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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.

  • Numerical Mathematics and Applications

    • 1st Edition
    • Volume 1
    • J. Vignes + 1 more
    • English
    IMACS Transactions on Scientific Computation – 85, Volume I: Numerical Mathematics and Applications contains papers on theoretical and applied aspects of numerical mathematics presented at the 11th IMACS World Congress on Scientific Computation, held in Oslo, Norway on August 5-9, 1985. The book focuses on the processes, methodologies, and approaches involved in computer arithmetic. The selection first highlights the use of CESTAC method in the parallel computation of roots of polynomials, CESTAC, and reducing abbreviation errors in iterative resolution of linear systems. Discussions focus on notations and theoretical processes, sequence of iterates in floating-point arithmetic, perturbation method, and CESTAC tested on algorithm and numerical results. The book then takes a look at optimal termination criterion and accuracy tests in mathematical programming; use of the normed residue to check the quality of the solution of a linear system; and computable bounds for solutions of integral equations. The manuscript examines arbitrarily accurate boundaries for solutions of ODEs with initial values using variable precision arithmetic and remarks on some modified Romberg algorithms for numerical integration. Topics include speed of convergence and a priori truncation error estimates, acceleration of convergence, extrapolation schemes, and the initial boundary value problem. The selection is a dependable source of data for mathematicians and researchers interested in numerical mathematics and applications.

  • Regiomontanus: His Life and Work

    • 1st Edition
    • Volume 1
    • E. Zinner + 1 more
    • English
    The 500th anniversary of Regiomontanus's birth has occasioned this depiction of his life and work. It is the first English translation of Ernst Zinner's monumental biography, plus a number of specially-written supplementary articles which help paint a more comprehensive picture of the current state of knowledge about Regiomontanus. The articles show the high regard in which the biography is still held by the community of scholars doing work on the mathematics of the Renaissance.Zinner's biography is a mine of information about early printing, astrolabes, tables of eclipses and the world of Henry of Langenstein, Johann of Gmunden, Georg Peuerbach, Cardinal Bessarion, Nicholas of Cusa and the extraordinary itinerant scholar, Johannes Müller of Königsberg — Regiomontanus. His contributions to mathematics are discussed (for example, he may have discovered the fifth and sixth perfect numbers) as well as the mysteries surrounding his life and death.

  • Scientific Computing

    An Introduction with Parallel Computing
    • 1st Edition
    • Gene H. Golub + 1 more
    • English
    This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case.

  • Statistical Methods in Longitudinal Research

    Principles and Structuring Change
    • 1st Edition
    • Volume 1
    • Alexander von Eye
    • English
    These edited volumes present new statistical methods in a way that bridges the gap between theoretical and applied statistics. The volumes cover general problems and issues and more specific topics concerning the structuring of change, the analysis of time series, and the analysis of categorical longitudinal data. The book targets students of development and change in a variety of fields - psychology, sociology, anthropology, education, medicine, psychiatry, economics, behavioural sciences, developmental psychology, ecology, plant physiology, and biometry - with basic training in statistics and computing.

  • The Fix-Point Approach to Interdependent Systems

    • 1st Edition
    • Volume 132
    • H. Wold
    • English
    Contributions to Economic Analysis, 132: The Fix-Point Approach to Interdependent Systems focuses on the Fix-Point method for the estimation of interdependent systems, including the Algebraic Fix-Point, Parametric Fix-Point, and Parametric Fractional Fix-Point methods. The selection first ponders on the fix-point approach to interdependent systems, iterative algorithms for fix-point estimation, and GEID specification. Discussions focus on the GEID estimator, convergence to multiple parameter sets, design of iterative algorithms, and challenges of simultaneous equations systems. The text then takes a look at the Parametric Fix-Point (PFP) and the Algebraic Fix-Point (AFP) methods; estimation of real-world models by fix-point and other methods; and a search for asymptotically efficient estimators. Topics include autoregressive errors, estimation of the Klein-Goldberger model, estimation of a model of the Czechoslovak economy, and the Parametric Fractional Fix-Point (PFFP) and Parametric Recursive Fix-Point (PRFP) methods. The text elaborates on fix-point estimates of the structure of a model using different Y proxy starts; analysis of the nonlinear Klein-Goldberger model using fix-point estimation and other methods; and fix-point estimation in interdependent systems with specification errors. The selection is a vital reference for researchers interested in the Fix-Point method for the estimation of interdependent systems.

  • Introduction to Non-Euclidean Geometry

    • 1st Edition
    • EISENREICH
    • English
    An Introduction to Non-Euclidean Geometry covers some introductory topics related to non-Euclidian geometry, including hyperbolic and elliptic geometries. This book is organized into three parts encompassing eight chapters. The first part provides mathematical proofs of Euclid’s fifth postulate concerning the extent of a straight line and the theory of parallels. The second part describes some problems in hyperbolic geometry, such as cases of parallels with and without a common perpendicular. This part also deals with horocycles and triangle relations. The third part examines single and double elliptic geometries. This book will be of great value to mathematics, liberal arts, and philosophy major students.

  • Pursuit-Evasion Differential Games

    • 1st Edition
    • Volume 14
    • Y. Yavin + 1 more
    • English
    Twenty papers are devoted to the treatment of a wide spectrum of problems in the theory and applications of dynamic games with the emphasis on pursuit-evasion differential games. The problem of capturability is thoroughly investigated, also the problem of noise-corrupted (state) measurements. Attention is given to aerial combat problems and their attendant modelling issues, such as variable speed of the combatants, the three-dimensionality of physical space, and the combat problem, i.e. problems related to 'role determination'.

  • Topics in Geometry

    • 1st Edition
    • Robert Bix
    • English
    This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered.The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.

  • Developments in Statistics

    • 1st Edition
    • Volume 4
    • Paruchuri R. Krishnaiah
    • English
    Developments in Statistics, Volume 4 reviews developments in the theory and applications of statistics, covering topics such as time series, identifiability and model selection, and missing data. The application of structured exploratory data analysis to human genetics, specifically, the mode of inheritance, is also considered. Comprised of four chapters, this volume begins with an introduction to spectrum parameter estimation in time series analysis, restricting the discussion to the simplest univariate (that is, scalar) real-valued time series X(t). An accurate formulation of the general problem is presented. The accuracy of different consistent estimates obtained for large but fixed values of T (maximum likelihood estimates, Whittle's estimates, and simplified asymptotically efficient estimates) is also compared. The next chapter deals with identifiability and modeling in econometrics, focusing on the theoretical framework relating realization theory, identification, and parametrization. The realization theory is illustrated on various levels of generality by means of examples related to econometrics, along with some advanced applications of system theory. The book also examines inference on parameters of multivariate normal populations when some data are missing before concluding with an evaluation of structured exploratory data as applied to the study of the mode of inheritance. This monograph will be of interest to students and practitioners of statistics.

  • Discrete Optimization

    • 1st Edition
    • R. Gary Parker + 1 more
    • English
    This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas of linear programming, graph theory, and combinatorics--prere... for readers of the text. Numerous exercises are included at the end of each chapter.

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