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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.

  • Theory of Differential Equations

    • 1st Edition
    • I. M. Gel'fand + 1 more
    • English
    Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations. This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cauchy problem, systems that are Petrovski?-correct, and generalized eigenfunctions of self-adjoint operators are also reviewed. This text likewise covers the differentiation of functionals of strongly and weakly bounded variation. This volume is beneficial to students and researchers interested in the theory of differential equations.

  • Non-Linear Transformations of Stochastic Processes

    • 1st Edition
    • P. I. Kuznetsov + 2 more
    • English
    Non-Linear Transformations of Stochastic Processes focuses on the approaches, methodologies, transformations, and computations involved in the non-linear transformations of stochastic processes. The selection first underscores some problems of the theory of stochastic processes and the transmission of random functions through non-linear systems. Discussions focus on the transformation of moment functions for the general non-linear transformation; conversion formulas for correlation functions; transformation of moment functions for the simplest type of non-linear transformation; and normalization of the linear system of probability distribution laws. The text then ponders on quasi-moment functions in the theory of random processes and correlation functions in the theory of the Brownian motion generalization of the Fokker-Planck equation. The manuscript elaborates on the correlation functions of random sequences of rectangular pulses; method of determining the envelope of quasi-harmonic fluctuations; and the problem of measuring electrical fluctuations with the aid of thermoelectric devices. The book then examines the effect of signal and noise on non-linear elements and the approximate method of calculating the correlation function of stochastic signals. The selection is a dependable source of information for researchers interested in the non-linear transformations of stochastic processes.

  • Computer Organization and Design

    The Hardware / Software Interface
    • 1st Edition
    • John L. Hennessy + 1 more
    • English
    Computer Organization and Design: The Hardware/Software Interface presents the interaction between hardware and software at a variety of levels, which offers a framework for understanding the fundamentals of computing. This book focuses on the concepts that are the basis for computers. Organized into nine chapters, this book begins with an overview of the computer revolution. This text then explains the concepts and algorithms used in modern computer arithmetic. Other chapters consider the abstractions and concepts in memory hierarchies by starting with the simplest possible cache. This book discusses as well the complete data path and control for a processor. The final chapter deals with the exploitation of parallel machines. This book is a valuable resource for students in computer science and engineering. Readers with backgrounds in assembly language and logic design who want to learn how to design a computer or understand how a system works will also find this book useful.

  • Axiomatic Projective Geometry

    • 2nd Edition
    • A. Heyting
    • N. G. De Bruijn + 2 more
    • English
    Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume V: Axiomatic Projective Geometry, Second Edition focuses on the principles, operations, and theorems in axiomatic projective geometry, including set theory, incidence propositions, collineations, axioms, and coordinates. The publication first elaborates on the axiomatic method, notions from set theory and algebra, analytic projective geometry, and incidence propositions and coordinates in the plane. Discussions focus on ternary fields attached to a given projective plane, homogeneous coordinates, ternary field and axiom system, projectivities between lines, Desargues' proposition, and collineations. The book takes a look at incidence propositions and coordinates in space. Topics include coordinates of a point, equation of a plane, geometry over a given division ring, trivial axioms and propositions, sixteen points proposition, and homogeneous coordinates. The text examines the fundamental proposition of projective geometry and order, including cyclic order of the projective line, order and coordinates, geometry over an ordered ternary field, cyclically ordered sets, and fundamental proposition. The manuscript is a valuable source of data for mathematicians and researchers interested in axiomatic projective geometry.

  • Multi-Objective Programming in the USSR

    • 1st Edition
    • Elliot R. Lieberman
    • Gerald J. Lieberman + 1 more
    • English
    Statistical Modeling and Decision Science: Multi-Objective Programming in the USSR provides information pertinent to multi-objective programming that has emerged as an increasingly active area of research in the fields of applied mathematics, operations research, and decision and management science. This book traces and analyzes the development of Soviet multi-objective programming. Organized into 24 chapters, this book begins with an overview of the research institutes most actively involved in multi-objective programming research. This text then presents an analytical framework for grouping and classifying the diverse Soviet methods. Other chapters consider the methods and then evaluated according to the significance and soundness of its basic approach and its kinship to other methods. This book discusses as well some significant Soviet theoretical research and several distinctive approaches proposed by Soviet researchers for comparing the effectiveness of alternative interactive multi-objective programming method. The final chapter deals with distinctive Soviet tendencies in multi-objective research. This book is a valuable resource for economists.

  • An Introduction to Probability and Mathematical Statistics

    • 1st Edition
    • Howard G. Tucker
    • Ralph P. Boas
    • English
    An Introduction to Probability and Mathematical Statistics provides information pertinent to the fundamental aspects of probability and mathematical statistics. This book covers a variety of topics, including random variables, probability distributions, discrete distributions, and point estimation. Organized into 13 chapters, this book begins with an overview of the definition of function. This text then examines the notion of conditional or relative probability. Other chapters consider Cochran's theorem, which is of extreme importance in that part of statistical inference known as analysis of variance. This book discusses as well the fundamental principles of testing statistical hypotheses by providing the reader with an idea of the basic problem and its relation to practice. The final chapter deals with the problem of estimation and the Neyman theory of confidence intervals. This book is a valuable resource for undergraduate university students who are majoring in mathematics. Students who are majoring in physics and who are inclined toward abstract mathematics will also find this book useful.

  • Properties and Operations

    • 1st Edition
    • I. M. Gel'fand + 1 more
    • English
    Generalized Functions, Volume 1: Properties and Operations provides a systematic development of the theory of generalized functions and problems in analysis connected with it. This book focuses on the concept of a convenient link that connects many aspects of analysis, functional analysis, theory of differential equations, representation theory of locally compact Lie groups, and theory of probability and statistics. This volume is essentially devoted to algorithmic questions of the theory, covering many applications of generalized functions to various problems of analysis. The topics discussed include the local properties of generalized functions, differentiation as a continuous operation, and Fourier Transforms of test functions. The wave equation in space of odd dimension, derivation of Green's theorem, and reducible singular points are also described. This publication is a good reference for mathematicians, researchers, and students concerned with generalized functions.

  • College Algebra and Trigonometry

    • 2nd Edition
    • Bernard Kolman + 1 more
    • English
    College Algebra and Trigonometry, Second Edition provides a comprehensive approach to the fundamental concepts and techniques of college algebra and trigonometry. The book incorporates improvements from the previous edition to provide a better learning experience. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, trigonometric functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book. College students will find the book very useful and invaluable.

  • Introductory Statistics for Psychology

    The Logic and the Methods
    • 1st Edition
    • Gustav Levine
    • English
    Introductory Statistics for Psychology: The Logic and the Methods presents the concepts of experimental design that are carefully interwoven with the statistical material. This book emphasizes the verbalization of conclusions to experiments, which is another means of communicating the reasons for statistical analyses. Organized into 17 chapters, this book begins with an overview of alternative ways of stating the conclusions from a significant interaction. This text then presents the analysis of variance and introduces the summation sign and its use. Other chapters consider frequency distribution as any presentation of data that offers the frequency with which each score occurs. This book discusses as well the differences in and among people, which are a constant source of variability in test scores, and in most other measurements of people. The final chapter deals with the working knowledge of arithmetic and elementary algebra. This book is a valuable resource for students and psychologists.

  • Euclidean and Affine Transformations

    Geometric Transformations
    • 1st Edition
    • P. S. Modenov + 1 more
    • Henry Booker + 2 more
    • English
    Geometric Transformations, Volume 1: Euclidean and Affine Transformations focuses on the study of coordinates, trigonometry, transformations, and linear equations. The publication first takes a look at orthogonal transformations, including orthogonal transformations of the first and second kinds; representations of orthogonal transformations as the products of fundamental orthogonal transformations; and representation of an orthogonal transformation of space as a product of fundamental orthogonal transformations. The text then examines similarity and affine transformations. Topics include properties of affine mappings, Darboux's lemma and its consequences, affine transformations in coordinates, homothetic transformations, similarity transformations of the plane in coordinates, and similarity mapping. The book takes a look at the representation of a similarity transformation as the product of a homothetic transformation and an orthogonal transformation; application of affine transformations to the investigation of properties of the ellipse; and representation of any affine transformation as a product of affine transformations of the simplest types. The manuscript is a valuable reference for high school teachers and readers interested in the Euclidean and affine transformations.

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