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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.

  • Dynamic Programming and Its Applications

    Proceedings of the International Conference on Dynamic Programming and Its Applications, University of British Columbia, Vancouver, British Columbia, Canada, April 14-16, 1977
    • 1st Edition
    • Martin L. Puterman
    • English
    Dynamic Programming and Its Applications provides information pertinent to the theory and application of dynamic programming. This book presents the development and future directions for dynamic programming. Organized into four parts encompassing 23 chapters, this book begins with an overview of recurrence conditions for countable state Markov decision problems, which ensure that the optimal average reward exists and satisfies the functional equation of dynamic programming. This text then provides an extensive analysis of the theory of successive approximation for Markov decision problems. Other chapters consider the computational methods for deterministic, finite horizon problems, and present a unified and insightful presentation of several foundational questions. This book discusses as well the relationship between policy iteration and Newton's method. The final chapter deals with the main factors severely limiting the application of dynamic programming in practice. This book is a valuable resource for growth theorists, economists, biologists, mathematicians, and applied management scientists.

  • The Mathematics of Finite Elements and Applications

    Proceedings of the Brunel University Conference of the Institute of Mathematics and Its Applications Held in April 1972
    • 1st Edition
    • J. R. Whiteman
    • English
    The Mathematics of Finite Elements and Applications provides information pertinent to the mathematics of finite elements, applications, algorithms, and computational techniques. This book discusses the developments in the mathematics of finite elements. Organized into 32 chapters, this book begins with an overview of the basis of the finite element process as a general approximation tool. This text then examines the methods for obtaining bounds on the errors in finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. Other chapters consider the practical implementation of the Galerkin and the Rayleigh–Ritz methods to equations of importance to physics and engineering. This book discusses as well a fundamental investigation into the problem of convergence in the finite element method. The final chapter deals with an algorithm that is applicable to the analysis of arbitrary plane stress or plane strain configurations. This book is a valuable resource for numerical analysts, mathematical physicist, applied mathematicians, computer scientists, and engineers.

  • Business Mathematics

    • 3rd Edition
    • Burton S. Kaliski
    • English
    Business Mathematics, Third Edition provides the step-by-step explanation of principles, practical aspects, and importance of business mathematics. This edition is organized into six sections encompassing 14 chapters that cover related topics of the metric system, no-fault insurance, individual retirement plans, charge account plans, home mortgages, and NOW accounts. Section 1 gives a thorough review of the fundamental processes, while Section 2 deals with buying and selling, the first factors considered in calculating a firm's profit or loss. Section 3 discusses the operating expenses that reduce the profit or increase the loss from buying and selling activities, and the actual calculation of net profit or loss. Sections 4 and 5 consider the principles of interest as a form of additional income or expense, as well as the investment in stocks, bonds, mutual funds, and other areas as still another source of income or expense. Section 6 describes the procedures for summarizing and analyzing data. The review part at the end of each section lists the important terms and reinforces the major principles learned in the unit. The summary problems in the Unit Review are intended as self-tests and should serve as effective review for examinations. This book will be of great value to business mathematicians, economists, and the general public who are interested in investments.

  • A Handbook of Integer Sequences

    • 1st Edition
    • N.J.A. Sloane
    • English
    A Handbook of Integer Sequences contains a main table of 2300 sequences of integers that are collected from all branches of mathematics and science. This handbook describes how to use the main table and provides methods for analyzing and describing unknown and important sequences. This compilation also serves as an index to the literature for locating references on a particular problem and quickly finds numbers such as 712, number of partitions of 30, 18th Catalan number, or expansion of ? to 60 decimal places. Other topics include the method of differences, self-generating sequences, polyominoes, permutations, and puzzle sequences. This publication is a good source for students and researchers who are confronted with strange and important sequences.

  • 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.

  • Computer Methods in Operations Research

    • 1st Edition
    • Arne Thesen
    • J. William Schmidt
    • English
    Computer Methods in Operations Research focuses on the computational methods used in operations research. Topics covered range from list processing to sorting and searching, networks, and critical path methods. Resource-constrained scheduling methods and linear programming methods are also discussed, along with the branch and bound concept. Comprised of 11 chapters, this book begins with a review of some of the basic principles that make a software development effort successful, emphasizing the need to keep things simple and understandable. The reader is then introduced to the basic principles of list processing, searching, and sorting; the concept of networks and several matrix- and list-oriented methods for representing networks in the computer; and the critical path method. Subsequent chapters deal with more complex programs and algorithms to handle scheduling of activities under precedence and resource restrictions; the resource-constrained scheduling problem, formulated both in an exact (using integer programming) and in a heuristic manner; the design of algorithms for the solution of large linear programming problems; and the application of list processing concepts to the development of branch and bound algorithms for solution of combinatorial optimization problems. The book also considers the design of random number generators and discrete event simulation programming before concluding with a description of two programming languages, GPSS and WIDES, for use in simulation modeling. This monograph will be of value to students and practitioners of operations research and industrial engineering.

  • Study Guide for College Algebra

    • 1st Edition
    • James W. Snow + 2 more
    • English
    Study Guide for College Algebra is a supplemental material for the basic text, College Algebra. Its purpose is to make the learning of college algebra and trigonometry easier and enjoyable. The book provides detailed solutions to exercises found in the text. Students are encouraged to use the study guide as a learning tool during the duration of the course, a reviewer prior to an exam, a reference book, and as a quick overview before studying a section of the text. The Study Guide and Solutions Manual consists of four major components: basic concepts that should be learned from each unit, what was learned upon completion of each unit, solutions to selected problems, and a short chapter quiz, including the answers, covering the concepts and problem types. College level students will find the book very useful.

  • Matrix Methods

    An Introduction
    • 1st Edition
    • Richard Bronson
    • English
    Matrix Methods: An Introduction is a nine-chapter text that emphasizes the methodological aspects of mathematical matrices. This book is intended for an introductory course in matrices similar to those given to sophomore and junior engineering students at Fairleigh Dickinson University. The first five chapters deal with the elementary aspects of matrices, including their definition, determinants, method of inversion, simultaneous linear equations, eigenvalues, and eigenvectors. The remaining chapters explore the materials of fundamental importance to both engineers and scientists. These chapters discuss the principles of matrix calculus, linear differential equations, Jordan canonical forms, and special matrices. A set of exercises is provided at the end of each section, which is basically routine in nature and serves primarily to enhance the reader's ability to use the methods just presented. On occasion, problems are assigned that will extend or complete topics previously introduced. This book is intended primarily for science, engineering, and applied mathematics students.

  • Mathematical Algorithms for Linear Regression

    • 1st Edition
    • Helmuth Späth
    • Werner Rheinboldt
    • English
    Mathematical Algorithms for Linear Regression discusses numerous fitting principles related to discrete linear approximations, corresponding numerical methods, and FORTRAN 77 subroutines. The book explains linear Lp regression, method of the lease squares, the Gaussian elimination method, the modified Gram-Schmidt method, the method of least absolute deviations, and the method of least maximum absolute deviation. The investigator can determine which observations can be classified as outliers (those with large errors) and which are not by using the fitting principle. The text describes the elimination of outliers and the selection of variables if too many or all of them are given by values. The clusterwise linear regression accounts if only a few of the relevant variables have been collected or are collectible, assuming that their number is small in relation to the number of observations. The book also examines linear Lp regression with nonnegative parameters, the Kuhn-Tucker conditions, the Householder transformations, and the branch-and-bound method. The text points out the method of least squares is mainly used for models with nonlinear parameters or for orthogonal distances. The book can serve and benefit mathematicians, students, and professor of calculus, statistics, or advanced mathematics.

  • Neural Networks for Perception

    Computation, Learning, and Architectures
    • 1st Edition
    • Harry Wechsler
    • English
    Neural Networks for Perception, Volume 2: Computation, Learning, and Architectures explores the computational and adaptation problems related to the use of neuronal systems, and the corresponding hardware architectures capable of implementing neural networks for perception and of coping with the complexity inherent in massively distributed computation. This book addresses both theoretical and practical issues related to the feasibility of both explaining human perception and implementing machine perception in terms of neural network models. The text is organized into two sections. The first section, computation and learning, discusses topics on learning visual behaviors, some of the elementary theory of the basic backpropagation neural network architecture, and computation and learning in the context of neural network capacity. The second section is on hardware architecture. The chapters included in this part of the book describe the architectures and possible applications of recent neurocomputing models. The Cohen-Grossberg model of associative memory, hybrid optical/digital architectures for neorocomputing, and electronic circuits for adaptive synapses are some of the subjects elucidated. Neuroscientists, computer scientists, engineers, and researchers in artificial intelligence will find the book useful.

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