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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

    • Nonlinear Partial Differential Equations in Engineering

      • 1st Edition
      • June 3, 2016
      • W. F. Ames
      • Richard Bellman
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 9 4 9 4
      • eBook
        9 7 8 1 4 8 3 2 2 2 9 2 9
      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.

    • Comparison and Oscillation Theory of Linear Differential Equations

      • 1st Edition
      • June 3, 2016
      • C. A. Swanson
      • Richard Bellman
      • English
      • Paperback
        9 7 8 1 4 8 3 2 5 3 2 7 5
      • eBook
        9 7 8 1 4 8 3 2 6 6 6 7 1
      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.

    • Nonarchimedean Fields and Asymptotic Expansions

      • 1st Edition
      • June 3, 2016
      • A. H. Lightstone + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 5 0 0 9 0
      • eBook
        9 7 8 1 4 8 3 2 5 7 4 4 0
      North-Holland Mathematical Library, Volume 13: Nonarchimedean Fields and Asymptotic Expansions focuses on the connection between nonarchimedean systems and the orders of infinity and smallness that are related with the asymptotic behavior of a function. The publication first explains nonarchimedean fields and nonstandard analysis. Discussions focus on the method of mathematical logic, ultrapower construction, principles of permanence, internal functions, many-sorted structures, nonarchimedean fields and groups, and fields with evaluation. The text then discusses the Euler-Maclaurin expansions and the formal concept of asymptotic expansions. Topics include a generalized criterion for asymptotic expansions, asymptotic power series, Watson's Lemma, asymptotic sequences, and the Euler-Maclaurin formula. The manuscript examines Popken space, including asymptotically finite functions, convergence, norm, algebraic properties of the norm, and Popken's description of the norm. The text is a dependable reference for mathematicians and researchers interested in nonarchimedean fields and asymptotic expansions.

    • The Theory of Splines and Their Applications

      • 1st Edition
      • June 3, 2016
      • J. H. Ahlberg + 2 more
      • Richard Bellman
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 9 5 2 4
      • eBook
        9 7 8 1 4 8 3 2 2 2 9 5 0
      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.

    • Optimization of Stochastic Systems

      • 1st Edition
      • June 3, 2016
      • Masanao Aoki
      • Richard Bellman
      • English
      • Paperback
        9 7 8 1 4 8 3 2 1 0 6 2 9
      • eBook
        9 7 8 1 4 8 3 2 2 4 0 5 3

    • 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 0 0
      • eBook
        9 7 8 1 4 8 3 2 1 6 7 3 7

    • Semihypergroup Theory

      • 1st Edition
      • June 2, 2016
      • Bijan Davvaz
      • English
      • Paperback
        9 7 8 0 1 2 8 0 9 8 1 5 8
      • eBook
        9 7 8 0 1 2 8 0 9 9 2 5 4
      Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled. Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject.

    • Theory and Methods of Statistics

      • 1st Edition
      • May 26, 2016
      • P.K. Bhattacharya + 1 more
      • English
      • Paperback
        9 7 8 0 1 2 8 0 2 4 4 0 9
      • eBook
        9 7 8 0 1 2 8 0 4 1 2 3 9
      Theory and Methods of Statistics covers essential topics for advanced graduate students and professional research statisticians. This comprehensive resource covers many important areas in one manageable volume, including core subjects such as probability theory, mathematical statistics, and linear models, and various special topics, including nonparametrics, curve estimation, multivariate analysis, time series, and resampling. The book presents subjects such as "maximum likelihood and sufficiency," and is written with an intuitive, heuristic approach to build reader comprehension. It also includes many probability inequalities that are not only useful in the context of this text, but also as a resource for investigating convergence of statistical procedures.

    • Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

      • 1st Edition
      • May 17, 2016
      • Michal Feckan + 1 more
      • English
      • Hardback
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      • eBook
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      Poincaré-Andronov-Me... Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switch... boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity.

    • Newnes Circuit Calculations Pocket Book

      • 1st Edition
      • April 20, 2016
      • Thomas J. Davies
      • English
      • Paperback
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      • eBook
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      Newnes Circuit Calculations Pocket Book: With Computer Programs presents equations, examples, and problems in circuit calculations. The text includes 300 computer programs that help solve the problems presented. The book is comprised of 20 chapters that tackle different aspects of circuit calculation. The coverage of the text includes dc voltage, dc circuits, and network theorems. The book also covers oscillators, phasors, and transformers. The text will be useful to electrical engineers and other professionals whose work involves electronic circuitry.

Related subjects

Mathematics and applied mathematics

Statistics and probability