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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.

  • Operational Calculus

    • 2nd Edition
    • Volume 110
    • Thomas K. Boehme
    • I.N. Sneddon
    • English
    Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included. Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-homogeneous equations and applications of operational calculus to partial differential equations. The section section deals with the integral of an operational function and its applications, along with integral transformations. A definition of operators in terms of abstract algebra is then presented. Operators as generalized functions, power series of operators, and Laplace transform are also discussed. Formulas of the operational calculus and tables of functions round out the book. This monograph will be useful to engineers, who regard the operational calculus merely as a tool in their work, and readers who are interested in proofs of theorems and mathematical problems.

  • Advances in Computers

    • 1st Edition
    • Volume 94
    • English
    Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.

  • Convergence Problems of Orthogonal Series

    • 1st Edition
    • Volume 20
    • G. Alexits
    • English
    Convergence Problems of Orthogonal Series deals with the theory of convergence and summation of the general orthogonal series in relation to the general theory and classical expansions. The book reviews orthogonality, orthogonalization, series of orthogonal functions, complete orthogonal systems, and the Riesz-Fisher theorem. The text examines Jacobi polynomials, Haar's orthogonal system, and relations to the theory of probability using Rademacher's and Walsh's orthogonal systems. The book also investigates the convergence behavior of orthogonal series by methods belonging to the general theory of series. The text explains some Tauberian theorems and the classical Abel transform of the partial sums of a series which the investigator can use in the theory of orthogonal series. The book examines the importance of the Lebesgue functions for convergence problems, the generalization of the Walsh series, the order of magnitude of the Lebesgue functions, and the Lebesgue functions of the Cesaro summation. The text also deals with classical convergence problems in which general orthogonal series have limited significance as orthogonal expansions react upon the structural properties of the expanded function. This reaction happens under special assumptions concerning the orthogonal system in whose functions the expansion proceeds. The book can prove beneficial to mathematicians, students, or professor of calculus and advanced mathematics.

  • Variational Methods in Economics

    • 1st Edition
    • Volume 1
    • G. Hadley + 1 more
    • C. J. Bliss
    • English
    Advanced Textbooks in Economics, Volume 1: Variational Methods in Economics focuses on the application of variational methods in economics, including autonomous system, dynamic programming, and phase spaces and diagrams. The manuscript first elaborates on growth models in economics and calculus of variations. Discussions focus on connection with dynamic programming, variable end points-free boundaries, transversality at infinity, sensitivity analysis-end point changes, Weierstrass and Legendre necessary conditions, and phase diagrams and phase spaces. The text then ponders on the constraints of classical theory, including unbounded intervals of integration, free boundary conditions, comparison functions, normality, and the problem of Bolza. The publication explains two-sector models of optimal economic growth, optimal control theory, and connections with the classical theory. Topics include capital good immobile between industries, constrained state variables, linear control problems, conversion of a control problem into a problem of Lagrange, and the conversion of a nonautonomous system into an autonomous system. The book is a valuable source of information for economists and researchers interested in the variational methods in economics.

  • Foundations of Econometrics

    • 1st Edition
    • Volume 7
    • Albert Madansky
    • C. J. Bliss + 1 more
    • English
    Advanced Textbooks in Economics, Volume 7: Foundations of Econometrics focuses on the principles, processes, methodologies, and approaches involved in the study of econometrics. The publication examines matrix theory and multivariate statistical analysis. Discussions focus on the maximum likelihood estimation of multivariate normal distribution parameters, point estimation theory, multivariate normal distribution, multivariate probability distributions, Euclidean spaces and linear transformations, orthogonal transformations and symmetric matrices, and determinants. The manuscript then ponders on linear expected value models and simultaneous equation estimation. Topics include random exogenous variables, maximum likelihood estimation of a single equation, identification of a single equation, linear stochastic difference equations, and errors-in-variables models. The book takes a look at a prolegomenon to econometric model building, tests of hypotheses in econometric models, multivariate statistical analysis, and simultaneous equation estimation. Concerns include maximum likelihood estimation of a single equation, tests of linear hypotheses, testing for independence, and causality in economic models. The publication is a valuable source of data for economists and researchers interested in the foundations of econometrics.

  • Axiomatics of Classical Statistical Mechanics

    • 1st Edition
    • Volume 11
    • Rudolf Kurth
    • I. N. Sneddon + 2 more
    • English
    Axiomatics of Classical Statistical Mechanics provides an understanding of classical statistical mechanics as a deductive system. This book presents the mechanical systems of a finite number of degrees of freedom. Organized into seven chapters, this book begins with an overview of the average behavior of mechanical systems. This text then examines the concept of a mechanical system and explains the equations of motion of the system. Other chapters consider an ensemble of mechanical systems wherein a Hamiltonian function and a truncated canonical probability density corresponds to each system. This book discusses as well the necessary and sufficient conditions that are given for the existence of statistically stationary states and for the approach of mechanical systems towards these states. The final chapter deals with the fundamental laws of thermodynamics. This book is a valuable resource for mathematicians.

  • Integral Equations

    And Their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology
    • 1st Edition
    • Volume 4
    • S. G. Mikhlin
    • I. N. Sneddon + 2 more
    • English
    Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm's equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz's method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.

  • Investment

    The Study of an Economic Aggregate
    • 1st Edition
    • Volume 13
    • Philip J. Lund
    • C. J. Bliss + 1 more
    • English
    Advanced Textbooks in Economics: Investment: The Study of an Economic Aggregate focuses on the principles, methodologies, and approaches involved in the determination of investments. The book first offers information on the theories of aggregate investment and statistical and questionnaire studies. Discussions focus on statistical studies, tax incentives and disincentives to investment, capital stock adjustment models, acceleration principle, replacement investment, level of aggregation, sources of funds, neoclassical theory of capital accumulation, and tax incentives and disincentives to investment. The text then examines the estimation of lag distributions, including geometrically declining lag distributions, Pascal and rational distributions, variable lag distributions, and the first-in first-out method. The publication ponders on econometric studies, as well as United Kingdom and United States studies, two-stage studies of investment, and guidelines for future research. The text is a dependable source of information for economists and researchers interested in economic aggregates.

  • Theory of Approximation of Functions of a Real Variable

    • 1st Edition
    • Volume 34
    • A. F. Timan
    • I. N. Sneddon + 2 more
    • English
    Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.

  • The Theory of Jets in an Ideal Fluid

    • 1st Edition
    • Volume 93
    • M. I. Gurevich
    • J. P. Kahane + 2 more
    • English
    Pure and Applied Mathematics, Volume 39: The Theory of Jets in an Ideal Fluid provides a general idea of the theory of jets. This book serves as an introduction to the classical problems in the theory and provides some knowledge of the fundamentals of hydromechanics. Organized into 12 chapters, this volume begins with an overview of the theory of plane, steady flow of an ideal, incompressible fluid. This text then examines the jet flow of an unbounded current about a flat plate, placed perpendicular to the flow. Other chapters consider a number of problems involving the plane flow of fluid out of vessels. This book discusses as well the physical importance of Brillouin's condition and also the problem of cavitational flow. The final chapter deals with the flows of weightless fluid in order to know the effect of surface tension forces. This book is a valuable resource for marine and hydraulic engineers.

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