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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.

  • Statistical Computation

    • 1st Edition
    • Roy C. Milton + 1 more
    • English
    Statistical Computation covers the proceedings of a conference held at the University of Wisconsin in Madison, Wisconsin on April 28-30, 1969. The book focuses on the methodologies, techniques, principles, and approaches involved in statistical computation. The selection first elaborates on the description of data structures for statistical computing, autocodes for the statistician, and an experimental data structure for statistical computing. Discussions focus on data-system organization, data structures, autocode requirements, data matrix, structure formulas, and structure formulas in data processing and output. The text then examines statistics and computers in relation to large data bases, statistical data language, facilities in a statistical program system for analysis of multiply-indexed data, and language design and the needs of statisticians. The book takes a look at time sharing and interactive statistics, an approach to conversational statistics, use of APL in statistics, and continuing development of a statistical system. Topics include arithmetic operations and branching statements, ASCOP system, application to statistics, semantics, pragmatics, and implementation. The selection is a valuable reference for statisticians and researchers interested in statistical computation.

  • Introductory College Mathematics

    with Linear Algebra and Finite Mathematics
    • 1st Edition
    • Harley Flanders + 1 more
    • English
    Introductory College Mathematics: With Linear Algebra and Finite Mathematics is an introduction to college mathematics, with emphasis on linear algebra and finite mathematics. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; the fundamental ideas of linear algebra; and complex numbers, elementary combinatorics, the binomial theorem, and mathematical induction. Comprised of 15 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors and matrices, and trigonometry are also explored, together with complex numbers, linear transformations, and the geometry of space. The book concludes by considering finite mathematics, with particular reference to mathematical induction and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

  • Computer-Assisted Analysis and Model Simplification

    Proceedings of the First Symposium on Computer-Assisted Analysis and Model Simplification, University of Colorado, Boulder, Colorado, March 28, 1980
    • 1st Edition
    • Harvey J. Greenberg + 1 more
    • English
    Computer-Assisted Analysis and Model Simplification deals with problems associated with the implementation, understanding, and management of large-scale, computer-resident models. This book focuses on five general research areas—structural modeling, qualitative economics, mathematical programming systems, relational databases, and combinatorics. In these topics, this compilation discusses the scope of computer-assisted analysis and model, structural models and graph theory, and qualitative stability of matrices and economic theory. The strong sign-solvability and weak satisfiability, automatic identification of embedded structure in large-scale optimization models, and query systems for linear programming models are also deliberated. This publication is a good source for students, specialists, and researchers interested in computer-assisted analysis and model simplification.

  • Table of Integrals, Series, and Products

    • 1st Edition
    • I. S. Gradshteyn + 1 more
    • English
    Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

  • Algebra for College Students

    • 1st Edition
    • Bernard Kolman + 1 more
    • English
    Algebra for College Students, Revised and Expanded Edition is a complete and self-contained presentation of the fundamentals of algebra which has been designed for use by the student. The book provides sufficient materials for use in many courses in college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, sets and set notation, matrices and their application in solving linear systems, and notation of functions. The theory of polynomial equations, formulas for factoring a sum and a difference of cubes, roots of polynomials, and the geometric definition of each conic are likewise included in the book. College students will find the book very useful and invaluable.

  • Analysis, et Cetera

    Research Papers Published in Honor of Jürgen Moser's 60th Birthday
    • 1st Edition
    • Paul H. Rabinowitz + 1 more
    • English
    Analysis, et cetera: Research Papers Published in Honor of Jürgen Moser's 60th Birthday provides a collection of papers dedicated to Jürgen Moser on the occasion of his 60th birthday. This book covers a variety of topics, including Helmholtz equation, algebraic complex integrability, theory of Lie groups, and trigonometric polynomials. Organized into 31 chapters, this book begins with an overview of some basic consequences of the definition of algebraic complete integrability. This text then derives a representation theorem for solutions of the Helmholtz equation. Other chapters consider the integrable generalizations of the Volterra system and explain the dynamical system in the finite-dimensional case. This book discusses as well the global periodic solutions for the planar triple pendulum. The final chapter deals with the problem of deriving the macroscopic conservation laws, or the Euler equations, in accurate fashion from the microscopic equations of classical mechanics. This book is a valuable resource for mathematicians.

  • Modeling of Complex Systems

    An Introduction
    • 1st Edition
    • V. Vemuri
    • J. William Schmidt
    • English
    Modeling of Complex Systems: An Introduction describes the framework of complex systems. This book discusses the language of system theory, taxonomy of system concepts, steps in model building, and establishing relations using physical laws. The statistical attributes of data, generation of random numbers fundamental problems of recognition, and input-output type models are also elaborated. This text likewise covers the optimization with equality constraints, transfer function models, and competition among species. This publication is written primarily for senior undergraduate students and beginning graduate students who are interested in an interdisciplinary or multidisciplinary approach to large-scale or complex problems of contemporary societal interest.

  • Calculus of One Variable

    • 2nd Edition
    • Stanley I. Grossman
    • English
    Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus. The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus, and various applications. Some of the topics discussed in the text include the concept of limits, one-variable theory, the derivatives of all six trigonometric functions, exponential and logarithmic functions, and infinite series. This textbook is intended for use by college students.

  • Elements of Differentiable Dynamics and Bifurcation Theory

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

  • Probabilistic Analysis and Related Topics

    Volume 3
    • 1st Edition
    • A. T. Bharucha-Reid
    • English
    Probabilistic Analysis and Related Topics, Volume 3 focuses on the continuity, integrability, and differentiability of random functions, including operator theory, measure theory, and functional and numerical analysis. The selection first offers information on the qualitative theory of stochastic systems and Langevin equations with multiplicative noise. Discussions focus on phase-space evolution via direct integration, phase-space evolution, linear and nonlinear systems, linearization, and generalizations. The text then ponders on the stability theory of stochastic difference systems and Markov properties for random fields. Topics include Markov property of solutions of stochastic partial differential equations; Markov property for generalized Gaussian random fields; Markov properties for generalized random fields; stochastic stability of nonlinear systems; and linear stochastic systems. The publication examines the method of random contractors and its applications to random nonlinear equations, including integral contractors and applications to random equations; random contractors with random nonlinear majorant functions; and random contractors and application to random nonlinear operator equations. The selection is a valuable reference for mathematicians and researchers interested in the general theory of random functions.

  • Real Analysis and Probability

    Solutions to Problems
    • 1st Edition
    • Robert P. Ash
    • English
    Real Analysis and Probability: Solutions to Problems presents solutions to problems in real analysis and probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability; the interplay between measure theory and topology; conditional probability and expectation; the central limit theorem; and strong laws of large numbers in terms of martingale theory. Comprised of eight chapters, this volume begins with problems and solutions for the theory of measure and integration, followed by various applications of the basic integration theory. Subsequent chapters deal with functional analysis, paying particular attention to structures that can be defined on vector spaces; the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also taken into account, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, with emphasis on the fundamental role of Prokhorov's weak compactness theorem. This book is intended primarily for students taking a graduate course in probability.

  • Optimizing Methods in Statistics

    Proceedings of a Symposium Held at the Center for Tomorrow, the Ohio State University, June 14-16, 1971
    • 1st Edition
    • Jagdish S. Rustagi
    • English
    Optimizing Method in Statistics is a compendium of papers dealing with variational methods, regression analysis, mathematical programming, optimum seeking methods, stochastic control, optimum design of experiments, optimum spacings, and order statistics. One paper reviews three optimization problems encountered in parameter estimation, namely, 1) iterative procedures for maximum likelihood estimation, based on complete or censored samples, of the parameters of various populations; 2) optimum spacings of quantiles for linear estimation; and 3) optimum choice of order statistics for linear estimation. Another paper notes the possibility of posing various adaptive filter algorithms to make the filter learn the system model while the system is operating in real time. By reducing the time necessary for process modeling, the time required to implement the acceptable system design can also be reduced One paper evaluates the parallel structure between duality relationships for the linear functional version of the generalized Neyman-Pearson problem, as well as the duality relationships of linear programming as these apply to bounded-variable linear programming problems. The compendium can prove beneficial to mathematicians, students, and professor of calculus, statistics, or advanced mathematics.

  • Finite Permutation Groups

    • 1st Edition
    • Helmut Wielandt
    • Henry Booker + 2 more
    • English
    Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.

  • Programming in an Object-Oriented Environment

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

  • Group Analysis of Differential Equations

    • 1st Edition
    • L. V. Ovsiannikov
    • English
    Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.

  • Thinking Computers and Virtual Persons

    Essays on the Intentionality of Machines
    • 1st Edition
    • Eric Dietrich
    • English
    Thinking Computers and Virtual Persons: Essays on the Intentionality of Machines explains how computations are meaningful and how computers can be cognitive agents like humans. This book focuses on the concept that cognition is computation. Organized into four parts encompassing 13 chapters, this book begins with an overview of the analogy between intentionality and phlogiston, the 17th-century principle of burning. This text then examines the objection to computationalism that it cannot prevent arbitrary attributions of content to the various data structures and representations involved in a computational process. Other chapters consider that the notion of original intentionality is incoherent. This book argues as well that the only way to build an intelligent machine is to build a neural network. The final chapter claims that an entire theoretical framework in cognitive psychology is incompatible with the view that human brains are computers of some sort. This book is a valuable resource for cognitive scientists.

  • Recent Developments in Clustering and Data Analysis

    Développements Récents en Classification Automatique et Analyse des Données: Proceedings of the Japanese-French Scientific Seminar March 24–26, 1987
    • 1st Edition
    • Chikio Hayashi + 2 more
    • English
    Recent Developments in Clustering and Data Analysis presents the results of clustering and multidimensional data analysis research conducted primarily in Japan and France. This book focuses on the significance of the data itself and on the informatics of the data. Organized into four sections encompassing 35 chapters, this book begins with an overview of the quantification of qualitative data as a method of analyzing statistically multidimensional data. This text then examines the rules of interpretation of correspondence cluster analysis by selecting classes and explaining variables involved in the algorithm of hierarchical classification. Other chapters consider the bootstrap and cross-validation methods, which are applied to the logistic ad nonparametric regression analyses of ordered categorical responses. The final chapter deals with a simpler treatment to classify the sleep state. This book is a valuable resource for researchers and workers in the fields from the behavioral sciences, biological sciences, medicine, and industrial sciences.

  • Numerical Solution of Differential Equations

    • 1st Edition
    • Isaac Fried
    • Werner Rheinboldt
    • English
    Numerical Solution of Differential Equations is a 10-chapter text that provides the numerical solution and practical aspects of differential equations. After a brief overview of the fundamentals of differential equations, this book goes on presenting the principal useful discretization techniques and their theoretical aspects, along with geometrical and physical examples, mainly from continuum mechanics. Considerable chapters are devoted to the development of the techniques of the numerical solution of differential equations and their analysis. The remaining chapters explore the influential invention in computational mechanics-finite elements. Each chapter emphasizes the relationship among the analytic formulation of the physical event, the discretization techniques applied to it, the algebraic properties of the discrete systems created, and the properties of the digital computer. This book will be of great value to undergraduate and graduate mathematics and physics students.

  • Transonic, Shock, and Multidimensional Flows

    Advances in Scientific Computing
    • 1st Edition
    • Richard E. Meyer
    • English
    Mathematics Research Center Symposium: Transonic, Shock, and Multidimensional Flows: Advances in Scientific Computing covers the lectures presented at a Symposium on Transonic, Shock, and Multidimensional Flows, held in Madison on May 13-15, 1981, under the auspices of the Mathematics Research Center of the University of Wisconsin. The book focuses on the advancements in the scientific computation of high-speed aerodynamic phenomena and related fluid motions. The selection first elaborates on computational fluid dynamics of airfoils and wings; shock-free configurations in two- and three-dimensional transonic flow; and steady-state solution of the Euler equations for transonic flow. Discussions focus on boundary conditions, convergence acceleration, indirect design of airfoils, and trailing edge and the boundary layer. The text then examines the calculation of transonic potential flow past three-dimensional configurations and remarks on the numerical solution of Tricomi-type equations. The manuscript ponders on the design and numerical analysis of vortex methods, shock calculations and the numerical solution of singular perturbation problems, tracking of interfaces for fluid flow, and transonic flows with viscous effects. Topics include numerical algorithm, difference approximation for scalar equations, boundary conditions, transonic flow in a tube, and governing equations. The selection is a dependable reference for researchers interested in transonic, shock, and multidimensional flows.

  • Classification and Clustering

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin at Madison, May 3–5, 1976
    • 1st Edition
    • J. Van Ryzin
    • English
    Classification and Clustering documents the proceedings of the Advanced Seminar on Classification and Clustering held in Madison, Wisconsin on May 3-5, 1976. This compilation discusses the relationship between multidimensional scaling and clustering, distribution problems in clustering, and botryology of botryology. The graph theoretic techniques for cluster analysis algorithms, data dependent clustering techniques, and linguistic approach to pattern recognition are also elaborated. This text likewise covers the discriminant analysis when scale contamination is present in the initial sample and statistical basis of computerized diagnosis using the electrocardiogram. Other topics include the simple histogram method for nonparametric classification and optimal smoothing of density estimates. This book is intended for mathematicians, biological scientists, social scientists, computer scientists, statisticians, and engineers interested in classification and clustering.

  • Structured Programming Using Turbo BASIC

    • 1st Edition
    • Wade Ellis + 1 more
    • English
    Structured Programming Using Turbo BASIC explains programming methods using this language through mathematical or business examples and problems. The book approaches problem-solving using a top-down, structured programming method. This method consists of 1) breaking a problem into smaller, more manageable tasks, and 2) using the action block, the decision block, and the loop block—the three fundamental programming structures—to perform each task. The text describes the Turbo Basic environment on an IBM PC or compatible, the fundamental programming structures and concepts, the two data structures (arrays, files), graphics creation, as well as computer simulations. The book explains in detail variables, screen formatting, the decision block, the loop block, functions. The text also discusses parameter lists, and libraries The student learns to use the OPEN statement to associate a buffer with a file, or the CLOSE statement to end the file/buffer. The text explains the use of the Turbo BASIC random generator that produces unique sequences of random numbers. The book can be used in introductory lecture courses in business, computer science, or mathematics. It can be beneficial for students in an open-entry/open-exit computer laboratory courses or for self-study.

  • Partial Differential Equations

    Theory and Technique
    • 1st Edition
    • George F. Carrier + 1 more
    • English
    Partial Differential Equations: Theory and Technique provides formal definitions, notational conventions, and a systematic discussion of partial differential equations. The text emphasizes the acquisition of practical technique in the use of partial differential equations. The book contains discussions on classical second-order equations of diffusion, wave motion, first-order linear and quasi-linear equations, and potential theory. Certain chapters elaborate Green's functions, eigenvalue problems, practical approximation techniques, perturbations (regular and singular), difference equations, and numerical methods. Students of mathematics will find the book very useful.

  • Nonnegative Matrices in the Mathematical Sciences

    • 1st Edition
    • Abraham Berman + 1 more
    • English
    Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.

  • Transformations

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

  • A Second Course in Elementary Differential Equations

    • 1st Edition
    • Paul Waltman
    • English
    A Second Course in Elementary Differential Equations deals with norms, metric spaces, completeness, inner products, and an asymptotic behavior in a natural setting for solving problems in differential equations. The book reviews linear algebra, constant coefficient case, repeated eigenvalues, and the employment of the Putzer algorithm for nondiagonalizable coefficient matrix. The text describes, in geometrical and in an intuitive approach, Liapunov stability, qualitative behavior, the phase plane concepts, polar coordinate techniques, limit cycles, the Poincaré-Bendixson theorem. The book explores, in an analytical procedure, the existence and uniqueness theorems, metric spaces, operators, contraction mapping theorem, and initial value problems. The contraction mapping theorem concerns operators that map a given metric space into itself, in which, where an element of the metric space M, an operator merely associates with it a unique element of M. The text also tackles inner products, orthogonality, bifurcation, as well as linear boundary value problems, (particularly the Sturm-Liouville problem). The book is intended for mathematics or physics students engaged in ordinary differential equations, and for biologists, engineers, economists, or chemists who need to master the prerequisites for a graduate course in mathematics.

  • Aphids as Virus Vectors

    • 1st Edition
    • Kerry F. Harris + 1 more
    • English
    Aphids as Virus Vectors focuses on aphids as vectors of plant viruses and the fundamentals of their relationship with virus and host. The mouthparts and feeding mechanism of aphids are discussed, along with aphid penetration of plant tissues and the transmission mechanisms of aphids as virus vectors. The intrinsic properties and taxonomy of aphid-borne viruses are also examined. Comprised of 22 chapters, this book begins with an overview of the importance of aphids as vectors, their biology, and the properties of the viruses they transmit. These introductory chapters prepare the reader for later ones on aphid-virus-plant interactions. The next section deals with transmission mechanisms, with emphasis on several novel alternatives to many of the traditionally held concepts of how aphids transmit viruses. Accessory factors in non-persistent virus transmission are considered. Subsequent chapters focus on technological advances in aphid-virus research, including the use of aphid cell culturing, radioisotope methodology, membrane feeding, and electrical measurement systems. The most promising frontiers in epidemiological and control-oriented research are discussed in the last two sections. This monograph will be a useful resource for researchers from such varied sciences as entomology, plant science, and virology, as well as for graduate students taking entomology and plant pathology courses on insects in relation to plant diseases.

  • Precalculus

    Functions & Graphs
    • 1st Edition
    • Bernard Kolman + 1 more
    • English
    Precalculus: Functions & Graphs provides a complete and self-contained presentation of the basic mathematical techniques and ideas required for the successful completion of a calculus course. The book emphasizes the learning and understanding of the concept of a function, using function notation, and being able to sketch graphs of functions with ease. The text employs a number of pedagogic devices that have been proven effective in teaching college mathematics. The mathematical concepts are presented in a style that is informal, supportive, and "user-friendly". Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appr This textbook is intended for college students.

  • Elementary Linear Programming with Applications

    • 1st Edition
    • Bernard Kolman + 1 more
    • Werner Rheinboldt
    • English
    Elementary Linear Programming with Applications presents a survey of the basic ideas in linear programming and related areas. It also provides students with some of the tools used in solving difficult problems which will prove useful in their professional career. The text is comprised of six chapters. The Prologue gives a brief survey of operations research and discusses the different steps in solving an operations research problem. Chapter 0 gives a quick review of the necessary linear algebra. Chapter 1 deals with the basic necessary geometric ideas in Rn. Chapter 2 introduces linear programming with examples of the problems to be considered, and presents the simplex method as an algorithm for solving linear programming problems. Chapter 3 covers further topics in linear programming, including duality theory and sensitivity analysis. Chapter 4 presents an introduction to integer programming. Chapter 5 covers a few of the more important topics in network flows. Students of business, engineering, computer science, and mathematics will find the book very useful.

  • Numerical Solution of Systems of Nonlinear Algebraic Equations

    • 1st Edition
    • George D. Byrne + 1 more
    • English
    Numerical Solution of Systems of Nonlinear Algebraic Equations contains invited lectures of the NSF-CBMS Regional Conference on the Numerical Solution of Nonlinear Algebraic Systems with Applications to Problems in Physics, Engineering and Economics, held on July 10-14, 1972. This book is composed of 10 chapters and begins with the concepts of nonlinear algebraic equations in continuum mechanics. The succeeding chapters deal with the numerical solution of quasilinear elliptic equations, the nonlinear systems in semi-infinite programming, and the solution of large systems of linear algebraic equations. These topics are followed by a survey of some computational techniques for the nonlinear least squares problem. The remaining chapters explore the problem of nonlinear functional minimization, the modification methods, and the computer-oriented algorithms for solving system. These chapters also examine the principles of contractor theory of solving equations. This book will prove useful to undergraduate and graduate students.

  • Transition and Turbulence

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 13–15, 1980
    • 1st Edition
    • Richard E. Meyer
    • English
    Mathematics Research Center Symposia and Advanced Seminar Series: Transition and Turbulence covers the lectures presented at the Symposium on Transition and Turbulence in Fluids, held in Madison, Wisconsin on October 13-15, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin-Madison. The book focuses on the relation between transition and turbulence in fluids and the importance of this relation for the understanding of many real fluid motions. The selection first elaborates on transition in flow between rotating concentric cylinders, observations in the Taylor experiment, and transition to turbulence in thermal convection with and without rotation. Discussions focus on low aspect ratio convection layers, random convection in a rotating layer, unsteady flows at high Reynolds numbers, transition to oscillatory motion, and experimental observations. The text then tackles instability and turbulence in jets, instability and transition in pipes and channels, and transition to turbulence in boundary layers. The book ponders on coherent structures in turbulence; interactions between large-scale coherent structures and fine-grained turbulence in free shear flows; and vortex interactions and coherent structures in turbulence. Topics include atomic and molecular representations, vortices in uniform strain, vortex pairs, numerical computations applied to a simple problem, agglomeration of large-scale structures and subharmonic formation, retrieving phase information, and dynamical equations. The selection is highly recommended for researchers interested in pursuing further studies on transition and turbulence.

  • Computer Literacy

    Issues and Directions for 1985
    • 1st Edition
    • Robert J. Seidel + 2 more
    • English
    Computer Literacy: Issues and Directions for 1985 is based on a conference entitled "National Goals for Computer Literacy in 1985", held in Reston, Virginia, on December 18-20, 1980, under the auspices of the National Science Foundation. The conference provided a forum for discussing views on computer literacy, as well as methods for infusion of computer-related objectives and activities into existing curricula for different age levels. Issues and barriers to developing national goals for achieving a computer-literate society in the United States are also examined. Comprised of 31 chapters, this book begins by presenting four major approaches to a perspective on computer literacy: impact of computer literacy on the citizenry; major national components of a computer literacy program; development of an information handling curriculum for an evolving computer literacy concept; and a 30-year historical overview of "computer events in three strands" (research/developmen... education, and social/political institutional). The next section considers the definitions and requirements of computer literacy as they impact society, students, and teachers. The use of the computer in cognitive research and in problem solving is also discussed, together with curriculum development in computer literacy. This monograph will be of interest to students, teachers, school administrators, and educational policymakers.

  • Applied Time Series Analysis II

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

  • Statistics for Experimentalists

    • 1st Edition
    • B. E. Cooper
    • English
    Statistics for Experimentalists aims to provide experimental scientists with a working knowledge of statistical methods and search approaches to the analysis of data. The book first elaborates on probability and continuous probability distributions. Discussions focus on properties of continuous random variables and normal variables, independence of two random variables, central moments of a continuous distribution, prediction from a normal distribution, binomial probabilities, and multiplication of probabilities and independence. The text then examines estimation and tests of significance. Topics include estimators and estimates, expected values, minimum variance linear unbiased estimators, sufficient estimators, methods of maximum likelihood and least squares, and the test of significance method. The manuscript ponders on distribution-free tests, Poisson process and counting problems, correlation and function fitting, balanced incomplete randomized block designs and the analysis of covariance, and experimental design. The publication is a valuable reference for statisticians and researchers interested in the use of statistical methods.

  • Differential Equations with Mathematica

    • 1st Edition
    • Martha L Abell + 1 more
    • English
    Differential Equations with Mathematica presents an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as some supplementary topics such as Laplace transforms, Fourier series, and partial differential equations. It also illustrates how Mathematica is used to enhance the study of differential equations not only by eliminating the computational difficulties, but also by overcoming the visual limitations associated with the solutions of differential equations. The book contains chapters that present differential equations and illustrate how Mathematica can be used to solve some typical problems. The text covers topics on differential equations such as first-order ordinary differential equations, higher order differential equations, power series solutions of ordinary differential equations, the Laplace Transform, systems of ordinary differential equations, and Fourier Series and applications to partial differential equations. Applications of these topics are provided as well. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

  • Analytical Geometry

    The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division
    • 1st Edition
    • Barry Spain
    • W. J. Langford + 2 more
    • English
    Analytical Geometry contains various topics in analytical geometry, which are required for the advanced and scholarship levels in mathematics of the various Examining Boards. This book is organized into nine chapters and begins with an examination of the coordinates, distance, ratio, area of a triangle, and the concept of a locus. These topics are followed by discussions of the straight line, straight lines, circle, systems of circles, ellipse, hyperbola, rectangular hyperbola and parabola. This work provides exercises for each section and each chapter ends with a miscellaneous set of examples. Answers are supplied at the end of the book. This book will prove useful to advanced analytical geometry students.

  • Some Modern Mathematics for Physicists and Other Outsiders

    An Introduction to Algebra, Topology, and Functional Analysis
    • 1st Edition
    • Paul Roman
    • English
    Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis, Volume 1 focuses on the operations, principles, methodologies, and approaches employed in algebra, topology, and functional analysis. The publication first offers information on sets, maps, and algebraic composition laws and systems. Discussions focus on morphisms of algebraic systems, sequences and families, cardinal numbers, ordered sets and maps, equivalence relations and maps, composite functions and inverses, operations with sets, and relations in sets. The text then ponders on special algebraic systems, topological spaces, and topological spaces with special properties. Topics include complete metric spaces, compact spaces, separable and connected spaces, homeomorphism and isometry, convergence, continuity, general structure of topological spaces, rings and fields, linear spaces, linear algebras, and nonassociative algebras. The book elaborates on the theory of integration and measure spaces, including measurable spaces, general properties of the integral, and measureable functions. The publication is a valuable reference for theoretical physicists, research engineers, and scientists who are concerned with structural problems.

  • Computer Arithmetic

    Pergamon Programmed Texts
    • 1st Edition
    • F. H. George
    • F. H. George
    • English
    Computer Arithmetic provides information pertinent to the fundamental aspects of a digital computer. This book discusses how the control unit uses the arithmetic unit to produce, under commands, the answers asked by the user. Organized into four chapters, this book begins with an overview of the binary code and provides a preview of the use of other arithmetic codes outside the computer. This text then explains in detail the codes employed in the representation of numbers inside the computer. Other chapters consider the number systems as well as other related matters to be able to understand computer arithmetic. This book discusses as well the signed numbers and their conversations, as well as the problems of scaling. The final chapter deals with the methods of fixed- and floating-point arithmetic, rounding off, and overflow. This book is a valuable resource for sixth form as well as university students who are interested in arithmetic codes.

  • The Mathematica Handbook

    • 1st Edition
    • Martha L Abell + 1 more
    • English
    The Mathematica Handbook provides all the Mathematica commands and objects along with typical examples of them. This handbook is intended as a reference of all built-in Mathematica Version 2.0 objects to both beginning and advanced users of Mathematica. The book contains commands and examples of those commands found in the packages of Mathematica, a system for doing mathematics on a computer. The Preface describes how to use the entries of The Handbook and then briefly discusses elementary rules of Mathematica syntax, defining functions, and using commands that are contained in the standard Mathematica packages. Subsequent chapters provide commands for calculations in Calculus, Statistics, and Numerical Math. The commands in these sections are listed within each package, and the packages are listed alphabetically within each folder (or directory) as well. The book will be of use to engineers, computer scientists, physical scientists, mathematicians, business professionals, and students.

  • Prepare for Science

    Introductory Mathematics for Physical and Engineering Sciences
    • 1st Edition
    • C. B. Hansson
    • English
    Prepare for Science: Introductory Mathematics for Physical and Engineering Sciences is an introductory text on mathematical concepts and skills needed in science and engineering, with particular reference to developing countries. Essential practical topics developed from first principles are discussed, and exercises are carefully arranged in order of difficulty so as to make the text suitable for self-study. Comprised of six chapters, this book begins with an introduction to physical quantities such as length, velocity, time, pressure, force, illumination, and electric current. Subsequent chapters deal with powers of ten (standard form, negative exponents, calculations; units (base units, prefixes, derived units, non-SI units; numerical methods (logarithms, slide rule); and error estimation (approximate numbers, experimental errors, combination of errors). The final chapter is devoted to functions, with emphasis on the mathematical relationships between measured physical quantities. This monograph is intended for students interested in learning mathematical concepts and skills necessary in the physical and engineering sciences.

  • Mathematica® by Example

    • 2nd Edition
    • Martha L Abell + 1 more
    • English
    Mathematica by Example, Revised Edition presents the commands and applications of Mathematica, a system for doing mathematics on a computer. This text serves as a guide to beginning users of Mathematica and users who do not intend to take advantage of the more specialized applications of Mathematica. The book combines symbolic manipulation, numerical mathematics, outstanding graphics, and a sophisticated programming language. It is comprised of 7 chapters. Chapter 1 gives a brief background of the software and how to install it in the computer. Chapter 2 introduces the essential commands of Mathematica. Basic operations on numbers, expressions, and functions are introduced and discussed. Chapter 3 provides Mathematica's built-in calculus commands. The fourth chapter presents elementary operations on lists and tables. This chapter is a prerequisite for Chapter 5 which discusses nested lists and tables in detail. The purpose of Chapter 6 is to illustrate various computations Mathematica can perform when solving differential equations. Chapter 7 discusses some of the more frequently used commands contained in various graphics packages available with Mathematica. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

  • Applied Calculus

    The Commonwealth and International Library: Programmed Texts Series
    • 1st Edition
    • D. J. Bell
    • F. H. George
    • English
    Applied Calculus, Volume 1 provides information pertinent to the fundamental principles of the calculus to problems that occur in Science and Technology. This book illustrates the use of the calculus to determine the motion of different systems, to find the areas and volumes of certain figures, and to determine the turning points on a curve. Organized into four chapters, this volume begins with an overview of the idea of the slope or gradient of a curve to derive further information from the distance-time graph. This text then examines the notation of the calculus to derive the equations of motion for a particle moving in a straight line with uniform acceleration. Other chapters consider the equation of the tangent of the curve. This book discusses as well the importance of an interval along the curve. The final chapter deals with the maximum and the minimum point on a curve. This book is a valuable resource for students.

  • Vectors and Matrices

    • 1st Edition
    • Pamela Liebeck
    • C. Plumpton
    • English
    Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

  • Problems and Methods in Analysis

    • 1st Edition
    • W. Krysicki + 2 more
    • W. J. Langford + 1 more
    • English
    Problems and Methods in Analysis, Volume 2 provides information pertinent to the methods of calculus. This book provides solutions to problems in analytical calculus. Organized into five chapters, this volume begins with an overview of the integration of functions that are not defined or are not bounded at a finite number of points, and with integrals in which the interval of integration is infinitely large. This text then defines the radius of curvature and provides the formula for curvature and radius of curvature. Other chapters consider the equation of tangent and normal. This book discusses as well the amplitudes of the harmonic components of a set of oscilloscope time base potentials. The final chapter deals with the Euler–Fourier formula, the Fourier series, and Dirichlet's conditions. This book is intended to be suitable for sixth form students, particularly scholarship students. First year university students who need a systematic course in calculus will also find this book useful.

  • Computer Mathematics for Programmers

    • 1st Edition
    • Darrell H. Abney + 2 more
    • English
    Computer Mathematics for Programmers presents the Mathematics that is essential to the computer programmer. The book is comprised of 10 chapters. The first chapter introduces several computer number systems. Chapter 2 shows how to perform arithmetic operations using the number systems introduced in Chapter 1. The third chapter covers the way numbers are stored in computers, how the computer performs arithmetic on real numbers and integers, and how round-off errors are generated in computer programs. Chapter 4 details the use of algorithms and flowcharting as problem-solving tools for computer programming. Subsequent chapters focuses on specific mathematical topics such as algebra, sets, logic, Boolean algebra, matrices, graphing and linear programming, and statistics. Students of computer programming will find the text very useful.

  • Sets: Naïve, Axiomatic and Applied

    A Basic Compendium with Exercises for Use in Set Theory for Non Logicians, Working and Teaching Mathematicians and Students
    • 1st Edition
    • D. Van Dalen + 2 more
    • I. N. Sneddon
    • English
    Sets: Naïve, Axiomatic and Applied is a basic compendium on naïve, axiomatic, and applied set theory and covers topics ranging from Boolean operations to union, intersection, and relative complement as well as the reflection principle, measurable cardinals, and models of set theory. Applications of the axiom of choice are also discussed, along with infinite games and the axiom of determinateness. Comprised of three chapters, this volume begins with an overview of naïve set theory and some important sets and notations. The equality of sets, subsets, and ordered pairs are considered, together with equivalence relations and real numbers. The next chapter is devoted to axiomatic set theory and discusses the axiom of regularity, induction and recursion, and ordinal and cardinal numbers. In the final chapter, applications of set theory are reviewed, paying particular attention to filters, Boolean algebra, and inductive definitions together with trees and the Borel hierarchy. This book is intended for non-logicians, students, and working and teaching mathematicians.

  • An Introduction to Digital Computing

    Pergamon Programmed Texts
    • 1st Edition
    • F. H. George
    • English
    An Introduction to Digital Computing provides information pertinent to the fundamental aspects of digital computing. This book represents a major step towards the universal availability of programmed material. Organized into four chapters, this book begins with an overview of the fundamental workings of the computer, including the way it handles simple arithmetic problems. This text then provides a brief survey of the basic features of a typical computer that is divided into three sections, namely, the input and output system, the memory system for data storage, and a processing system. Other chapters focus on programming and on the workings of the computer control unit. This book discusses as well the various arithmetic codes such as binary, decimal, octal, duodecimal, and hexadecimal codes. The final chapter deals with some of the more detailed workings of the control unit. This book is a valuable resource for university students and computer specialists.

  • Programming — ALGOL

    • 1st Edition
    • D. J. Malcolme-Lawes
    • English
    Programming — ALGOL describes the basics of computer programming using Algol. Commands that could be added to Algol and could increase its scope are described, including multiplication and division and the use of brackets. The idea of labeling or naming a command is also explained, along with a command allowing two alternative results. Most of the important features of Algol syntax are discussed, and examples of compound statements (that is, sets of commands enclosed by a begin ... end command) are given. Comprised of 11 chapters, this book begins with an introduction to the digital computer and how it works using a list of instructions known as a program. The "punched-tape" method of feeding information into a computer is described together with the flexowriter. The next chapter provides an overview of Algol by studying a very simple program and comparing it with the same sequence of instructions written in normal English. The third chapter is about building a program, first by increasing the complexity of the actual computation and then economizing on memory stores. Subsequent chapters focus on how computer programs can be built up of simple commands; labeling or naming a command; facilities in the Algol language which allow the addition of a second alternative command to an if ... then statement; and the use of a flow diagram to translate a problem into Algol. The final chapter examines the method of running a program on a computer. This monograph will be of interest to computer programmers.

  • Mathematica by Example

    • 1st Edition
    • Martha L Abell + 1 more
    • English
    Mathematica by Example presents the commands and applications of Mathematica, a system for doing mathematics on a computer. This text serves as a guide to beginning users of Mathematica and users who do not intend to take advantage of the more specialized applications of Mathematica. The book combines symbolic manipulation, numerical mathematics, outstanding graphics, and a sophisticated programming language. It is comprised of 10 chapters. Chapter 1 gives a brief background of the software and how to install it in the computer. Chapter 2 introduces the essential commands of Mathematica. Basic operations on numbers, expressions, and functions are introduced and discussed. Chapter 3 provides Mathematica's built-in calculus commands. The fourth chapter presents elementary operations on lists and tables. This chapter is a prerequisite for Chapter 5 which discusses nested lists and tables in detail. The purpose of Chapter 6 is to illustrate various computations Mathematica can perform when solving differential equations. Chapters 7, 8, and 9 introduce Mathematica Packages that are not found in most Mathematica reference book. The final chapter covers the Mathematica Help feature. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

  • Elementary Vectors

    The Commonwealth and International Library: Mathematics Division
    • 1st Edition
    • E. Å’. Wolstenholme
    • W. J. Langford + 1 more
    • English
    Elementary Vectors is an introductory course in vector analysis which is both rigorous and elementary, and demonstrates the elegance of vector methods in geometry and mechanics. Topics covered range from scalar and vector products of two vectors to differentiation and integration of vectors, as well as central forces and orbits. Comprised of seven chapters, this book begins with an introduction to relevant definitions; addition and subtraction of vectors; multiplication of a vector by a real number; position vectors and distance between two points; and direction cosines and direction ratios. The discussion then turns to scalar and vector products of two vectors; application of vector methods to simple kinematical and dynamical problems concerning the motion of a particle; and differentiation and integration of vectors. Central forces and orbits are also considered, along with the equation of a straight line and that of a plane. A parametric treatment of certain three-dimensional curves and curved surfaces, including the helix, is presented. This monograph will be of value to students, teachers, and practitioners of mathematics.

  • Minicomputer Research and Applications

    Proceedings of the First Conference of the HP/1000 International Users Group
    • 1st Edition
    • Helen K. Brown
    • English
    Minicomputer Research and Applications covers the proceedings of the First Conference of the HP/1000 International Users Group, held on August 25-27, 1980 in San Jose, California. The book focuses on the operations, applications, and functions of the HP/1000 computer driver. The selection first underscores an interactive color display station for IC layout and computer aided design in automatic control and logical automata. Discussions focus on automatic control, logical automata, organization of sirena, hardware and software configurations, interactive input support, and display processing. The text then examines a mini-based sculptured surface system and real-time performance analysis system for computers. The publication ponders on variations on a theme (RTE) by Hewlett-Packard, circumventing RTE system memory and disc restrictions, and the Gerber data management system. Topics include user interface, system security, command file, implementation of shared-EMA, and real-time executive modifications. The manuscript also elaborates on ultra low level programming using a high level language and future directions of the HP/1000. The selection is a dependable reference for readers interested in the HP/1000 computer driver.

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