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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.

  • Optimizing Methods in Statistics

    Proceedings of a Symposium Held at the Center for Tomorrow, the Ohio State University, June 14-16, 1971
    • 1st Edition
    • Jagdish S. Rustagi
    • English
    Optimizing Method in Statistics is a compendium of papers dealing with variational methods, regression analysis, mathematical programming, optimum seeking methods, stochastic control, optimum design of experiments, optimum spacings, and order statistics. One paper reviews three optimization problems encountered in parameter estimation, namely, 1) iterative procedures for maximum likelihood estimation, based on complete or censored samples, of the parameters of various populations; 2) optimum spacings of quantiles for linear estimation; and 3) optimum choice of order statistics for linear estimation. Another paper notes the possibility of posing various adaptive filter algorithms to make the filter learn the system model while the system is operating in real time. By reducing the time necessary for process modeling, the time required to implement the acceptable system design can also be reduced One paper evaluates the parallel structure between duality relationships for the linear functional version of the generalized Neyman-Pearson problem, as well as the duality relationships of linear programming as these apply to bounded-variable linear programming problems. The compendium can prove beneficial to mathematicians, students, and professor of calculus, statistics, or advanced mathematics.

  • Fourier Expansions

    A Collection of Formulas
    • 1st Edition
    • Fritz Oberhettinger
    • English
    Fourier Expansions: A Collection of Formulas provides a collection of Fourier series. Its limited scope made a number of compromises necessary. The question regarding the choice and organization of the material to be included posed certain problems. In order to preserve some consistency it seemed best to stay within the framework of what one could call the ""classical"" Fourier series, i.e., those of the trigonometric and their simplest generalization the Fourier-Bessel series. The book is organized into five sections: Section I presents Fourier series with elementary coefficients representing elementary functions. Section II presents Fourier series with elementary coefficients representing higher functions. Section III presents Fourier series with higher function coefficients representing elementary functions. Section IV presents Fourier series with higher function coefficients representing higher functions. Section V presents exponential Fourier and Fourier-Bessel series. This arrangement should be helpful in equally balancing the task of either establishing the sum function of a given Fourier series or finding the Fourier expansion of a given function. It is hoped that this book will meet the requirements so often needed in applied mathematics, physics, and engineering.

  • Algebraic Analysis

    Papers Dedicated to Professor Mikio Sato on the Occasion of His Sixtieth Birthday
    • 1st Edition
    • Masaki Kashiwara + 1 more
    • English
    Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion of his 60th Birthday, Volume I is a collection of research papers on algebraic analysis and related topics in honor to Professor Mikio Sato’s 60th birthday. This volume is composed of 35 chapters and begins with papers concerning Sato’s early career in algebraic analysis. The succeeding chapters deal with research works on the existence of local holomorphic solutions, the holonomic q-difference systems, partial differential equations, and the properties of solvable models. Other chapters explore the fundamentals of hypergeometric functions, the Toda lattice in the complex domain, the Lie algebras, b-functions, p-adic integrals, analytic parameters of hyperfunctions, and some applicatioins of microlocal energy methods to analytic hypoeellipticity. This volume also presents studies on the complex powers of p-adic fields, operational calculus, extensions of microfunction sheaves up to the boundary, and the irregularity of holonomic modules. The last chapters feature research works on error analysis of quadrature formulas obtained by variable transformation and the analytic functional on the complex light cone, as well as their Fourier-Borel transformations. This book will prove useful to mathematicians and advance mathematics students.

  • Random Polynomials

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • A. T. Bharucha-Reid + 1 more
    • Z. W. Brinbaum + 1 more
    • English
    Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Random Polynomials focuses on a comprehensive treatment of random algebraic, orthogonal, and trigonometric polynomials. The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials. The text then elaborates on the number and expected number of real zeros of random algebraic polynomials; number and expected number of real zeros of other random polynomials; and variance of the number of real zeros of random algebraic polynomials. Topics include the expected number of real zeros of random orthogonal polynomials and the number and expected number of real zeros of trigonometric polynomials. The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials. The publication is a dependable reference for probabilists, statisticians, physicists, engineers, and economists.

  • Constrained Optimization and Lagrange Multiplier Methods

    • 1st Edition
    • Dimitri P. Bertsekas
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Constrained Optimization and Lagrange Multiplier Methods focuses on the advancements in the applications of the Lagrange multiplier methods for constrained minimization. The publication first offers information on the method of multipliers for equality constrained problems and the method of multipliers for inequality constrained and nondifferentiable optimization problems. Discussions focus on approximation procedures for nondifferentiable and ill-conditioned optimization problems; asymptotically exact minimization in the methods of multipliers; duality framework for the method of multipliers; and the quadratic penalty function method. The text then examines exact penalty methods, including nondifferentiable exact penalty functions; linearization algorithms based on nondifferentiable exact penalty functions; differentiable exact penalty functions; and local and global convergence of Lagrangian methods. The book ponders on the nonquadratic penalty functions of convex programming. Topics include large scale separable integer programming problems and the exponential method of multipliers; classes of penalty functions and corresponding methods of multipliers; and convergence analysis of multiplier methods. The text is a valuable reference for mathematicians and researchers interested in the Lagrange multiplier methods.

  • Group Analysis of Differential Equations

    • 1st Edition
    • L. V. Ovsiannikov
    • English
    Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.

  • Large Scale Scientific Computation

    Proceedings of a Conference Conducted by the Mathematics Research Center, the University of Wisconsin - Madison, May 17-19, 1983
    • 1st Edition
    • Seymour V. Parter
    • English
    Large Scale Scientific Computation is a collection of papers that deals with specialized architectural considerations, efficient use of existing computers, software developments, large scale projects in diverse disciplines, and mathematical approaches to basic algorithmic problems. One paper describes numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques applied in many institutions such as in Laboratoire Central des Ponts et Chaussees, Avions Marcel Dassault et Breguet Aviation. Another paper discusses computer-structured design techniques to improve the reliability, efficiency, and accuracy of future production codes. Computer modelling is a potent tool in numerical weather prediction relying on observation, analysis, initialization, and model development. One paper illustrates a systolic algorithm for matrix triangulation, as well as its uses in the Cholesky decomposition of covariance matrices. Another paper describes the Transient Reactor Analysis Code (TRAC) designed to deal with internal flow problems of nuclear reactors. One paper explains the application of large-scale aerodynamic simulation where the programmer can use finite difference techniques in which a large number of mesh points are strategically and orderly placed in the domain of the flow field. The collection is intended for undergraduates in mathematics, programming, computer science, or engineering courses, and designers or researchers involved in industrial facilities, aeronautics, and nuclear design.

  • Advanced Programming with Microsoft QuickC

    • 1st Edition
    • Keith Weiskamp
    • English
    Advanced Programming with Microsoft QuickC provides the necessary programming tools for programmers who are interested in learning new skills in developing some useful tools and PC applications using the QuickC programming language. The book emphasizes practical and useful programming examples. It is organized into five sections. The first section introduces the proposed ANSI standard features, tips and techniques about C programming style, working with the C preprocessor, and tips for using pointers and managing memory allocation tasks. Section 2 presents data structures, discussing techniques for constructing useful and reliable data structures from linked lists to binary trees. The third section covers the many tools that QuickC provides for accessing files and other I/O devices. Section 4 explains the techniques for interacting with DOS and the special features of QuickC. The final chapter presents the tools and techniques for developing QuickC-like user interfaces. Computer programmers will find the text very useful.

  • Teaching of Statistics and Statistical Consulting

    • 1st Edition
    • Jagdish S. Rustagi + 1 more
    • English
    Teaching of Statistics and Statistical Consulting is a collection of papers dealing with graduate programs in statistics; teaching service courses and short courses; and training statisticians for employment in industry and government. Some papers also deal with the role of statistical consulting in graduate training and teaching statistics at the Open University. One paper describes some observations made on graduate program in statistics, citing concerns of professionalism, competency, and a highly structured university curriculum. Another paper takes a task analysis approach to designing a regression analysis course where, with proper course structuring, students will actively learn to do the objectives of the course. Other papers discuss consulting and research work at the Australian Government's research organization, as well as how to prepare statisticians for future government service or for the private industry. One paper deals with some important things that a practicing statistician should know, but which are seldom taught in statistics courses. Another paper describes teaching statistics at a distance from the Open University in the United Kingdom. The collection can prove helpful for academic statisticians in educational institutions, to statisticians, or to mathematicians employed in the public or private sectors.

  • Frontiers of Pattern Recognition

    The Proceedings of the International Conference on Frontiers of Pattern Recognition
    • 1st Edition
    • Satosi Watanabe
    • English
    Frontiers of Pattern Recognition contains the proceedings of the International Conference on Frontiers of Pattern Recognition which took place on January 18-20, 1971, at the University of Hawaii, Honolulu. The compendium consists of 30 papers from authorities from eleven different countries, which describe the frontiers of pattern recognition as viewed from diverse viewpoints. Topics discussed include some techniques for recognizing structures in pictures, grammatical inference, syntactic pattern recognition and stochastic languages, and pattern cognition and the organization of information. Also covered are subjects on human face recognition, cluster analysis, and learning algorithms of pattern recognition in non-stationary conditions. Computer scientists, mathematicians, statisticians, linguists, and psychologists will find the book informative.

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