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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.

  • Nonlinear Partial Differential Equations in Engineering

    Mathematics in Science and Engineering: A Series of Monographs and Textbooks, Vol. 18
    • 1st Edition
    • W. F. Ames
    • Richard Bellman
    • English
    Nonlinear Partial Differential Equations in Engineering discusses methods of solution for nonlinear partial differential equations, particularly by using a unified treatment of analytic and numerical procedures. The book also explains analytic methods, approximation methods (such as asymptotic processes, perturbation procedures, weighted residual methods), and specific numerical procedures associated with these equations. The text presents exact methods of solution including the quasi-linear theory, the Poisson-Euler-Darbou... equation, a general solution for anisentropic flow, and other solutions obtained from ad hoc assumptions. The book explores analytic methods such as an ad hoc solution from magneto-gas dynamics. Noh and Protter have found the Lagrange formulation to be a convenient vehicle for obtaining "soft" solutions of the equations of gas dynamics. The book notes that developing solutions in two and three dimensions can be achieved by employing Lagrangian coordinates. The book explores approximate methods that use analytical procedures to obtain solutions in the form of functions approximating solutions of nonlinear problems. Approximate methods include integral equations, boundary theory, maximum operation, and equations of elliptic types. The book can serve and benefit mathematicians, students of, and professors of calculus, statistics, or advanced mathematics.

  • Introduction to the Mathematical Theory of Control Processes

    Linear Equations and Quadratic Criteria
    • 1st Edition
    • Richard Bellman
    • Richard Bellman
    • English

  • The Theory of Splines and Their Applications

    Mathematics in Science and Engineering: A Series of Monographs and Textbooks, Vol. 38
    • 1st Edition
    • J. H. Ahlberg + 2 more
    • Richard Bellman
    • English
    The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.

  • Safety of Computer Control Systems 1985 (Safecomp '85)

    Achieving Safe Real Time Computer Systems
    • 1st Edition
    • W. J. Quirk
    • English
    Safety of Computer Control Systems 1985 (Safecomp '85): Achieving Safe Real Time Computer Systems presents the proceedings of the Fourth IFAC Workshop, held in Como, Italy, on October 1–3, 1985. This book discusses a wide range of topics ranging from direct process control through robotics to operator assistance. Organized into 28 chapters, this compilation of papers begins with an overview of the implementation of atomic actions by means of concurrent programming constructs. This text then examines the safety-related applications that usually demand the provision of redundant resources within the system. Other chapters consider the safe performance of an industrial robot system that relies on several factors. This book discusses as well the increasing demand for Computer Assisted Decision Making (CADM) both in engineering and service industries. The final chapter deals with the ways of reducing the effects of an error introduced during the design of a program. This book is a valuable resource for software engineers.

  • Localization of Nilpotent Groups and Spaces

    • 1st Edition
    • Peter Hilton + 2 more
    • Leopoldo Nachbin
    • English
    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.

  • Training for Tomorrow

    Educational Aspects of Computerized Automation
    • 1st Edition
    • J. E. Rijnsdorp + 2 more
    • English
    Training for Tomorrow: Educational Aspects of Computerized Automation is a collection of papers that discusses the introduction of automated systems in all sectors of industry, business, and society. The materials in the title particularly tackle the training concerns in the implementation of automated systems. The issues addressed in the text include training in administrative automation; development of operator training as an integrated part of the specification, design, and implementation of a process control system; and training for the planning of large-scale control systems. The selection also talks about the maintenance of professionals’ training course; the feasibility of success in retraining non-EDP college graduates for EDP occupations; and the future of automation. The book will be of great interest to individuals concerned with the implication of implementing automated systems in various sectors of industry, business, and society.

  • Concepts from Tensor Analysis and Differential Geometry

    • 1st Edition
    • Tracy Y. Thomas
    • Richard Bellman
    • English
    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.

  • Comparison and Oscillation Theory of Linear Differential Equations

    • 1st Edition
    • C. A. Swanson
    • Richard Bellman
    • English
    Mathematics in Science and Engineering, Volume 48: Comparison and Oscillation Theory of Linear Differential Equations deals primarily with the zeros of solutions of linear differential equations. This volume contains five chapters. Chapter 1 focuses on comparison theorems for second order equations, while Chapter 2 treats oscillation and nonoscillation theorems for second order equations. Separation, comparison, and oscillation theorems for fourth order equations are covered in Chapter 3. In Chapter 4, ordinary equations and systems of differential equations are reviewed. The last chapter discusses the result of the first analog of a Sturm-type comparison theorem for an elliptic partial differential equation. This publication is intended for college seniors or beginning graduate students who are well-acquainted with advanced calculus, complex analysis, linear algebra, and linear differential equations.

  • Real-Variable Methods in Harmonic Analysis

    • 1st Edition
    • Alberto Torchinsky
    • Samuel Eilenberg + 1 more
    • English
    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.

  • Structural Design and Analysis

    Composite Materials, Vol. 7
    • 1st Edition
    • C. C. Chamis
    • English

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