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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.

  • Ordinary Differential Equations

    1971 NRL—MRC Conference
    • 1st Edition
    • Leonard Weiss
    • English
    Ordinary Differential Equations: 1971 NRL–MRC Conference provides information pertinent to the fundamental aspects of ordinary differential equations. This book covers a variety of topics, including geometric and qualitative theory, analytic theory, functional differential equation, dynamical systems, and algebraic theory. Organized into two parts encompassing 51 chapters, this book begins with an overview of the results on the existence of periodic solutions of a differential equation. This text then describes an index for the isolated invariant sets of a flow on a compact metric space, which contains exactly the information of the Morse index. Other chapters consider the studies of certain classes of equations that can be interpreted as models of biological or economic processes. This book discusses as well the absolute stability of some classes of integro-differential systems. The final chapter deals with first-order differential equations. This book is a valuable resource for mathematicians, graduate students, and research workers.

  • 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.

  • Associative Networks

    Representation and Use of Knowledge by Computers
    • 1st Edition
    • Nicholas V. Findler
    • English
    Associative Networks: Representation and Use of Knowledge by Computers is a collection of papers that deals with knowledge base of programs exhibiting some operational aspects of understanding. One paper reviews network formalism that utilizes unobstructed semantics, independent of the domain to which it is applied, that is also capable of handling significant epistemological relationships of concept structuring, attribute/value inheritance, multiple descriptions. Another paper explains network notations that encode taxonomic information; general statements involving quantification; information about processes and procedures; the delineation of local contexts, as well as the relationships between syntactic units and their interpretations. One paper shows that networks can be designed to be intuitively and formally interpretable. Network formalisms are computer-oriented logics which become distinctly significant when access paths from concepts to propositions are built into them. One feature of a topical network organization is its potential for learning. If one topic is too large, it could be broken down where groupings of propositions under the split topics are then based on "co-usage" statistics. As an example, one paper cites the University of Maryland artificial intelligence (AI) group which investigates the control and interaction of a meaning-based parser. The group also analyzes the inferences and predictions from a number of levels based on mundane inferences of actions and causes that can be used in AI. The collection can be useful for computer engineers, computer programmers, mathematicians, and researchers who are working on artificial intelligence.

  • Theory and Application of Special Functions

    Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31-April 2, 1975
    • 1st Edition
    • Richard Askey
    • English
    Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.

  • Differential Equations

    • 1st Edition
    • Shair Ahmad + 2 more
    • English
    Differential Equations is a collection of papers from the "Eight Fall Conference on Differential Equations" held at Oklahoma State University in October 1979. The papers discuss hyperbolic problems, bifurcation function, boundary value problems for Lipschitz equations, and the periodic solutions of systems of ordinary differential equations. Some papers deal with the existence of periodic solutions for nonlinearly perturbed conservative systems, the saddle-point theorem, the periodic solutions of the forced pendulum equation, as well as the structural identification (inverse) problem for illness-death processes. One paper presents an elementary proof of the work of deOliveira and Hale, and applies the stability for autonomous systems in the critical case of one zero root. Another paper explains the necessary and sufficient conditions for structural identification prior to application in states of illness-death processes. An illness-death process is a continuous Markov model with n illness (transient) states each having one (and only one) transfer into a death state. The paper examines two theorems whether these apply to an illness-death process under certain given elements. The collection is an ideal source of reference for mathematicians, students, and professor of calculus and advanced mathematics.

  • Nonlinear Programming 4

    Proceedings of the Nonlinear Programming Symposium 4 Conducted by the Computer Sciences Department at the University of Wisconsin–Madison, July 14-16, 1980
    • 1st Edition
    • Olvi L. Mangasarian + 2 more
    • English
    Nonlinear Programming, 4 focuses on linear, quadratic, and nonlinear programming, unconstrained minimization, nonsmooth and discrete optimization, ellipsoidal methods, linear complementarity problems, and software evaluation. The selection first elaborates on an upper triangular matrix method for quadratic programming, solving quadratic programs by an exact penalty function, and QP-based methods for large-scale nonlinearly constrained optimization. Discussions focus on large-scale linearly constrained optimization, search direction for superbasic variables, finite convergence, basic properties, comparison of three active set methods, and QP-based methods for dense problems. The book then examines an iterative linear programming algorithm based on an augmented Lagrangian and iterative algorithms for singular minimization problems. The publication ponders on the derivation of symmetric positive definite secant updates, preconditioned conjugate gradient methods, and finding the global minimum of a function of one variable using the method of constant signed higher order derivatives. Topics include effects of calculation errors, application to polynomial minimization, using moderate additional storage, updating Cholesky factors, and utilizing sparse second order information. The selection is a valuable source of data for researchers interested in nonlinear programming.

  • Nonlinear Functional Analysis and Applications

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, October 12-14, 1970
    • 1st Edition
    • Louis B. Rall
    • English
    Nonlinear Functional Analysis and Applications provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This book provides an introduction to the basic concepts and techniques of this field. Organized into nine chapters, this book begins with an overview of the possibilities for applying ideas from functional analysis to problems in analysis. This text then provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. Other chapters consider the various settings in nonlinear functional analysis in which differentials play a significant role. This book discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. The final chapter deals with the equations of hydrodynamics, which are usually highly nonlinear and difficult to solve. This book is a valuable resource for mathematicians. Readers who are interested in nonlinear functional analysis will also find this book useful.

  • Artificial Intelligence

    • 1st Edition
    • Earl B. Hunt
    • Edward C. Carterette + 1 more
    • English
    Artificial Intelligence provides information pertinent to the fundamental aspects of artificial intelligence. This book presents the basic mathematical and computational approaches to problems in the artificial intelligence field. Organized into four parts encompassing 16 chapters, this book begins with an overview of the various fields of artificial intelligence. This text then attempts to connect artificial intelligence problems to some of the notions of computability and abstract computing devices. Other chapters consider the general notion of computability, with focus on the interaction between computability theory and artificial intelligence. This book discusses as well the concepts of pattern recognition, problem solving, and machine comprehension. The final chapter deals with the study of machine comprehension and reviews the fundamental mathematical and computing techniques underlying artificial intelligence research. This book is a valuable resource for seniors and graduate students in any of the computer-related sciences, or in experimental psychology. Psychologists, general systems theorists, and scientists will also find this book useful.

  • 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.

  • Geometric Measure Theory

    A Beginner's Guide
    • 1st Edition
    • Frank Morgan
    • English
    Geometric Measure Theory: A Beginner's Guide provides information pertinent to the development of geometric measure theory. This book presents a few fundamental arguments and a superficial discussion of the regularity theory. Organized into 12 chapters, this book begins with an overview of the purpose and fundamental concepts of geometric measure theory. This text then provides the measure-theoretic foundation, including the definition of Hausdorff measure and covering theory. Other chapters consider the m-dimensional surfaces of geometric measure theory called rectifiable sets and introduce the two basic tools of the regularity theory of area-minimizing surfaces. This book discusses as well the fundamental theorem of geometric measure theory, which guarantees solutions to a wide class of variational problems in general dimensions. The final chapter deals with the basic methods of geometry and analysis in a generality that embraces manifold applications. This book is a valuable resource for graduate students, mathematicians, and research workers.

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