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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.

  • Numerical Methods for Partial Differential Equations

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 23-25, 1978
    • 1st Edition
    • Seymour V. Parter
    • English
    Numerical Methods for Partial Differential Equations is a collection of papers dealing with techniques and practical solutions to problems concerning continuum mechanics, fluid dynamics, and plasma physics. One paper discusses the important considerations that lead to an efficient nonlinear dynamic finite element analysis using improved analysis techniques. Another paper describes the results obtained from fully discrete methods of higher order in time (order 3 and 4) for second order parabolic initial boundary value problems in which the equations have time dependent (or nonlinear) coefficients. Another paper reviews concepts of ellipticity of finite-difference approximations to general elliptic partial differential systems, with examples utilizing Cauchy-Riemann equations or Navier-Stokes equations. One paper describes fluid-dynamic computing using basic equations, boundary conditions, time dependent gas dynamics, shock waves, stream-function-vort... methods, and an example on the formation of a spherical vortex. Another paper evaluates a specific problem arising in the study of the equilibrium of plasma confined in a machine of the Tokomak type. The collection is suitable for mathematicians, physicists, and investigators in the field of continuum mechanics, fluid dynamics, plasma physics.

  • Ideas and Their Reception

    Proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989
    • 1st Edition
    • David E. Rowe + 1 more
    • English
    The History of Modern Mathematics, Volume I: Ideas and their Reception documents the proceedings of the Symposium on the History of Modern Mathematics held at Vassar College in Poughkeepsie, New York on June 20-24, 1989. This book is concerned with the emergence and reception of major ideas in fields that range from foundations and set theory, algebra and invariant theory, and number theory to differential geometry, projective and algebraic geometry, line geometry, and transformation groups. Other topics include the theory of reception for the history of mathematics and British synthetic vs. French analytic styles of algebra in the early American Republic. The early geometrical works of Sophus Lie and Felix Klein, background to Gergonne's treatment of duality, and algebraic geometry in the late 19th century are also elaborated. This volume is intended for students and researchers interested in developments in pure mathematics.

  • Nonlinear Problems in Abstract Cones

    • 1st Edition
    • Dajun Guo + 1 more
    • William F. Ames
    • English
    Notes and Reports in Mathematics in Science and Engineering, Volume 5: Nonlinear Problems in Abstract Cones presents the investigation of nonlinear problems in abstract cones. This book uses the theory of cones coupled with the fixed point index to investigate positive fixed points of various classes of nonlinear operators. Organized into four chapters, this volume begins with an overview of the fundamental properties of cones coupled with the fixed point index. This text then employs the fixed point theory developed to discuss positive solutions of nonlinear integral equations. Other chapters consider several examples from integral and differential equations to illustrate the abstract results. This book discusses as well the fixed points of increasing and decreasing operators. The final chapter deals with the development of the theory of nonlinear differential equations in cones. This book is a valuable resource for graduate students in mathematics. Mathematicians and researchers will also find this book useful.

  • 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.

  • 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.

  • Contributions to Nonlinear Functional Analysis

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, April 12-14, 1971
    • 1st Edition
    • Eduardo H. Zarantonello
    • English
    Contributions to Nonlinear Functional Analysis contains the proceedings of a Symposium on Nonlinear Functional Analysis, held in Madison, Wisconsin, on April 12-14, 1971, under the sponsorship of the University of Wisconsin's Mathematics Research Center. The symposium provided a forum for discussing various topics related to nonlinear functional analysis, from transversality in nonlinear eigenvalue problems to monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. Comprised of 15 chapters, this book begins by presenting an extension of Leray-Schauder degree and an application to a nonlinear elliptic boundary value problem. The discussion then turns to the use of degree theory to prove the existence of global continua of solutions of nonlinear eigenvalue problems; transversality in nonlinear eigenvalue problems; and how variational structure can be used to study some local questions in bifurcation theory. Subsequent chapters deal with the notion of monotone operators and monotonicity theory; a nonlinear version of the Hille-Yosida theorem; a version of the penalty method for the Navier-Stokes equations; and various types of weak solutions for minimizing problems in the spirit of duality theory for convex functionals. This monograph will be of interest to students and practitioners in the field of mathematics who want to learn more about nonlinear functional analysis.

  • Progress in Combinatorial Optimization

    • 1st Edition
    • William R. Pulleyblank
    • English
    Progress in Combinatorial Optimization provides information pertinent to the fundamental aspects of combinatorial optimization. This book discusses how to determine whether or not a particular structure exists. Organized into 21 chapters, this book begins with an overview of a polar characterization of facets of polyhedra obtained by lifting facets of lower dimensional polyhedra. This text then discusses how to obtain bounds on the value of the objective in a graph partitioning problem in terms of spectral information about the graph. Other chapters consider the notion of a triangulation of an oriented matroid and show that oriented matroid triangulation yield triangulations of the underlying polytopes. This book discusses as well the selected results and problems on perfect ad imperfect graphs. The final chapter deals with the weighted parity problem for gammoids, which can be reduced to the weighted graphic matching problem. This book is a valuable resource for mathematicians and research workers.

  • 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.

  • Almost Everywhere Convergence II

    Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Evanston, Illinois, October 16–20, 1989
    • 1st Edition
    • Alexandra Bellow + 1 more
    • English
    Almost Everywhere Convergence II presents the proceedings of the Second International Conference on Almost Everywhere Convergence in Probability and Ergodotic Theory, held in Evanston, Illinois on October 16–20, 1989. This book discusses the many remarkable developments in almost everywhere convergence. Organized into 19 chapters, this compilation of papers begins with an overview of a generalization of the almost sure central limit theorem as it relates to logarithmic density. This text then discusses Hopf's ergodic theorem for particles with different velocities. Other chapters consider the notion of a log–convex set of random variables, and proved a general almost sure convergence theorem for sequences of log–convex sets. This book discusses as well the maximal inequalities and rearrangements, showing the connections between harmonic analysis and ergodic theory. The final chapter deals with the similarities of the proofs of ergodic and martingale theorems. This book is a valuable resource for mathematicians.

  • Proceedings of the Conference on Finite Groups

    • 1st Edition
    • William R. Scott + 1 more
    • English
    Proceedings of the Conference on Finite Groups provides information pertinent to the fundamental aspects of finite group theory. This book presents the problem of characterizing simple groups in terms of the local structure of a group. Organized into five parts encompassing 43 chapters, this book begins with an overview of the characterization of the Chevalley groups over fields of odd order and indicates the role of this characterization in the theory of component type groups. This text then examines the structure as well as the representations of specific simple groups. Other chapters consider the general theory of representations and characters of finite groups. This book discusses as well permutation groups and the connection between group theory and geometry. The final chapter deals with finite solvable groups as well as the theory of formations. This book is a valuable resource for mathematicians, graduate students, and research workers.

  • Generatingfunctionology

    • 1st Edition
    • Herbert S. Wilf
    • English
    Generatingfunctionol... provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

  • Recent Advances in Statistics

    Papers in Honor of Herman Chernoff on His Sixtieth Birthday
    • 1st Edition
    • M. Haseeb Rizvi + 2 more
    • English
    Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday is a collection of papers on statistics in honor of Herman Chernoff on the occasion of his 60th birthday. Topics covered range from sequential analysis (including designs) to optimization (including control theory), nonparametrics (including large sample theory), and statistical graphics. Comprised of 27 chapters, this book begins with a discussion on optimal stopping of Brownian motion, followed by an analysis of sequential design of comparative clinical trials. A two-sample sequential test for shift with one sample size fixed in advance is then presented. Subsequent chapters focus on set-valued parameters and set-valued statistics; large deviations of the maximum likelihood estimate in the Markov chain case; the limiting behavior of multiple roots of the likelihood equation; and optimal uniform rate of convergence for nonparametric estimators of a density function and its derivatives. The book concludes by considering significance and confidence levels, closed regions and models, and discrete distributions. This monograph should be of interest to students, researchers, and specialists in the fields of mathematics and statistics.

  • 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.

  • 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.

  • 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.

  • Iterative Methods for Large Linear Systems

    • 1st Edition
    • David R. Kincaid + 1 more
    • English
    Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.

  • Statistical Computer Performance Evaluation

    • 1st Edition
    • Walter Freiberger
    • English
    Statistical Computer Performance Evaluation contains the proceedings of a Conference on Statistical Computer Performance Evaluation held at Brown University in Providence, Rhode Island, on November 22-23, 1971, under the auspices of the Division of Applied Mathematics and the Center for Computer and Information Sciences. The papers review the application of quantitative, and particularly statistical, methods to the study of computer performance. Comprised of 19 chapters, this book begins with an overview of the state of the art of computer system evaluation and some quantitative methods (analytical, simulation, and empirical methods) that are applicable to the problem. A utility theoretic approach to evaluation of a time-sharing system is then described, followed by a discussion on the results of a multi-factor paging experiment. Subsequent chapters focus on statistical quantification of instruction and operand traces; measurement and improvement of program behavior under paging systems; free-storage algorithms; and probabilistic models for predicting software reliability. This monograph will be of interest to practitioners in the fields ofcomputer science and applied mathematics.

  • Discrete Algorithms and Complexity

    Proceedings of the Japan-US Joint Seminar, June 4 – 6, 1986, Kyoto, Japan
    • 1st Edition
    • David S. Johnson + 2 more
    • English
    Perspectives in Computing, Volume 15: Discrete Algorithms and Complexity provides an understanding of discrete algorithms and complexity. This book covers a variety of topics, including discrete logarithm algorithms, parallel bubbling, electronic prototyping, number theoretic complexity, and linear programming. Organized into 27 chapters, this volume begins with an overview of the basic solutions of the primal and dual that can be characterized in graph-theoretic terms. This text then explores the principal partition of vertex-weighted graphs, which is utilized to solve certain assignment problems or flow problems that are formulated using such graphs. Other chapters consider a polynomial-time algorithm for finding the geodesic center of a simple polygon. This book discusses as well the three efficient algorithms for the routing problems around a rectangle. The final chapter deals with a snoopy cache multiprocessor system wherein each processor has a cache in which it stores blocks of data. This book is a valuable resource for mathematicians and researchers.

  • Data Structures

    Theory and Practice
    • 1st Edition
    • A. T. Berztiss
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Data Structures: Theory and Practice focuses on the processes, methodologies, principles, and approaches involved in data structures, including algorithms, decision trees, Boolean functions, lattices, and matrices. The book first offers information on set theory, functions, and relations, and graph theory. Discussions focus on linear formulas of digraphs, isomorphism of digraphs, basic definitions in the theory of digraphs, Boolean functions and forms, lattices, indexed sets, algebra of sets, and order pair and related concepts. The text then examines strings, trees, and paths and cycles in digraphs. Topics include algebra of strings, Markov algorithms, algebraic structures, languages and grammars, decision trees and decision tables, trees as grammatic markers, shortest path problems, and representation of prefix formulas. The publication ponders on digraphs of programs, arrays, pushdown stores, lists, and list structures, and organization of files. Concerns include scatter storage techniques, files and secondary storage, representation of digraphs as list structures, storage of arrays, and sparse matrices. The text is a valuable reference for computer science experts, mathematicians, and researchers interested in data structures.

  • 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.

  • Study Guide to Accompany Computers Data and Processing

    • 1st Edition
    • Harvey M. Deitel + 1 more
    • English
    Study Guide to Accompany Computer and Data Processing provides information pertinent to the fundamental aspects of computers and computer technology. This book presents the key benefits of using computers. Organized into five parts encompassing 19 chapters, this book begins with an overview of the evolution of modern computing systems from the earliest mechanical calculating devices to microchips. This text then introduces computer hardware and describes the processor. Other chapters describe how microprocessors are made and describe the physical operation of computers. This book discusses as well how computers present their outputs and explains the storage and retrieval of massive amounts of computer-accessible information from secondary storage devices. The final chapter discusses the use of computers in the transportation systems and the ways in which they make possible other innovations in transportation. This book is a valuable resource for computer scientists, systems analysts, computer programmers, mathematicians, historians, computer specialists, and students.

  • Elliptic Problem Solvers

    • 1st Edition
    • Martin H. Schultz
    • English
    Elliptic Problem Solvers provides information pertinent to some aspects of the numerical solution of elliptic partial differential equations. This book presents the advances in developing elliptic problem solvers and analyzes their performance. Organized into 40 chapters, this book begins with an overview of the approximate solution of using a standard Galerkin method employing piecewise linear triangular finite elements. This text then defines the types of vector architecture and discusses the variation in performance that can occur on a vector processor as a function of algorithm and implementation. Other chapters consider the implementation of techniques for elliptical problems. This book discusses as well the six techniques for the solution of nonsymmetric linear systems arising from finite difference discretization of the convection-diffusion equation. The final chapter deals with the basic semiconductor device equations. This book is a valuable resource for electrical and computer engineers, scientists, computer programmers, pure mathematicians, and research workers.

  • Boundary Value Problems

    • 2nd Edition
    • David L. Powers
    • English
    Boundary Value Problems is a text material on partial differential equations that teaches solutions of boundary value problems. The book also aims to build up intuition about how the solution of a problem should behave. The text consists of seven chapters. Chapter 1 covers the important topics of Fourier Series and Integrals. The second chapter deals with the heat equation, introducing separation of variables. Material on boundary conditions and Sturm-Liouville systems is included here. Chapter 3 presents the wave equation; estimation of eigenvalues by the Rayleigh quotient is mentioned briefly. The potential equation is the topic of Chapter 4, which closes with a section on classification of partial differential equations. Chapter 5 briefly covers multidimensional problems and special functions. The last two chapters, Laplace Transforms and Numerical Methods, are discussed in detail. The book is intended for third and fourth year physics and engineering students.

  • Delay and Functional Differential Equations and Their Applications

    • 1st Edition
    • Klaus Schmitt
    • English
    Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.

  • 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.

  • Nonlinear Differential Equations

    Invariance, Stability, and Bifurcation
    • 1st Edition
    • Piero de Mottoni + 1 more
    • English
    Nonlinear Differential Equations: Invariance, Stability, and Bifurcation presents the developments in the qualitative theory of nonlinear differential equations. This book discusses the exchange of mathematical ideas in stability and bifurcation theory. Organized into 26 chapters, this book begins with an overview of the initial value problem for a nonlinear wave equation. This text then focuses on the interplay between stability exchange for a stationary solution and the appearance of bifurcating periodic orbits. Other chapters consider the development of methods for ascertaining stability and boundedness and explore the development of bifurcation and stability analysis in nonlinear models of applied sciences. This book discusses as well nonlinear hyperbolic equations in further contributions, featuring stability properties of periodic and almost periodic solutions. The reader is also introduced to the stability problem of the equilibrium of a chemical network. The final chapter deals with suitable spaces for studying functional equations. This book is a valuable resource for mathematicians.

  • Parallel Computations

    • 1st Edition
    • Garry Rodrigue
    • English
    Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed. Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techniques for performing matrix operations on them. The reader is then introduced to FFTs and the tridiagonal linear system as well as the ICCG method. Different versions of the conjugate gradient method for solving the time-dependent diffusion equation are considered. Subsequent chapters deal with two- and three-dimensional fluid flow calculations, paying particular attention to the principal issues in designing efficient numerical methods for hydrodynamic calculations; the decisions that a numerical modeler must make to optimize chemically reactive flow simulations; and how to handle disk-to-core data transfer and storage allocation for the solution of the implicit equations for three-dimensional flows. The book also describes the time-split finite difference scheme for solving the two-dimensional Navier-Stokes equation for flows through slotted nozzles. Finally, the large-scale stimulation of plasmas, as carried out on a small computer with an array processor, is discussed. This monograph should be of interest to specialists in computer science.

  • Teaching of Statistics and Statistical Consulting

    • 1st Edition
    • Jagdish S. Rustagi + 1 more
    • English
    Teaching of Statistics and Statistical Consulting is a collection of papers dealing with graduate programs in statistics; teaching service courses and short courses; and training statisticians for employment in industry and government. Some papers also deal with the role of statistical consulting in graduate training and teaching statistics at the Open University. One paper describes some observations made on graduate program in statistics, citing concerns of professionalism, competency, and a highly structured university curriculum. Another paper takes a task analysis approach to designing a regression analysis course where, with proper course structuring, students will actively learn to do the objectives of the course. Other papers discuss consulting and research work at the Australian Government's research organization, as well as how to prepare statisticians for future government service or for the private industry. One paper deals with some important things that a practicing statistician should know, but which are seldom taught in statistics courses. Another paper describes teaching statistics at a distance from the Open University in the United Kingdom. The collection can prove helpful for academic statisticians in educational institutions, to statisticians, or to mathematicians employed in the public or private sectors.

  • Nonlinear Programming 3

    Proceedings of the Special Interest Group on Mathematical Programming Symposium Conducted by the Computer Sciences Department at the University of Wisconsin–Madison, July 11-13, 1977
    • 1st Edition
    • Olvi L. Mangasarian + 2 more
    • English
    Nonlinear Programming 3 covers the proceedings of the Special Interest Group on Mathematical Programming Symposium conducted by the Computer Sciences Department at the University of Wisconsin, Madison, on July 11-13, 1977. This book is composed of 17 chapters. The first eight chapters describe some of the most effective methods available for solving linearly and nonlinearly constrained optimization problems. The subsequent chapter gives algorithms for the solution of nonlinear equations together with computational experience. Other chapters provide some applications of optimization in operations research and a measurement procedure for optimization algorithm efficiency. These topics are followed by discussion of the methods for solving large quadratic programs and algorithms for solving stationary and fixed point problems. The last chapters consider the minimization of certain types of nondifferentiable functions and a type of Newton method. This book will prove useful to mathematicians and computer scientists.

  • Mathematics for Dynamic Modeling

    • 1st Edition
    • Edward Beltrami
    • English
    Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction–diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.

  • Topics in Multivariate Approximation

    • 1st Edition
    • C. K. Chui + 2 more
    • English
    Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.

  • Combinatorial Algorithms

    For Computers and Calculators
    • 2nd Edition
    • Albert Nijenhuis + 1 more
    • Werner Rheinboldt
    • English
    Combinatorial Algorithms for Computers and Calculators, Second Edition deals with combinatorial algorithms for computers and calculators. Topics covered range from combinatorial families such as the random subset and k-subset of an n-set and Young tableaux, to combinatorial structures including the cycle structure of a permutation and the spanning forest of a graph. Newton forms of a polynomial and the composition of power series are also discussed. Comprised of 30 chapters, this volume begins with an introduction to combinatorial algorithms by considering the generation of all of the 2n subsets of the set {1, 2,...,n}. The discussion then turns to the random subset and k-subset of an n-set; next composition of n into k parts; and random composition of n into k parts. Subsequent chapters focus on sequencing, ranking, and selection algorithms in general combinatorial families; renumbering rows and columns of an array; the cycle structure of a permutation; and the permanent function. Sorting and network flows are also examined, along with the backtrack method and triangular numbering in partially ordered sets. This book will be of value to both students and specialists in the fields of applied mathematics and computer science.

  • Mathematics with Applications for the Management, Life, and Social Sciences

    • 2nd Edition
    • Howard Anton + 1 more
    • English
    Mathematics with Applications for the Management, Life, and Social Sciences, Second Edition presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications in management, life sciences, and social sciences. Some applications of probability, game theory, and Markov chains are given. Comprised of 16 chapters, this book begins with an introduction to set theory, followed by a discussion on Cartesian coordinate systems and graphs. Subsequent chapters focus on linear programming from a geometric point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and permutations, combinations, and counting methods. Probability for finite sample spaces and basic concepts in statistics are also considered, along with the mathematics of finance and applications of calculus. This monograph is intended for students and instructors of applied mathematics.

  • Probability, Statistics, and Queueing Theory

    With Computer Science Applications
    • 1st Edition
    • Arnold O. Allen
    • Werner Rheinboldt
    • English
    Probability, Statistics, and Queueing Theory: With Computer Science Applications focuses on the use of statistics and queueing theory for the design and analysis of data communication systems, emphasizing how the theorems and theory can be used to solve practical computer science problems. This book is divided into three parts. The first part discusses the basic concept of probability, probability distributions commonly used in applied probability, and important concept of a stochastic process. Part II covers the discipline of queueing theory, while Part III deals with statistical inference. This publication is designed as a junior-senior level textbook on applied probability and statistics with computer science applications, but is also a self-study book for practicing computer science (data processing) professionals.

  • Virtual Reality Excursions with Programs in C

    • 1st Edition
    • Christopher D. Watkins + 1 more
    • English
    Virtual Reality Excursions with Programs in C provides the history, theory, principles and an account of the milestones in the development of virtual reality technology. The book is organized into five chapters. The first chapter explores the applications in the vast field of virtual reality. The second chapter presents a brief history of the field and its founders. Chapter 3 discusses human perception and how it works. Some interesting notes and much of the hot debate in the field are covered in Chapter 4. The fifth chapter describes many of the complexities involved in implementing virtual environments on real equipment. Computer scientists and programmers will find the book interesting.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • Mathematics for Financial Analysis

    • 1st Edition
    • Michael Gartenberg + 1 more
    • English
    Mathematics for Financial Analysis focuses on the application of mathematics in financial analysis, including applications of differentiation, logarithmic functions, and compounding. The publication first ponders on equations and graphs, vectors and matrices, and linear programming. Discussions focus on duality and minimization problems, systems of linear inequalities, linear programs, matrix inversion, properties of matrices and vectors, vector products, equations and graphs, higher dimensional spaces, distance in the plane, coordinate geometry, and inequalities and absolute value. The text then examines differential calculus, applications of differentiation, and antidifferentiation and definite integration. Topics include fundamental theorem of calculus, definite integral, profit optimization in a monopoly, revenue from taxation, curve sketching, concavity and points of inflection, and rules for differentiation. The book examines the applications of integration and differentiation and integration of exponential and logarithmic functions, including exponential and logarithmic functions, differentiation and integration of logarithmic functions, and continuous compounding. The publication is a valuable source of data for researchers interested in the application of mathematics in financial analysis.

  • 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.

  • Issues of Organizational Design

    A Mathematical Programming View of Organizations
    • 1st Edition
    • Børge Obel
    • English
    Issues of Organizational Design: A Mathematical Programming View of Organizations analyzes the view that organizations can be represented satisfactorily by a mathematical programming model and relates it to other theories of organizational behavior. The potential of this approach to organizational analysis is evaluated. Comprised of seven chapters, this book begins with an overview of the three major schools of organizational theory: the classical/structural school, the human relations school, and the contingency school. It then defines what an organization is and outlines the relationship between organizational elements. The example of the two-product firm is used to illustrate the basic model framework, and how coordination, diversification, and incentives can be treated in this framework.Subsequent chapters explore the relationship between the contingency approach and the mathematical programming approach to organizational design; the coordination problem and the process of decision making in a decentralized organization; the decomposition of the organization into a number of smaller units; and types of evaluation and incentive schemes for addressing cheating in a multi-level organization. The book also presents a series of empirical studies where a mathematical programming view of organizations has been assumed before concluding with a discussion on the process of designing organizations. This monograph will be useful for students of organizational design and for practitioners who use models in connection with decision making.

  • Exploring University Mathematics

    Lectures Given at Bedford College, London
    • 1st Edition
    • P. Chadwick + 2 more
    • N. J. Hardiman
    • English
    Exploring University Mathematics 1 provides information pertinent to pure and applied mathematics. This book discusses a variety of topics, including sets and functions, relativity, integers, waves, isometric problems, and digital computers. Organized into seven chapters, this book begins with an overview of the axiomatic way of introducing natural numbers that is completely satisfactory for mathematical purposes. This text then examines the special theory of relativity, which is a certain kind of geometry of four dimensions that connects three spatial coordinates x, y, z, and a time coordinate t. Other chapters consider the impact that the study of wave phenomena has had on the historical development of mathematics. This book discusses as well the development of the electronic digital computers. The final chapter deals with solving the isoperimetric problem. This book is intended to be suitable for students about to embark upon a degree course of which mathematics is a major part.

  • The Origins of Infinitesimal Calculus

    • 1st Edition
    • Margaret E. Baron
    • English
    The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.

  • Statistical Analysis

    A Computer Oriented Approach
    • 1st Edition
    • A. A. Afifi + 1 more
    • English
    Statistical Analysis: A Computer Oriented Approach discusses the probabilistic foundations of statistics, the standard statistical inference procedures, regression, and correlation analysis. The book also explains the analysis of variance and multivariate analysis, with an emphasis on the applications and interpretations of statistical tools. The text defines computer terminologies, coding sheets, format statements, and packaged statistical programs or software. Software and other related programs are tools for data analysis: the "frequency count program" analyzes discrete observations; and the "descriptive program" investigates one continuous variable. Other similar tools are the "descriptive program with strata" that evaluates more than one continuous random variable, and the "crosstabulation program" that reviews contingency tables. The book also explains the general linear model which is applied to the estimators and tests of hypotheses for simple and multiple linear regression models. The text shows how different packaged computer programs can be used to perform analyses of variance. For example, the factorial programs can analyze special designs of randomized blocks, replicated randomized blocks, and nested designs. For other special designs, including the split plot and Latin square designs, the investigator can make adaptations to the standard factorial program. The book is intended for students of statistical inference, computer programming, and readers interested in advanced mathematics.

  • 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.

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