • Philip J. Davis + 1 more
    • Werner Rheinbolt
    • English
    Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.

  • Combinatorics

    • 1st Edition
    • N. Ya. Vilenkin
    • English
    Combinatorics deals with simple combinatorial problems, recurrence relations, and generating functions, particularly the binomial expansions. The book expounds on the general rules of combinatorics, the rule of sum, the rule of product, samples, permutations, combinations, and arrangements of subjects with various restrictions. The text also explains ordered or unordered partitions of numbers, geometric methods, random walk problems, and variants of the arithmetical triangle. One example of the use of combinatorics is the choice of the number 3 in the genetic code. Another example involves the choice of crew for a spaceship where it is necessary to consider the psychological conditions of the applicants for space travel. The text also investigates the sieve of Erastothenes whose problem concerns finding all the primes in the sequence of natural numbers from 1 to N. The book also tackles the application of power series to proof of identities, the binomial series expansion, decomposition into elementary fractions, and nonlinear recurrence relation. The book can be highly educational and interesting to students or academicians involved in mathematics, algebra, and statistics.

  • Handbook of Mathematical Formulas

    • 1st Edition
    • Hans-Jochen Bartsch
    • English
    Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.

  • Calculus

    • 2nd Edition
    • Stanley I. Grossman
    • English
    Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis. This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics include the sequences of real numbers, dot product, arc length as a parameter, quadric surfaces, higher-order partial derivatives, and Green's theorem in the plane. This publication is a good source for students learning calculus.

  • Geometry and Combinatorics

    • 1st Edition
    • J. J. Seidel
    • D. G. Corneil + 1 more
    • English
    Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.

  • Statistical Methods and the Improvement of Data Quality

    • 1st Edition
    • Tommy Wright
    • English
    Statistical Methods and the Improvement of Data Quality contains the proceedings of The Small Conference on the Improvement of the Quality of Data Collected by Data Collection Systems, held on November 11-12, 1982, in Oak Ridge, Tennessee. The conference provided a forum for discussing the use of statistical methods to improve data quality, with emphasis on the problems of data collection systems and how to handle them using state-of-the-art techniques. Comprised of 16 chapters, this volume begins with an overview of some of the limitations of surveys, followed by an annotated bibliography on frames from which the probability sample is selected. The reader is then introduced to sample designs and methods for collecting data over space and time; response effects to behavior and attitude questions; and how to develop and use error profiles. Subsequent chapters focus on principles and methods for handling outliers in data sets; influence functions, outlier detection, and data editing; and application of pattern recognition techniques to data analysis. The use of exploratory data analysis as an aid in modeling and statistical forecasting is also described. This monograph is likely to be of primary benefit to students taking a general course in survey sampling techniques, and to individuals and groups who deal with large data collection systems and are constantly seeking ways to improve the overall quality of their data.

  • College Algebra

    • 2nd Edition
    • Bernard Kolman + 1 more
    • English
    College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book. College students will find the book very useful and invaluable.

  • Introduction to Abstract Mathematics

    • 1st Edition
    • T. A. Bick
    • English
    Introduction to Abstract Mathematics focuses on the principles, approaches, and operations involved in abstract mathematics, including metric spaces, sets, axiom systems, and open sentences. The book first offers information on logic and set theory, natural numbers, and integers and rational numbers. Discussions focus on rational numbers and ordered fields, ordering, arithmetic, axiom systems and methods of proof, functions of kindred matters, ordered pairs and relations, sets, and statements and open sentences. The text then examines real and complex numbers, metric spaces, and limits. Topics include generalized limits, continuous functions, openness, closedness, and neighborhood systems, definition and basic properties, and construction of R. The publication is a vital reference for mathematicians and students interested in abstract mathematics.

  • First Course in Algebra and Number Theory

    • 1st Edition
    • Edwin Weiss
    • English
    First Course in Algebra and Number Theory presents the basic concepts, tools, and techniques of modern algebra and number theory. It is designed for a full year course at the freshman or sophomore college level. The text is organized into four chapters. The first chapter is concerned with the set of all integers - positive, negative, and zero. It investigates properties of Z such as division algorithm, Euclidean algorithm, unique factorization, greatest common divisor, least common multiple, congruence, and radix representation. In chapter 2, additional axioms about Z were introduced and some of their consequences are discussed. The third chapter sets up terminologies about polynomials, solutions or roots of polynomial equations, and factorization of polynomials. Finally, chapter 4 studies logically simpler algebraic systems, known as "groups", algebraic objects with a single operation. The book is intended for students in the freshman and sophomore levels in college.

  • Operating Systems

    • 1st Edition
    • Dionysios C. Tsichritzis + 1 more
    • Werner Rheinboldt
    • English
    Operating Systems deals with the fundamental concepts and principles that govern the behavior of operating systems. Many issues regarding the structure of operating systems, including the problems of managing processes, processors, and memory, are examined. Various aspects of operating systems are also discussed, from input-output and files to security, protection, reliability, design methods, performance evaluation, and implementation methods. Comprised of 10 chapters, this volume begins with an overview of what constitutes an operating system, followed by a discussion on the definition and properties of the basic unit of computation within an operating system, the process. The reader is then introduced to processor allocation schemes as well as various classes of scheduling disciplines and their implementations; memory management functions; and virtual memory. Subsequent chapters focus on input-output and files; protection in an operating system; and design and implementation of an operating system. The book concludes by describing two operating systems to help the reader visualize how the major components of a system interact in a complete system: the Venus Operating System developed by MITRE Corp. and the SUE nucleus, designed at the University of Toronto. This monograph is intended for fourth-year undergraduates and first-year graduate students, as well as lecturers who plans to institute a course on operating systems.

  • Numerical Methods for Initial Value Problems in Ordinary Differential Equations

    • 1st Edition
    • Simeon Ola Fatunla
    • Werner Rheinboldt + 1 more
    • English
    Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implic... singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.

  • Mathematical Functions and Their Approximations

    • 1st Edition
    • Yudell L. Luke
    • English
    Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

  • 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.

  • Programming Language Structures

    • 1st Edition
    • Elliott I. Organick + 2 more
    • English
    Programming Language Structures deals with the structures of programming languages and introduces the reader to five important programming languages: Algol, Fortran, Lisp, Snobol, and Pascal. The fundamental similarities and differences among these languages are discussed. A unifying framework is constructed that can be used to study the structure of other languages, such as Cobol, PL/I, and APL. Several of the tools and methodologies needed to construct large programs are also considered. Comprised of 10 chapters, this book begins with a summary of the relevant concepts and principles about algorithms, flowcharts, and computation that a student is expected to know from the first course. The discussion then turns to the semantics of procedure and function call as well as argument-parameter matching with various kinds of parameters; recursion and its relation to tree traversal; syntax formalism for context-free languages; and ALGOL 60 and block structuring. Case study programs are presented to reinforce the reader's understanding of ALGOL 60 and Fortran semantics. The remaining chapters deal with Lisp, Snobol, and Pascal. This monograph is intended for working programmers and students in computer science who have an interest in the subject of programming.

  • Computability, Complexity, and Languages

    Fundamentals of Theoretical Computer Science
    • 1st Edition
    • Martin D. Davis + 1 more
    • Werner Rheinboldt
    • English
    Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science provides an introduction to the various aspects of theoretical computer science. Theoretical computer science is the mathematical study of models of computation. This text is composed of five parts encompassing 17 chapters, and begins with an introduction to the use of proofs in mathematics and the development of computability theory in the context of an extremely simple abstract programming language. The succeeding parts demonstrate the performance of abstract programming language using a macro expansion technique, along with presentations of the regular and context-free languages. Other parts deal with the aspects of logic that are important for computer science and the important theory of computational complexity, as well as the theory of NP-completeness. The closing part introduces the advanced recursion and polynomial-time computability theories, including the priority constructions for recursively enumerable Turing degrees. This book is intended primarily for undergraduate and graduate mathematics students.

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