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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.

BooksJournals

    • Solution of Equations and Systems of Equations

      • 2nd Edition
      • June 3, 2016
      • A. M. Ostrowski
      • Paul A. Smith + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 1 0 2 1 6
      • eBook
        9 7 8 1 4 8 3 2 2 3 6 4 3
      Solution of Equations and Systems of Equations, Second Edition deals with the Laguerre iteration, interpolating polynomials, method of steepest descent, and the theory of divided differences. The book reviews the formula for confluent divided differences, Newton's interpolation formula, general interpolation problems, and the triangular schemes for computing divided differences. The text explains the method of False Position (Regula Falsi) and cites examples of computation using the Regula Falsi. The book discusses iterations by monotonic iterating functions and analyzes the connection of the Regula Falsi with the theory of iteration. The text also explains the idea of the Newton-Raphson method and compares it with the Regula Falsi. The book also cites asymptotic behavior of errors in the Regula Falsi iteration, as well as the theorem on the error of the Taylor approximation to the root. The method of steepest descent or gradient method proposed by Cauchy ensures "global convergence" in very general conditions. This book is suitable for mathematicians, students, and professor of calculus, and advanced mathematics.

    • Treatise on Analysis

      • 1st Edition
      • June 3, 2016
      • J. Dieudonné
      • H. Bass + 2 more
      • English
      • eBook
        9 7 8 1 4 8 3 2 6 6 8 3 1
      Treatise on Analysis, Volume 10–VIII provides information pertinent to the study of the most common boundary problems for partial differential equations. This book presents the study of Cauchy's problem in its most elementary form. Comprised of one chapter, this volume begins with an overview of Hilbert-von Neumann spectral theory and explores all possible boundary conditions related to spectral theory. This text then examines the link of Cauchy's problem with the behavior of the equation's characteristics. This book discusses as well the case of linear elliptic operators. The reader is also introduced to Sobolev spaces and some of their generalizations that provide an essential tool in the study of these elliptic problems, and their manipulation requires delicate upper bounds to obtain the best possible results. This book is a valuable resource for mathematicians.

    • Adaptive Processes in Economic Systems

      • 1st Edition
      • June 3, 2016
      • Roy E. Murphy
      • Richard Bellman
      • English
      • Paperback
        9 7 8 1 4 8 3 2 5 3 4 2 8
      • eBook
        9 7 8 1 4 8 3 2 6 4 0 7 3
      Mathematics in Science and Engineering, Volume 20, Adaptive Processes in Economic Systems demonstrates the usefulness of communications theory, self-adaptive control theory, and thermodynamic theory to certain economic processes. This book discusses the common properties of adaptive processes, role of the decision maker, and mixed adaptive processes of the first and second kind. The economic environmental processes, concept of entropy time, and stochastic dynamic economic process are also elaborated. This text likewise covers the investment model with full liquidity, adaptive capital allocation process, and concept of an economic state space. Other topics include the stochastic equilibrium in the market and individual adaptive behavior. This volume is suitable for engineers, economists, and specialists of disciplines related to economic systems.

    • Advanced Topics in the Theory of Dynamical Systems

      • 1st Edition
      • June 3, 2016
      • G. Fusco + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 4 4 6 8
      • eBook
        9 7 8 1 4 8 3 2 1 7 8 9 5
      Advanced Topics in the Theory of Dynamical Systems covers the proceedings of the international conference by the same title, held at Villa Madruzzo, Trento, Italy on June 1-6, 1987. The conference reviews research advances in the field of dynamical systems. This book is composed of 20 chapters that explore the theoretical aspects and problems arising from applications of these systems. Considerable chapters are devoted to finite dimensional systems, with special emphasis on the analysis of existence of periodic solutions to Hamiltonian systems. Other chapters deal with infinite dimensional systems and the developments of methods in the general approach to existence and qualitative analysis problems in the general theory, as well as in the study of particular systems concerning natural sciences. The final chapters discuss the properties of hyperbolic sets, equivalent period doubling, Cauchy problems, and quasiperiodic solitons for nonlinear Klein-Gordon equations. This book is of value to mathematicians, physicists, researchers, and advance students.

    • Concepts from Tensor Analysis and Differential Geometry

      • 1st Edition
      • June 3, 2016
      • Tracy Y. Thomas
      • Richard Bellman
      • English
      • Paperback
        9 7 8 1 4 8 3 2 5 3 4 3 5
      • eBook
        9 7 8 1 4 8 3 2 6 3 7 1 7
      Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.

    • Topological Vector Spaces, Distributions and Kernels

      • 1st Edition
      • June 3, 2016
      • François Treves
      • Paul A. Smith + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 1 0 1 9 3
      • eBook
        9 7 8 1 4 8 3 2 2 3 6 2 9
      Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.

    • Scattering Theory

      • 1st Edition
      • June 3, 2016
      • Peter D. Lax + 1 more
      • Paul A. Smith + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 1 0 2 0 9
      • eBook
        9 7 8 1 4 8 3 2 2 3 6 3 6
      Scattering Theory describes classical scattering theory in contrast to quantum mechanical scattering theory. The book discusses the formulation of the scattering theory in terms of the representation theory. The text also explains the relation between the behavior of the solution of the perturbed problem at small distances for large positive times and the analytic continuation of the scattering matrix. To prove the representation theorem, the text cites the methods used by Masani and Robertson in their work dealing with stationary stochastic processes. The book also applies the translation representation theory to a wave equation to obtain a comparison of the asymptotic properties of the free space solution with those of the solution in an exterior domain. The text discusses the solution of the wave equation in an exterior domain by fitting this problem into the abstract framework to get a verification of the hypotheses in some other theorems. The general theory of scattering can be applied to symmetric hyperbolic systems in which all sound speeds are different from zero, as well as to the acoustic equation which has a potential that can cause an energy form to become indefinite. The book is suitable for proponents of analytical mathematics, particle physics, and quantum physics.

    • Structural Design and Analysis

      • 1st Edition
      • June 3, 2016
      • C. C. Chamis
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 3 3 1 7
      • eBook
        9 7 8 1 4 8 3 2 1 6 7 4 4
      Composite Materials, Volume 8: Structural Design and Analysis, Part II covers the methods of structural design and analysis. The book discusses the discrete element analysis of composite structures; the concepts of probabilistic design and reliability as it pertains to composites; and the experimental methods for characterizing composites and composite components. The text also describes the state-of-the-art of the analysis of discontinuities, edge effects, and joints in composites; as well as the methodology for designing composite structural components. Materials scientists, materials engineers, and researchers of fiber composites will find the book invaluable.

    • Real-Variable Methods in Harmonic Analysis

      • 1st Edition
      • June 3, 2016
      • Alberto Torchinsky
      • Samuel Eilenberg + 1 more
      • English
      • eBook
        9 7 8 1 4 8 3 2 6 8 8 8 0
      Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.

    • Localization of Nilpotent Groups and Spaces

      • 1st Edition
      • June 3, 2016
      • Peter Hilton + 2 more
      • Leopoldo Nachbin
      • English
      • eBook
        9 7 8 1 4 8 3 2 5 8 7 4 4
      North-Holland Mathematics Studies, 15: Localization of Nilpotent Groups and Spaces focuses on the application of localization methods to nilpotent groups and spaces. The book first discusses the localization of nilpotent groups, including localization theory of nilpotent groups, properties of localization in N, further properties of localization, actions of a nilpotent group on an abelian group, and generalized Serre classes of groups. The book then examines homotopy types, as well as mixing of homotopy types, localizing H-spaces, main (pullback) theorem, quasifinite nilpotent spaces, localization of nilpotent complexes, and nilpotent spaces. The manuscript takes a look at the applications of localization theory, including genus and H-spaces, finite H-spaces, and non-cancellation phenomena. The publication is a vital source of data for mathematicians and researchers interested in the localization of nilpotent groups and spaces.

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