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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.

  • Projective Transformations

    Geometric Transformations
    • 1st Edition
    • P. S. Modenov + 1 more
    • Henry Booker + 2 more
    • English
    Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserv... transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

  • Population Dynamics

    Proceedings of a Symposium Conducted by the Mathematics Research Center The University of Wisconsin, Madison June 19–21, 1972
    • 1st Edition
    • T. N. E. Greville
    • English
    Population Dynamics covers the proceedings of a symposium conducted by the Mathematics Research Center, The University of Wisconsin, Madison on June 19-21, 1972. The book focuses on the application of mathematics to the study of human population growth. The selection first offers information on population waves and the properties of a stochastic attraction model. Discussions focus on social distance, limiting behavior of the model, mathematical development, population increase and retirement pensions, natural periodicity in the demographic system, trends in generational stability, mobility in unstable populations, and the Easterlin effect. The text then takes a look at the sampling frame as a determinant of observed distributions of duration variables and comparison of alternative marriage models, including plausible marriage models, axioms for marriage functions, birth intervals, and computer simulation of prospective and interior birth interval lengths. The manuscript ponders on contraceptive impact over several generations, estimation of the risk of conception from censored data, and influence of cause of death structure on age-patterns of mortality. Topics include distributions of conception times, simulation of experiments, potential fertility of users, and length of protection. The selection is a valuable reference for researchers interested in population dynamics.

  • Theoretical Numerical Analysis

    • 1st Edition
    • Burton Wendroff
    • English
    Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.

  • Elementary Differential Geometry

    • 1st Edition
    • Barrett O'Neill
    • English
    Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

  • An Introduction to Numerical Mathematics

    • 1st Edition
    • Eduard L. Stiefel
    • English
    An Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear programming, linear and nonlinear algebra, polynomials, numerical differentiation, and approximations. Organized into seven chapters, this book begins with an overview of the solution of linear problems wherein numerical mathematics provides very effective algorithms consisting of finitely many computational steps. This text then examines the method for the direct solution of a definite problem. Other chapters consider the determination of frequencies in freely oscillating mechanical or electrical systems. This book discusses as well eigenvalue problems for oscillatory systems of finitely many degrees of freedom, which can be reduced to algebraic equations. The final chapter deals with the approximate representation of a function f(x) given by I-values as in the form of a table. This book is a valuable resource for physicists, mathematicians, theoreticians, engineers, and research workers.

  • Theoretical Aspects of Reasoning About Knowledge

    Proceedings of the 1986 Conference
    • 1st Edition
    • Joseph Y. Halpern
    • English
    Theoretical Aspects of Reasoning About Knowledge: Proceedings of the 1986 Conference focuses on the principles, methodologies, approaches, and concepts involved in reasoning about knowledge. The selection first provides an overview of reasoning about knowledge, varieties of self-reference, and pegs and alecs. Topics covered include data semantics, partial objects and identity, circumstance, self, and causal connection, structure of circumstance, varieties and limits of self-reference, problem of logical omniscience, and knowledge, communication, and action. The book then explores reasoning about knowledge in artificial intelligence; synthesis of digital machines with provable epistemic properties; and a first order theory of planning, knowledge, and action. The publication ponders on the consistency of syntactical treatments of knowledge, foundations of knowledge for distributed systems, knowledge and implicit knowledge in a distributed environment, and the logic of distributed protocols. Topics include formal syntax and semantics, structure of models, message-based knowledge worlds, changing the class of messages, implicit knowledge in message-based knowledge worlds, conservation and implicit knowledge, and distributed protocols. The selection is a dependable source of data for researchers interested in the theoretical aspects of reasoning about knowledge.

  • Differential and Riemannian Geometry

    • 1st Edition
    • Detlef Laugwitz
    • English
    Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces. The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry. The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations. The book is a valuable reference for researchers interested in differential and Riemannian geometry.

  • Generalized Functions

    Applications of Harmonic Analysis
    • 1st Edition
    • I. M. Gel'fand + 1 more
    • English
    Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.

  • Philosophy and Foundations of Mathematics

    L. E. J. Brouwer
    • 1st Edition
    • A. Heyting
    • English
    L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

  • Computing Methods in Optimization Problems

    Proceedings of a Conference Held at University of California, Los Angeles January 30-31, 1964
    • 1st Edition
    • A. V. Balakrishnan + 1 more
    • English
    Computing Methods in Optimization Problems deals with hybrid computing methods and optimization techniques using computers. One paper discusses different numerical approaches to optimizing trajectories, including the gradient method, the second variation method, and a generalized Newton-Raphson method. The paper cites the advantages and disadvantages of each method, and compares the second variation method (a direct method) with the generalized Newton-Raphson method (an indirect method). An example problem illustrates the application of the three methods in minimizing the transfer time of a low-thrust ion rocket between the orbits of Earth and Mars. Another paper discusses an iterative process for steepest-ascent optimization of orbit transfer trajectories to minimize storage requirements such as in reduced memory space utilized in guidance computers. By eliminating state variable storage and control schedule storage, the investigator can achieve reduced memory requirements. Other papers discuss dynamic programming, invariant imbedding, quasilinearization, Hilbert space, and the computational aspects of a time-optimal control problem. The collection is suitable for computer programmers, engineers, designers of industrial processes, and researchers involved in aviation or control systems technology.

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