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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.

  • Graphical Representation of Multivariate Data

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

  • Integer Programming

    Theory, Applications, and Computations
    • 1st Edition
    • Hamdy A. Taha
    • J. William Schmidt
    • English
    Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming. Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other chapters consider the branch-and-bound methods, the cutting-plane method, and its closely related asymptotic problem. This book discusses as well several specialized algorithms for certain well-known integer models and provides an alternative approach to the solution of the integer problem. The final chapter deals with a number of observations about the formulations and executions of integer programming models. This book is a valuable resource for industrial engineers and research workers.

  • Finite Element Solution of Boundary Value Problems

    Theory and Computation
    • 1st Edition
    • O. Axelsson + 1 more
    • Werner Rheinboldt
    • English
    Finite Element Solution of Boundary Value Problems: Theory and Computation provides an introduction to both the theoretical and computational aspects of the finite element method for solving boundary value problems for partial differential equations. This book is composed of seven chapters and begins with surveys of the two kinds of preconditioning techniques, one based on the symmetric successive overrelaxation iterative method for solving a system of equations and a form of incomplete factorization. The subsequent chapters deal with the concepts from functional analysis of boundary value problems. These topics are followed by discussions of the Ritz method, which minimizes the quadratic functional associated with a given boundary value problem over some finite-dimensional subspace of the original space of functions. Other chapters are devoted to direct methods, including Gaussian elimination and related methods, for solving a system of linear algebraic equations. The final chapter continues the analysis of preconditioned conjugate gradient methods, concentrating on applications to finite element problems. This chapter also looks into the techniques for reducing rounding errors in the iterative solution of finite element equations. This book will be of value to advanced undergraduates and graduates in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined workers in engineering and the physical sciences.

  • Asymptotics and Special Functions

    • 1st Edition
    • F. W. J. Olver
    • Werner Rheinbolt
    • English
    Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.

  • 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.

  • Elliptic Problem Solvers

    Volume II
    • 1st Edition
    • Garrett Birkhoff + 1 more
    • English
    Elliptic Problem Solvers, II covers the proceedings of the Elliptic Problem Solvers Conference, held at the Naval Postgraduate School in Monterey, California from January 10 to 12, 1983. The book focuses on various aspects of the numerical solution of elliptic boundary value problems. The selection first offers information on building elliptic problem solvers with ELLPACK; presentation and evolution of the club module; and a fourth order accurate fast direct method for the Helmholtz equation. The text then examines the ITPACK project, CMMPAK, solving elliptic problems on an array processor system, and parallel architectures for iterative methods on adaptive, block structured grids. Topics include adaptive solution algorithm, data structure, elliptic problem solvers, input data, and vector ITPACK. The publication ponders on conjugate gradient preconditioners for vector and parallel processors; an algebra for systolic computation; and an incomplete-Cholesky factorization by a matrix partition algorithm. The book also tackles the numerical solution of a model equation near the onset of the Rayleigh-Benard instability; numerical methods for solving coupled semiconductor equations on a minicomputer; and analysis of nonlinear elliptic systems arising in reaction/diffusion modeling. The selection is highly recommended for researchers interested in elliptic problem solvers.

  • Programming Language Structures

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

  • Applied Time Series Analysis

    Proceedings of the First Applied Time Series Symposium Held in Tulsa, Oklahoma, May 14-15, 1976
    • 1st Edition
    • David F. Findley
    • English
    Applied Time Series Analysis contains the proceedings of the First Applied Time Series Symposium held in Tulsa, Oklahoma, on May 14-15, 1976. The symposium provided a forum for reviewing various applications of time series analysis and covered topics ranging from nonlinear time series modeling and G-spectral estimation to multivariate autoregression estimation using residuals. Adaptive processing of seismic data and the application of homomorphic filtering to seismic data processing are also discussed. Comprised of 10 chapters, this book begins by describing the application of parametric models to the analysis and control of time series using some numerical examples. The reader is then introduced to nonlinear time series modeling; two-dimensional recursive filtering in theory and practice; and spectral estimators. Waves propagating in random media as statistical time series are also considered. The book concludes with a chapter that illustrates how the intensity of a Poisson process is estimated, with emphasis on a time series approach to the fixed signal case, invariant testing, and spline estimation. This monograph will be a useful resource for students and practitioners in the fields of mathematics and statistics, electrical engineering, and computer science.

  • Generative Modeling for Computer Graphics and Cad

    Symbolic Shape Design Using Interval Analysis
    • 1st Edition
    • John M. Snyder
    • English
    Generative Modeling for Computer Graphics and Cad: Symbolic Shape Design Using Interval Analysis presents a symbolic approach to shape representation that is useful to the CAD/CAM and computer graphics communities. This book discusses the kinds of operators useful in a geometric modeling system, including arithmetic operators, vector and matrix operators, integration, differentiation, constraint solution, and constrained minimization. Associated with each operator are several methods that compute properties about the parametric functions represented with the operators. This text also elaborates how numerous rendering and analytical operations can be supported with only three methods—evaluation of the parametric function at a point, symbolic differentiation of the parametric function, and evaluation of an inclusion function for the parametric function. This publication is intended for people working in the area of computational geometry who are interested in a robust class of algorithms for manipulating shapes and those who want to know how human beings can specify and manipulate shape.

  • Mathematical Perspectives

    Essays on Mathematics and Its Historical Development
    • 1st Edition
    • Joseph W. Dauben
    • English
    Mathematical Perspectives: Essays on Mathematics and its Historical Development is a collection of 13 biographical essays on the historical advances of science. This collection is originally meant to comprise an issue of the journal Historia Mathematica in honor of Professor Kurt R. Biermann’s 60th birthday. This 12-chapter text includes essays on studies and commentaries on the problem of “figures of equal perimeter” by various authors in antiquity, including Zenodorus, Theon, and Pappus. Other essays explore the comparison of the areas of polygons with equal perimeter; the concept of function; history of mathematics; the development of mathematical physics in France; and the history of Logicism and Formalism. The remaining chapters deal with essays on an early version of Gauss’ Disquisitiones Arithmeticae, ideal numbers, a mathematical-philoso... theory of probability, and historical examples of problem of number sequence interpolation. This book will be of value to mathematicians, historians, and researchers.

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