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Elsevier

Academic Press

  • Multivariable Calculus with Linear Algebra and Series

    • 1st Edition
    • William F. Trench + 1 more
    • English
    Multivariable Calculus with Linear Algebra and Series presents a modern, but not extreme, treatment of linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples. Comprised of seven chapters, this book begins with an introduction to linear equations and matrices, including determinants. The next chapter deals with vector spaces and linear transformations, along with eigenvalues and eigenvectors. The discussion then turns to vector analysis and analytic geometry in R3; curves and surfaces; the differential calculus of real-valued functions of n variables; and vector-valued functions as ordered m-tuples of real-valued functions. Integration (line, surface, and multiple integrals) is also considered, together with Green's and Stokes's theorems and the divergence theorem. The final chapter is devoted to infinite sequences, infinite series, and power series in one variable. This monograph is intended for students majoring in science, engineering, or mathematics.

  • Forecasting Economic Time Series

    • 2nd Edition
    • C. W. J. Granger + 1 more
    • Karl Shell
    • English
    Economic Theory, Econometrics, and Mathematical Economics, Second Edition: Forecasting Economic Time Series presents the developments in time series analysis and forecasting theory and practice. This book discusses the application of time series procedures in mainstream economic theory and econometric model building. Organized into 10 chapters, this edition begins with an overview of the problem of dealing with time series possessing a deterministic seasonal component. This text then provides a description of time series in terms of models known as the time-domain approach. Other chapters consider an alternative approach, known as spectral or frequency-domain analysis, that often provides useful insights into the properties of a series. This book discusses as well a unified approach to the fitting of linear models to a given time series. The final chapter deals with the main advantage of having a Gaussian series wherein the optimal single series, least-squares forecast will be a linear forecast. This book is a valuable resource for economists.

  • Analytic Geometry

    • 1st Edition
    • A. C. Burdette
    • English
    Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus. This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes. This book will prove useful to undergraduate trigonometric students.

  • Methods of Numerical Integration

    • 2nd Edition
    • Philip J. Davis + 1 more
    • Werner Rheinbolt
    • English
    Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.

  • Combinatorics

    • 1st Edition
    • N. Ya. Vilenkin
    • English
    Combinatorics deals with simple combinatorial problems, recurrence relations, and generating functions, particularly the binomial expansions. The book expounds on the general rules of combinatorics, the rule of sum, the rule of product, samples, permutations, combinations, and arrangements of subjects with various restrictions. The text also explains ordered or unordered partitions of numbers, geometric methods, random walk problems, and variants of the arithmetical triangle. One example of the use of combinatorics is the choice of the number 3 in the genetic code. Another example involves the choice of crew for a spaceship where it is necessary to consider the psychological conditions of the applicants for space travel. The text also investigates the sieve of Erastothenes whose problem concerns finding all the primes in the sequence of natural numbers from 1 to N. The book also tackles the application of power series to proof of identities, the binomial series expansion, decomposition into elementary fractions, and nonlinear recurrence relation. The book can be highly educational and interesting to students or academicians involved in mathematics, algebra, and statistics.

  • Handbook of Mathematical Formulas

    • 1st Edition
    • Hans-Jochen Bartsch
    • English
    Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.

  • Calculus

    • 2nd Edition
    • Stanley I. Grossman
    • English
    Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis. This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics include the sequences of real numbers, dot product, arc length as a parameter, quadric surfaces, higher-order partial derivatives, and Green's theorem in the plane. This publication is a good source for students learning calculus.

  • Montague Grammar

    • 1st Edition
    • Barbara H Partee
    • English
    Montague Grammar is a collection of papers that discusses Richard Montague's work on the syntax and semantics of natural languages. The papers examine the applications of Montague's theory to problems of syntax and semantics, and compares Montague's approach to other theories of language. One paper describes the features in Montague's "The Proper Treatment of Quantification in Ordinary English" (PTQ), namely, the grammatical categories and lexicon, the rules most similar to CF-rules, and the treatment of quantification. Another paper presents mechanisms to Montague's grammatical framework which will allow a variety of English constructions—especi... those involving sentence embedding. The paper discusses syntactic rules, such as noun phrases, verb phrases, subject-predicate sentences, variable binding, abstracts, verbs taking infinitive complements, the copula, participles. One paper describes a fragment of English that is a variation and extension of the fragment presented in Montague. It also analyses adjectival phrases, three-place and other kinds of verbs, the passive voice, reflexive pronouns, and sentences using the dummy subject "it." Another paper proposes rules, syntactics, and semantics for use in nonrestrictive clauses in a Montague grammar. One paper analyzes factives, their semantic and syntactic properties using the work of Kiparsky and Kiparsky (1971). Montague's "Universal Grammar" (UG) invokes expositions of Montague syntax, Cooper syntax, theorems on conversion process, semantic interpretation, semantic equivalence of the two systems, and interpretive semantics. The collection is intended for readers of Montague, as well as for linguists, philosophers, and students of language.

  • Geometry and Combinatorics

    • 1st Edition
    • J. J. Seidel
    • D. G. Corneil + 1 more
    • English
    Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.

  • Statistical Methods and the Improvement of Data Quality

    • 1st Edition
    • Tommy Wright
    • English
    Statistical Methods and the Improvement of Data Quality contains the proceedings of The Small Conference on the Improvement of the Quality of Data Collected by Data Collection Systems, held on November 11-12, 1982, in Oak Ridge, Tennessee. The conference provided a forum for discussing the use of statistical methods to improve data quality, with emphasis on the problems of data collection systems and how to handle them using state-of-the-art techniques. Comprised of 16 chapters, this volume begins with an overview of some of the limitations of surveys, followed by an annotated bibliography on frames from which the probability sample is selected. The reader is then introduced to sample designs and methods for collecting data over space and time; response effects to behavior and attitude questions; and how to develop and use error profiles. Subsequent chapters focus on principles and methods for handling outliers in data sets; influence functions, outlier detection, and data editing; and application of pattern recognition techniques to data analysis. The use of exploratory data analysis as an aid in modeling and statistical forecasting is also described. This monograph is likely to be of primary benefit to students taking a general course in survey sampling techniques, and to individuals and groups who deal with large data collection systems and are constantly seeking ways to improve the overall quality of their data.

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