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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.

  • Annual Review in Automatic Programming

    International Tracts in Computer Science and Technology and Their Application, Vol. 2
    • 1st Edition
    • Richard Goodman
    • English
    Annual Review in Automatic Programming, Volume 2 is a collection of papers that discusses the controversy about the suitability of COBOL as a common business oriented language, and the development of different common languages for scientific computation. A couple of papers describes the use of the Genie system in numerical calculation and analyzes Mercury autocode in terms of a phrase structure language, such as in the source language, target language, the order structure of ATLAS, and the meta-syntactical language of the assembly program. Other papers explain interference or an "intermediate return" using ALGOL, the National-Elliot 803 Computer, and the MADCAP II. MADCAP II is A version of the automatic programming compiler for MANIAC II. One paper discusses the APT which serves as a common computer language for computational problems. Another paper explains SAKO which can bypass machine language almost entirely in the field of numerical and logical problems, particularly in programs using XYZ and ZAM II. A report of the Working Committee of the British Computer Society Discussion Group No. 5 concludes that COBOL is unnecessarily complex due to its close machine orientation. Computer engineers, computer instructors, programmers, and students of computer science will find the collection highly valuable.

  • Analytical Solution Methods for Boundary Value Problems

    • 1st Edition
    • A.S. Yakimov
    • English
    Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods.

  • Biostatistics and Computer-based Analysis of Health Data using R

    • 1st Edition
    • Christophe Lalanne + 1 more
    • English
    Biostatistics and Computer-Based Analysis of Health Data Using the R Software addresses the concept that many of the actions performed by statistical software comes back to the handling, manipulation, or even transformation of digital data. It is therefore of primary importance to understand how statistical data is displayed and how it can be exploited by software such as R. In this book, the authors explore basic and variable commands, sample comparisons, analysis of variance, epidemiological studies, and censored data. With proposed applications and examples of commands following each chapter, this book allows readers to apply advanced statistical concepts to their own data and software.

  • Statistical Aspects of the Microbiological Examination of Foods

    • 3rd Edition
    • Basil Jarvis
    • English
    Statistical Aspects of the Microbiological Examination of Foods, Third Edition, updates some important statistical procedures following intensive collaborative work by many experts in microbiology and statistics, and corrects typographic and other errors present in the previous edition. Following a brief introduction to the subject, basic statistical concepts and procedures are described including both theoretical and actual frequency distributions that are associated with the occurrence of microorganisms in foods. This leads into a discussion of the methods for examination of foods and the sources of statistical and practical errors associated with the methods. Such errors are important in understanding the principles of measurement uncertainty as applied to microbiological data and the approaches to determination of uncertainty. The ways in which the concept of statistical process control developed many years ago to improve commercial manufacturing processes can be applied to microbiological examination in the laboratory. This is important in ensuring that laboratory results reflect, as precisely as possible, the microbiological status of manufactured products through the concept and practice of laboratory accreditation and proficiency testing. The use of properly validated standard methods of testing and the verification of ‘in house’ methods against internationally validated methods is of increasing importance in ensuring that laboratory results are meaningful in relation to development of and compliance with established microbiological criteria for foods. The final chapter of the book reviews the uses of such criteria in relation to the development of and compliance with food safety objectives. Throughout the book the theoretical concepts are illustrated in worked examples using real data obtained in the examination of foods and in research studies concerned with food safety.

  • Fixed Point Theory and Graph Theory

    Foundations and Integrative Approaches
    • 1st Edition
    • Monther Alfuraidan + 1 more
    • English
    Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets.

  • Cybersecurity and Applied Mathematics

    • 1st Edition
    • Leigh Metcalf + 1 more
    • English
    Cybersecurity and Applied Mathematics explores the mathematical concepts necessary for effective cybersecurity research and practice, taking an applied approach for practitioners and students entering the field. This book covers methods of statistical exploratory data analysis and visualization as a type of model for driving decisions, also discussing key topics, such as graph theory, topological complexes, and persistent homology. Defending the Internet is a complex effort, but applying the right techniques from mathematics can make this task more manageable. This book is essential reading for creating useful and replicable methods for analyzing data.

  • A Collection of Problems on a Course of Mathematical Analysis

    International Series of Monographs in Pure and Applied Mathematics
    • 1st Edition
    • G. N. Berman
    • I. N. Sneddon + 2 more
    • English
    A Collection of Problems on a Course of Mathematical Analysis is a collection of systematically selected problems and exercises (with corresponding solutions) in mathematical analysis. A common instruction precedes a group of problems of the same type. Problems with a physics content are preceded by the necessary physical laws. In the case of more or less difficult problems, hints are given in the answers. This book is comprised of 15 chapters and begins with an overview of functions and methods of specifying them; notation for and classification of functions; elementary investigation of functions; and trigonometric and inverse trigonometric functions. The following chapters deal with limits and tests for their existence; differential calculus, with emphasis on derivatives and differentials; functions and curves; definite and indefinite integrals; and methods of evaluating definite integrals. Some applications of the integral in geometry, statics, and physics are also considered; along with functions of several variables; multiple integrals and iterated integration; line and surface integrals; and differential equations. The final chapter is devoted to trigonometric series. This monograph is intended for students studying mathematical analysis within the framework of a technical college course.

  • A Collection of Problems in Analytical Geometry

    Three-Dimensional Analytical Geometry
    • 1st Edition
    • D. V. Kletenik
    • W. J. Langford + 1 more
    • English
    A Collection of Problems in Analytical Geometry, Part II: Three-Dimensional Analytical Geometry is a collection of problems dealing with analytical geometry in the field of theoretical mechanics. The book discusses rectangular Cartesian coordinates in three-dimensional space and the division of an interval in a given ratio. The sample questions concern problems dealing with isosceles triangles, vertices, and center of gravity of equal masses. The book defines the concept of a vector and then lists problems concerning the triangle law and the scalar product of two vectors. Other problems focus on the equations of a surface and a curve and on questions related to the intersection of three surfaces. The text lists other problems such as the equation of a plane, the direction-vector of a straight line, and miscellaneous problems pertaining to the equations of a plane, of a straight line, and of a sphere in a direction-vector. The selection is useful for professors in analytical geometry and for other courses in physic-mathematics and general engineering.

  • Exploring University Mathematics

    Lectures Given at Bedford College, London
    • 1st Edition
    • Mary Bradburn + 2 more
    • N. J. Hardiman
    • English
    Exploring University Mathematics, Volume 3 provides information pertinent to pure and applied mathematics. This book discusses the close relationship between mathematics and physics. Organized into seven chapters, this volume begins with an overview of the concept of mapping in mathematics, which provides a correspondence between elements of one set with elements of another. This text then examines the theory of inflatable structures in the study of the hovercrafs in two dimensions. Other chapters consider the explicit investigation of logic by mathematicians whereby mathematics has been conceived as pre-eminently a deductive science. This book discusses as well how Taylor's formula is used in various aspects, including integration, approximating functions, finding roots of algebraic equations, and solving differential equations in forms suitable for computer calculations. This book is intended to be suitable for students on a degree course in mathematics. Mathematicians, teachers, and research workers will also find this book extremely useful.

  • An Introduction to Mathematical Analysis

    International Series of Monographs on Pure and Applied Mathematics
    • 1st Edition
    • Robert A. Rankin
    • I. N. Sneddon + 2 more
    • English
    An Introduction to Mathematical Analysis is an introductory text to mathematical analysis, with emphasis on functions of a single real variable. Topics covered include limits and continuity, differentiability, integration, and convergence of infinite series, along with double series and infinite products. This book is comprised of seven chapters and begins with an overview of fundamental ideas and assumptions relating to the field operations and the ordering of the real numbers, together with mathematical induction and upper and lower bounds of sets of real numbers. The following chapters deal with limits of real functions; differentiability and maxima, minima, and convexity; elementary properties of infinite series; and functions defined by power series. Integration is also considered, paying particular attention to the indefinite integral; interval functions and functions of bounded variation; the Riemann-Stieltjes integral; the Riemann integral; and area and curves. The final chapter is devoted to convergence and uniformity. This monograph is intended for mathematics students.

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