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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 Solution of Ordinary and Partial Differential Equations

    Based on a Summer School Held in Oxford, August-September 1961
    • 1st Edition
    • L. Fox
    • English
    Numerical Solution of Ordinary and Partial Differential Equations is based on a summer school held in Oxford in August-September 1961. The book is organized into four parts. The first three cover the numerical solution of ordinary differential equations, integral equations, and partial differential equations of quasi-linear form. Most of the techniques are evaluated from the standpoints of accuracy, convergence, and stability (in the various senses of these terms) as well as ease of coding and convenience of machine computation. The last part, on practical problems, uses and develops the techniques for the treatment of problems of the greatest difficulty and complexity, which tax not only the best machines but also the best brains. This book was written for scientists who have problems to solve, and who want to know what methods exist, why and in what circumstances some are better than others, and how to adapt and develop techniques for new problems. The budding numerical analyst should also benefit from this book, and should find some topics for valuable research. The first three parts, in fact, could be used not only by practical men but also by students, though a preliminary elementary course would assist the reading.

  • Finite and Infinite Sets

    Colloquia Mathematica Societatis János Bolyai, 37.
    • 1st Edition
    • A. Hajnal + 2 more
    • English
    Colloquia Mathematica Societatis Jânos Bolyai, 37: Finite and Infinite Sets, Vol. I focuses on the principles, operations, and approaches involved in finite and infinite sets. The selection first elaborates on essential chains and squares, cellular automata in trees, almost disjoint families of countable sets, and application of Lovasz local lemma. Discussions focus on deleting operations, number of all and self-dual E-chains, transversality of E-chains and E-squares, and binary E-chains and E-squares. The text then elaborates on induced subgraphs, inverse extremal digraph problems, two Sperner-type conditions, and minimal decomposition of all graphs with equinumerous vertices and edges into mutually isomorphic subgraphs. Topics include general digraph extremal problem, matrix graphs and quadratic forms, augmentation of matrices, set of attained densities, proof of the continuity theorem, and inverse extremal multigraph problems. The text examines circular flows in graphs, two-colorings of simple arrangements, monochromatic paths in infinite colored graphs, and graphs associated with an integral domain and their applications. The selection is a dependable reference for researchers interested in finite and infinite sets.

  • Piaget—a Practical Consideration

    A Consideration of the General Theories and Work of Jean Piaget, with an Account of a Short Follow Up Study of His Work on the Development of the Concept of Geometry
    • 1st Edition
    • G. A. Helmore
    • English
    Piaget—A Practical Consideration deals with the general theories and work of Jean Piaget, with an account of a short follow up study of his work on the development of the concept of geometry. Piaget's theory concerning the general pattern of intellectual development in children is discussed, along with his study of children from two English primary schools in differing environments. This book is comprised of seven chapters and opens with a brief background on the life of Piaget and his approach to his work. The next chapter summarizes Piaget's general theories, including his concept of intelligence and its development; his studies of the progress made by children towards higher levels of equilibrium; and the Piagetian stages of development. The reader is then introduced to Piaget's experiments and their results on the development of the thought, language, and moral judgment of the child. The final chapter considers some recorded criticisms of Piaget's methods and maturation system. This monograph will be a useful resource for educators and psychologists.

  • Sixth Form Pure Mathematics

    Volume 2
    • 1st Edition
    • C. Plumpton + 1 more
    • English
    Sixth Form Pure Mathematics, Volume 2, provides an introduction to inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, and a range of mathematical methods including the use of determinants, the manipulation of inequalities, the solution of easy differential equations, and the use of approximate numerical methods. Complex numbers are defined and the various ways of representing and manipulating them are considered. Polar coordinates, curvature, an elementary study of lengths of curves and areas of surfaces of revolution, a more mature discussion of two-dimensional coordinate geometry than was possible in Volume 1, and an elementary introduction to the methods of three dimensional coordinate geometry comprise the geometrical content of the book. Throughout, the authors have tried to preserve the concentric style which they used in Volume 1 and the many worked examples and exercises in each chapter are designed or chosen to provide a continuous reminder of the work of the preceding chapters. Except for Pure Geometry, the two volumes cover almost all of the syllabuses for Advanced Pure Mathematics of the nine Examining Boards. This book provides an adequate course for mathematical pupils at Grammar Schools and a useful introductory course for Science and Engineering students in their first year at University or Technical College or engaged in private study.

  • Vector Analysis for Mathematicians, Scientists and Engineers

    The Commonwealth and International Library: Physics Division
    • 2nd Edition
    • S. Simons
    • W. Ashhurst
    • English
    Vector Analysis for Mathematicians, Scientists and Engineers, Second Edition, provides an understanding of the methods of vector algebra and calculus to the extent that the student will readily follow those works which make use of them, and further, will be able to employ them himself in his own branch of science. New concepts and methods introduced are illustrated by examples drawn from fields with which the student is familiar, and a large number of both worked and unworked exercises are provided. The book begins with an introduction to vectors, covering their representation, addition, geometrical applications, and components. Separate chapters discuss the products of vectors; the products of three or four vectors; the differentiation of vectors; gradient, divergence, and curl; line, surface, and volume integrals; theorems of vector integration; and orthogonal curvilinear coordinates. The final chapter presents an application of vector analysis. Answers to odd-numbered exercises are provided as the end of the book.

  • Ordinary Differential Equations

    Adiwes International Series in Mathematics
    • 1st Edition
    • L. S. Pontryagin
    • A. J. Lohwater
    • English
    Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.

  • Safety Aspects of Computer Control

    • 1st Edition
    • Phil Bennett
    • English
    Safety Aspects of Computer Control focuses on the increased usage of computers and safety procedures for the control of their applications. The selection first elaborates on software in safety-related systems, regulatory issues, and legal liability. Topics cover product liability, liability under the contract law, liability under the law of negligence, methods of ensuring safety, some aspects of regulation of software safety, purpose and principles of regulation, and direct regulation. The book then examines standardization efforts worldwide; real-time software requirements specification and animation using extended Petri nets; and independent software verification and validation in practice. Discussions focus on verification and validation principles, organizational principles, specification language, extended Petri nets environment, history of software standards, and standardization work realized through ISO or IEC. The manuscript takes a look at design and licensing of safety-related software, fault-tolerant control for safety, and use and relevance for the development of safety-critical systems. Concerns include formal methods in the safety-critical systems life cycle, random and systematic failures, hardware and systematic failures, and software quality standards. The book is highly recommended for computer science experts and researchers interested in the safety aspects of computer control.

  • Computer Science

    A Concise Introduction
    • 1st Edition
    • Ian Sinclair
    • English
    Computer Science: A Concise Introduction covers the fundamentals of computer science. The book describes micro-, mini-, and mainframe computers and their uses; the ranges and types of computers and peripherals currently available; applications to numerical computation; and commercial data processing and industrial control processes. The functions of data preparation, data control, computer operations, applications programming, systems analysis and design, database administration, and network control are also encompassed. The book then discusses batch, on-line, and real-time systems; the basic concepts of computer architecture; and the characteristics of main memory and backing storage. The main characteristics of common types of input, output, and input/output devices used in commercial computer applications and data transmission system are also considered. The book tackles the organization and accessing of serial, sequential, and indexed sequential file; file processing and management; and the concepts and functions of operating systems. The text describes on-line and off-line programming methods as well. Computer science students will find the book useful.

  • Planning IT

    • 1st Edition
    • David J Silk
    • English
    Planning IT provides a framework for assessing and improving the practice of information management in organizations. It describes the ways in which senior managers can diagnose the situation in their enterprise and generate an appropriate action plan. The book thus helps the manage, to make a more proactive and informed response to the opportunities of modern information technology and information systems. Comprised of nine chapters, this book begins with an introduction to six guidelines for information management: establish an information management partnership; distinguish the potential benefits of information technology and information systems; think strategically about information management; identify the benefits and their value; manage the achievement of the benefits; and prepare for the future. The next six chapters address each of these guidelines in more detail, and each chapter ends with a set of questions which the manager should consider in the context of himself/herself and his/her enterprise. This will produce a score, and some action points, as part of an information management audit. The eighth chapter explains how to produce a consolidated action plan, structured according to the time scale of the individual actions (short- or long-term) and according to whether they are personal or team actions in the enterprise. The last chapter consolidates the book's main points and exhorts the manager to action. This monograph is intended for both senior managers and non-specialists in information technology.

  • Readings in Artificial Intelligence

    • 1st Edition
    • Bonnie Lynn Webber + 1 more
    • English
    Readings in Artificial Intelligence focuses on the principles, methodologies, advancements, and approaches involved in artificial intelligence. The selection first elaborates on representations of problems of reasoning about actions, a problem similarity approach to devising heuristics, and optimal search strategies for speech understanding control. Discussions focus on comparison with existing speech understanding systems, empirical comparisons of the different strategies, analysis of distance function approximation, problem similarity, problems of reasoning about action, search for solution in the reduction system, and relationship between the initial search space and the higher level search space. The book then examines consistency in networks of relations, non-resolution theorem proving, using rewriting rules for connection graphs to prove theorems, and closed world data bases. The manuscript tackles a truth maintenance system, elements of a plan-based theory of speech acts, and reasoning about knowledge and action. Topics include problems in reasoning about knowledge, integration knowledge and action, models of plans, compositional adequacy, truth maintenance mechanisms, dialectical arguments, and assumptions and the problem of control. The selection is a valuable reference for researchers wanting to explore the field of artificial intelligence.

  • The Handbook of Artificial Intelligence

    Volume 2
    • 1st Edition
    • Avron Barr + 1 more
    • English
    The Handbook of Artificial Intelligence, Volume II focuses on the improvements in artificial intelligence (AI) and its increasing applications, including programming languages, intelligent CAI systems, and the employment of AI in medicine, science, and education. The book first elaborates on programming languages for AI research and applications-oriente... AI research. Discussions cover scientific applications, teiresias, applications in chemistry, dependencies and assumptions, AI programming-language features, and LISP. The manuscript then examines applications-oriente... AI research in medicine and education, including ICAI systems design, intelligent CAI systems, medical systems, and other applications of AI to education. The manuscript explores automatic programming, as well as the methods of program specification, basic approaches, and automatic programming systems. The book is a valuable source of data for computer science experts and researchers interested in conducting further research in artificial intelligence.

  • The Handbook of Artificial Intelligence

    Volume 1
    • 1st Edition
    • Avron Barr + 1 more
    • English
    The Handbook of Artificial Intelligence, Volume I focuses on the progress in artificial intelligence (AI) and its increasing applications, including parsing, grammars, and search methods. The book first elaborates on AI, AI handbook and literature, problem representation, search methods, and sample search programs. The text then ponders on representation of knowledge, including survey of representation techniques and representation schemes. The manuscript explores understanding natural languages, as well as machine translation, grammars, parsing, test generation, and natural language processing systems. The book also takes a look at understanding spoken language, including systems architecture and the ARPA SUR projects. The text is a valuable source of information for computer science experts and researchers interested in pursuing further research in artificial intelligence.

  • A Second Course in Calculus

    • 1st Edition
    • Harley Flanders + 2 more
    • English
    This text, designed for a second year calculus course, can follow any standard first year course in one-variable calculus. Its purpose is to cover the material most useful at this level, to maintain a balance between theory and practice, and to develop techniques and problem solving skills. The topics fall into several categories: Infinite series and integrals Chapter 1 covers convergence and divergence of series and integrals. It ?ontains proofs of basic convergence tests, relations between series and Integrals, and manipulation with geometric, exponential, and related series. Chapter 2 covers approximation of functions by Taylor polynomials, with emphasis on numerical approximations and estimates of remainders. Chapt~r 3 deals with power series, including intervals of convergence, expanSIOns of functions, and uniform convergence. It features calculations with s~ries by algebraic operations, substitution, and term-by-term differentiation and integration. Vector methods Vector algebra is introduced in Chapter 4 and applied to solid analytic geometry. The calculus of one-variable vector functions and its applications to space curves and particle mechanics comprise Chapter 5. Linear algebra Chapter 7 contains a practical introduction to linear algebra in two and three dimensions. We do not attempt a complete treatment of foundations, but rather limit ourselves to thoRe topics that have immediate application to calculus. The main topics are linear transformations in R2 and R3, their matrix representations, manipulation with matrices, linear systems, quadratic forms, and quadric surfaces. Differential calculus of several variables Chapter 6 contains preliminary material on sets in the plane and space, and the definition and basic properties of continuous functions. This is followed by partial derivatives with applications to maxima and minima. Chapter 8 continues with a careful treatment of differentiability and applications to tangent planes, gradients, directional derivatives, and differentials. Here ideas from linear algebra are used judiciously. Chapter 9 covers higher xii Preface order partial derivatives, Taylor polynomials, and second derivative tests for extrema. Multiple integrals In Chapters 10 and 11 we treat double and triple integrals intuitively, with emphasis on iteration, geometric and physical applications, and coordinate changes. In Chapter 12 we develop the theory of the Riemann integral starting with step functions. We continue with Jacobians and the change of variable formula, surface area, and Green's Theorem. Differential equations Chapter 13 contains an elementary treatment of first order equations, with emphasis on linear equations, approximate solutions, and applications. Chapter 14 covers second order linear equations and first order linear systems, including matrix series solutions. These chapters can be taken up any time after Chapter 7. Complex analysis The final chapter moves quickly through basic complex algebra to complex power series, shortcuts using' the complex exponential function, and applications to integration and differential equations. Features The key points of one-variable calculus are reviewed briefly as needed. Optional topics are scattered throughout, for example Stirling's Formula, characteristic roots and vectors, Lagrange multipliers, and Simpson's Rule for double integrals. Numerous worked examples teach practical skills and demonstrate the utility of the theory. We emphaRize Rimple line drawingR that a student can learn to do himself.

  • Quadratic Forms and Matrices

    An Introductory Approach
    • 1st Edition
    • N. A. Yefimov
    • English
    Quadratic Forms and Matrices: An Introductory Approach focuses on the principles, processes, methodologies, and approaches involved in the study of quadratic forms and matrices. The publication first offers information on the general theory of quadratic curves, including reduction to canonical form of the general equation of a quadratic curve, invariants and classification, reduction to canonical form of the equation of a quadratic curve with center at the origin, and transformation of coordinates in the plane. The text then examines the general theory of quadratic surfaces. Topics include transformation of rectangular coordinates in space; general deductions based on the formulas for the transformation of coordinates; reduction to canonical form of the equation of a quadric with center at the origin; and reduction to canonical form of the general equation of a quadric surface. The manuscript ponders on linear transformations and matrices, including reduction of a quadratic form to canonical form; reduction to canonical form of the matrix of a symmetric linear transformation of space; change of the matrix of a linear transformation due to a change of basis; and geometric meaning of the determinant of a linear transformation. The publication is a vital reference for researchers interested in the study of quadratic forms and matrices.

  • Modern Mathematics

    Made Simple
    • 1st Edition
    • Patrick Murphy
    • English
    Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed. Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional statements; and biconditional sentences. Subsequent chapters focus on switching circuits; multibase arithmetic; finite systems; relations, vectors, and matrices; tessellations; and linear programming. The book concludes with an analysis of motion geometry and rubber sheet geometry, paying particular attention to radial enlargement and composite reflections as well as topological equivalence, networks for maps, and incidence matrices. This monograph is intended for students, parents, and teachers who are interested in modern mathematics.

  • Integral Geometry and Representation Theory

    • 1st Edition
    • I. M. Gel'fand + 2 more
    • English
    Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.

  • Introduction to Ordinary Differential Equations

    Academic Press International Edition
    • 1st Edition
    • Albert L. Rabenstein
    • English
    Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.

  • Nonlinear Partial Differential Equations

    A Symposium on Methods of Solution
    • 1st Edition
    • W. F. Ames
    • English
    Nonlinear Partial Differential Equations: A Symposium on Methods of Solution is a collection of papers presented at the seminar on methods of solution for nonlinear partial differential equations, held at the University of Delaware, Newark, Delaware on December 27-29, 1965. The sessions are divided into four Symposia: Analytic Methods, Approximate Methods, Numerical Methods, and Applications. Separating 19 lectures into chapters, this book starts with a presentation of the methods of similarity analysis, particularly considering the merits, advantages and disadvantages of the methods. The subsequent chapters describe the fundamental ideas behind the methods for the solution of partial differential equation derived from the theory of dynamic programming and from finite systems of ordinary differential equations. These topics are followed by reviews of the principles to the lubrication approximation and compressible boundary-layer flow computation. The discussion then shifts to several applications of nonlinear partial differential equations, including in electrical problems, two-phase flow, hydrodynamics, and heat transfer. The remaining chapters cover other solution methods for partial differential equations, such as the synergetic approach. This book will prove useful to applied mathematicians, physicists, and engineers.

  • The Remarkable Sine Functions

    • 1st Edition
    • A. I. Markushevich
    • English
    The Remarkable Sine Functions focuses on the trigonometric functions of sine and cosine. The publication first offers information on the geometric definition of circular, hyperbolic, and lemniscate functions, generalized sines, and integration in the complex plane. Discussions focus on the properties and characteristics of circular, lemniscate, and hyperbolic functions, uniform approach to generalized sines, and the process of integration in complex variables. The text then elaborates on the use of Euler's method in deriving the addition theorems and study of complex values, including the employment of the relationship between the sine and cosine in rewriting addition theorems and formulas that can be used in the determination of real values. The manuscript ponders on zeros and poles, simple and double periodicity, and the concept of an elliptic function. Concerns include circular and hyperbolic functions, Jacobian functions, and the functions of sine and cosine. The book is a valuable reference for mathematicians and researchers interested in the functions of sine and cosine.

  • Protecting Information on Local Area Networks

    • 1st Edition
    • James A Schweitzer
    • English
    Protecting Information on Local Area Networks presents the various types of networks and explains why they are being expanded at such a rapid pace. This book considers how management can gain control of the valuable network-services information resources generally available. Organized into three parts encompassing seven chapters, this book begins with an overview of the various networks and their operations. This text then discusses the appropriate management actions to ensure some control over the use of networks and the business information resource. Other chapters consider the management rationale for network information security and explain the development of a company information network security policy. This book discusses as well security or network-connected personal computers. The final chapter deals with a number of major vulnerabilities of information when communicated or processed on network-connected personal computers. This book is a valuable resource for research scientists, technical security specialists, information systems specialists, and systems administrators.

  • A Course in Ordinary and Partial Differential Equations

    • 1st Edition
    • Zalman Rubinstein
    • English
    A Course in Ordinary and Partial Differential Equations discusses ordinary differential equations and partial differential equations. The book reviews the solution of elementary first-order differential equations, existence theorems, singular solutions, and linear equations of arbitrary order. It explains the solutions of linear equations with constant coefficients, operational calculus, and the solutions of linear differential equations. It also explores the techniques of computing for the solution of systems of linear differential equations, which is similar to the solutions of linear equations of arbitrary order. The text proves that if the coefficients of some differential equations possess certain restricted types of singularities, the solution will have Taylor series expansions about the singular points. The investigator can calculate a divergent series whose partial sums numerically approximate the solution for large x if the point in question is infinity, of which the series will be a Taylor series of negative powers of x. The book also explains the Fourier transform, its applications to partial differential equations, as well as the Hilbert space approach to partial differential equations. The book is a stimulating material for mathematicians, for professors, or for students of pure and applied mathematics, physics, or engineering.

  • Digital Computer Design

    Logic, Circuitry, and Synthesis
    • 1st Edition
    • Edward L. Braun
    • English
    Digital Computer Design: Logic, Circuitry, and Synthesis focuses on the logical structure, electronic realization, and application of digital information processors. The manuscript first offers information on numerical symbols, fundamentals of computing aids, quantization, representation of numbers in an electronic digital computer, and computer applications. The text then ponders on the nature of automatic computation and Boolean algebra. Discussions focus on the advantages of a Boolean algebraic description of a digital computer; clock pulse generators and timing circuits; sequential switching networks; elements of information processing systems and types of digital computers; and automatic sequencing methods. The book elaborates on circuit descriptions of switching and storage elements and large capacity storage systems. Topics include static magnetic storage, dynamic delay line storage, cathode-ray storage, vacuum tube systems of circuit logic, and magnetic core systems of circuit logic. The publication also examines the system design of GP computers, digital differential analyzer, and the detection and correction of errors. The text is a valuable source of data for mathematicians and engineers interested in digital computer design.

  • Nonlinear Problems of Engineering

    • 1st Edition
    • William F. Ames
    • English
    Nonlinear Problems of Engineering reviews certain nonlinear problems of engineering. This book provides a discussion of nonlinear problems that occur in four areas, namely, mathematical methods, fluid mechanics, mechanics of solids, and transport phenomena. Organized into 15 chapters, this book begins with an overview of some of the fundamental ideas of two mathematical theories, namely, invariant imbedding and dynamic programming. This text then explores nonlinear integral equations, which have long occupied a prominent place in mathematical analysis. Other chapters consider the phenomena associated with essentially divergent small-divisor series, such as may occur in the formal solution of differential equations that represent the oscillations of conservative dynamical systems. This book discusses as well the mechanics of idealized textiles consisting of inextensible filaments. The final chapter deals with the use of the Peaceman–Rachford alternating direction implicit method for solving the finite difference analogs of boundary value problems. This book is a valuable resource for engineers and mathematicians.

  • Non-Linear Structures

    Matrix Methods of Analysis and Design by Computers
    • 1st Edition
    • K. I. Majid
    • English
    Non-Linear Structures: Matrix Methods of Analysis and Design by Computers presents the use of matrix methods of structural analysis suitable for computers. The book consists of 10 chapters. In the first chapter a brief introduction to the behavior of structures in general is given with reference to the linear elastic and simple plastic methods of structural analysis. Chapter 2 is devoted to linear matrix methods, both force and displacement. Chapter 3 examines the stability of an individual member with various end conditions. It also derives the stability functions used in Matrix force and Matrix displacement methods. Chapter 4 tackles the elastic stability of complete frames. Chapter 5 deals with the elastic instability of frames. The sixth chapter covers the elastic-plastic analysis of frames. This is followed in Chapter 7 by a number of approximate methods for the evaluation of the failure load of frames without following the sequence of hinge formation. The last three chapters are devoted to the design of structures and the non-linear aspects of design problems. A description of non-linear programming by piecewise linearization is included in Chapter 10. Structural engineers, architects, researchers, and engineering students will find the book useful.

  • The Statistics of Bioassay

    With Special Reference to the Vitamins
    • 1st Edition
    • C. I. Bliss
    • English
    The Statistics of Bioassay: With Special Reference to the Vitamins, Volume II focuses on the processes, reactions, principles, and approaches involved in the biological assay of vitamins. The publication first offers information on the general principles of biological assay, dosage-response curve and its error, and designs for segregating nonrandom variation. Discussions focus on replacement of missing values, randomized groups, calculation of the line, analysis of the variation about the line, comparative biological assays, analytical biological assays, and determination of activity. The text then ponders on measurement of relative potency and correction of quantitative variables. The manuscript takes a look at assays where the variation in response is a function of the dose and slope-ratio assays. Topics include microbiological assays and the slope-ratio technique, analysis of balanced slope-ratio assays, analysis of assays with an all-or-none response, and graded response with unequal variance. The publication then tackles multiple or repeated assays, including quality control in repeated assays and combination of independent assays of a single unknown. The publication is a valuable source of information for researchers interested in the biological assay of vitamins.

  • The Political Economy of U.S. Tariffs

    An Empirical Analysis
    • 1st Edition
    • Réal P. Lavergne
    • Karl Shell
    • English
    The Political Economy of U.S. Tariffs: An Empirical Analysis provides information pertinent to the political economy of trade barriers. This book discusses the cross-sectional regression analysis across industries to understand why some industries have been more privileged than others. Organized into seven chapters, this book begins with an overview of the structure of protection and identifies the primary actors or principles that condition the formation of trade policy more generally. This text then evaluates the institutional and theoretical reasons why political leverage should not be expected to play a significant role in explaining tariffs. Other chapters consider the notion that the structure of protection at any point in time represents some sort of equilibrium. This book discusses as well the distinction between nominal and effective tariffs. The final chapter deals with individual regressors and groups of regressors. This book is a valuable resource for economists and specialists in quantitative analysis.

  • Elementary Differential Geometry

    • 1st Edition
    • Barrett O'Neill
    • English
    Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

  • Generalized Functions

    Applications of Harmonic Analysis
    • 1st Edition
    • I. M. Gel'fand + 1 more
    • English
    Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.

  • Mathematical Methods and Theory in Games, Programming, and Economics

    Volume 2: The Theory of Infinite Games
    • 1st Edition
    • Samuel Karlin
    • Z. W. Birnbaum
    • English
    Mathematical Methods and Theory in Games, Programming, and Economics, Volume II provides information pertinent to the mathematical theory of games of strategy. This book presents the mathematical tools for manipulating and analyzing large sets of strategies. Organized into nine chapters, this volume begins with an overview of the fundamental concepts in game theory, namely, strategy and pay-off. This text then examines the identification of strategies with points in Euclidean n-space, which is a convenience that simplifies the mathematical analysis. Other chapters provide a discussion of the theory of finite convex games. This book discusses as well the extension of the theory of convex continuous games to generalized convex games, which leads to the characterization that such games possess optimal strategies of finite type. The final chapter deals with the components of a simple two-person poker game. This book is a valuable resource for mathematicians, statisticians, economists, social scientists, and research workers.

  • Projective Transformations

    Geometric Transformations
    • 1st Edition
    • P. S. Modenov + 1 more
    • Henry Booker + 2 more
    • English
    Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserv... transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

  • Symplectic Geometry

    • 1st Edition
    • Carl Ludwig Siegel
    • English
    Symplectic Geometry focuses on the processes, methodologies, and numerical approaches involved in symplectic geometry. The book first offers information on the symplectic and discontinuous groups, symplectic metric, and hermitian forms. Numerical calculations are presented to show the values and transformations of these groups. The text then examines the fundamental domain of the modular group and the volume of the fundamental domain of the modular group. Equations and matrices are provided to show the fundamental domain and volume of the fundamental domain of the modular group. The publication ponders on commensurable groups and unit groups of quinary quadratic forms. Numerical analyses are also offered to show the values and characteristics of commensurable and unit groups. The text is a helpful reference for researchers interested in symplectic geometry.

  • Methodologies of Pattern Recognition

    • 1st Edition
    • Satosi Watanabe
    • English
    Methodologies of Pattern Recognition is a collection of papers that deals with the two approaches to pattern recognition (geometrical and structural), the Robbins-Monro procedures, and the implications of interactive graphic computers for pattern recognition methodology. Some papers describe non-supervised learning in statistical pattern recognition, parallel computation in pattern recognition, and statistical analysis as a tool to make patterns emerge from data. One paper points out the importance of cluster processing in visual perception in which proximate points of similar brightness values form clusters. At higher levels of mental activity humans are efficient in clumping complex items into clusters. Another paper suggests a recognition method which combines versatility and an efficient noise-proofness in dealing with the two main problems in the field of recognition. These difficulties are the presence of a large variety of observed signals and the presence of interference. One paper reports on a possible feature selection for pattern recognition systems employing the minimization of population entropy. Electronic engineers, physicists, physiologists, psychologists, logicians, mathematicians, and philosophers will find great rewards in reading the above collection.

  • Curves and Surfaces

    • 1st Edition
    • Pierre-Jean Laurent + 2 more
    • English
    Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Other chapters consider a nonparametric technique for estimating under random censorship the amplitude of a change point in change point hazard models. This book discusses as well the algorithm for ray tracing rational parametric surfaces based on inversion and implicitization. The final chapter deals with the results concerning the norm of the interpolation operator and error estimates for a square domain. This book is a valuable resource for mathematicians.

  • Theoretical Aspects of Reasoning About Knowledge

    Proceedings of the 1986 Conference
    • 1st Edition
    • Joseph Y. Halpern
    • English
    Theoretical Aspects of Reasoning About Knowledge: Proceedings of the 1986 Conference focuses on the principles, methodologies, approaches, and concepts involved in reasoning about knowledge. The selection first provides an overview of reasoning about knowledge, varieties of self-reference, and pegs and alecs. Topics covered include data semantics, partial objects and identity, circumstance, self, and causal connection, structure of circumstance, varieties and limits of self-reference, problem of logical omniscience, and knowledge, communication, and action. The book then explores reasoning about knowledge in artificial intelligence; synthesis of digital machines with provable epistemic properties; and a first order theory of planning, knowledge, and action. The publication ponders on the consistency of syntactical treatments of knowledge, foundations of knowledge for distributed systems, knowledge and implicit knowledge in a distributed environment, and the logic of distributed protocols. Topics include formal syntax and semantics, structure of models, message-based knowledge worlds, changing the class of messages, implicit knowledge in message-based knowledge worlds, conservation and implicit knowledge, and distributed protocols. The selection is a dependable source of data for researchers interested in the theoretical aspects of reasoning about knowledge.

  • Conceptual Information Processing

    • 1st Edition
    • Roger C. Schank
    • English
    Fundamental Studies in Computer Science, 3: Conceptual Information Processing discusses a theory of natural language and implementation of that theory on a computer, focusing basically on an Artificial Intelligence approach to linguistics. This book aims to write computer programs that could understand and generate sentences, which is intended as a first step towards the long range goal of a computer that can communicate with people in natural language. The topics covered include computational linguistics, conceptual dependency theory, history of the analyzer, representation in memory, and structure of BABEL. This publication is a good reference for researchers and specialists working in the field of computer science.

  • A Course of Higher Mathematics

    Adiwes International Series in Mathematics, Volume 4
    • 1st Edition
    • V. I. Smirnov
    • A. J. Lohwater
    • English
    A Course of Higher Mathematics, Volume IV provides information pertinent to the theory of the differential equations of mathematical physics. This book discusses the application of mathematics to the analysis and elucidation of physical problems. Organized into four chapters, this volume begins with an overview of the theory of integral equations and of the calculus of variations which together play a significant role in the discussion of the boundary value problems of mathematical physics. This text then examines the basic theory of partial differential equations and of systems of equations in which characteristics play a key role. Other chapters consider the theory of first order equations. This book discusses as well some concrete problems that indicate the aims and ideas of the calculus of variations. The final chapter deals with the boundary value problems of mathematical physics. This book is a valuable resource for mathematicians and readers who are embarking on the study of functional analysis.

  • Computing Methods in Optimization Problems

    Proceedings of a Conference Held at University of California, Los Angeles January 30-31, 1964
    • 1st Edition
    • A. V. Balakrishnan + 1 more
    • English
    Computing Methods in Optimization Problems deals with hybrid computing methods and optimization techniques using computers. One paper discusses different numerical approaches to optimizing trajectories, including the gradient method, the second variation method, and a generalized Newton-Raphson method. The paper cites the advantages and disadvantages of each method, and compares the second variation method (a direct method) with the generalized Newton-Raphson method (an indirect method). An example problem illustrates the application of the three methods in minimizing the transfer time of a low-thrust ion rocket between the orbits of Earth and Mars. Another paper discusses an iterative process for steepest-ascent optimization of orbit transfer trajectories to minimize storage requirements such as in reduced memory space utilized in guidance computers. By eliminating state variable storage and control schedule storage, the investigator can achieve reduced memory requirements. Other papers discuss dynamic programming, invariant imbedding, quasilinearization, Hilbert space, and the computational aspects of a time-optimal control problem. The collection is suitable for computer programmers, engineers, designers of industrial processes, and researchers involved in aviation or control systems technology.

  • 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.

  • An Introduction to Numerical Mathematics

    • 1st Edition
    • Eduard L. Stiefel
    • English
    An Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear programming, linear and nonlinear algebra, polynomials, numerical differentiation, and approximations. Organized into seven chapters, this book begins with an overview of the solution of linear problems wherein numerical mathematics provides very effective algorithms consisting of finitely many computational steps. This text then examines the method for the direct solution of a definite problem. Other chapters consider the determination of frequencies in freely oscillating mechanical or electrical systems. This book discusses as well eigenvalue problems for oscillatory systems of finitely many degrees of freedom, which can be reduced to algebraic equations. The final chapter deals with the approximate representation of a function f(x) given by I-values as in the form of a table. This book is a valuable resource for physicists, mathematicians, theoreticians, engineers, and research workers.

  • Complex Numbers in Geometry

    • 1st Edition
    • I. M. Yaglom
    • Henry Booker + 2 more
    • English
    Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the Lobachevskii plane; dual numbers as oriented lines of a plane; most general complex numbers; and double, hypercomplex, and dual numbers. The text then takes a look at circular transformations and circular geometry, including ordinary circular transformations, axial circular transformations of the Lobachevskii plane, circular transformations of the Lobachevskii plane, axial circular transformations, and ordinary circular transformations. The manuscript is intended for pupils in high schools and students in the mathematics departments of universities and teachers' colleges. The publication is also useful in the work of mathematical societies and teachers of mathematics in junior high and high schools.

  • Distributions and the Boundary Values of Analytic Functions

    • 1st Edition
    • E. J. Beltrami + 1 more
    • English
    Distributions and the Boundary Values of Analytic Functions focuses on the tools and techniques of distribution theory and the distributional boundary behavior of analytic functions and their applications. The publication first offers information on distributions, including spaces of testing functions, distributions of finite order, convolution and regularization, and testing functions of rapid decay and distributions of slow growth. The text then examines Laplace transform, as well as Laplace transforms of distributions with arbitrary support. The manuscript ponders on distributional boundary values of analytic functions, including causal and passive operators, analytic continuation and uniqueness, boundary value theorems and generalized Hilbert transforms, and representation theorems for half-plane holomorphic functions with S' boundary behavior. The publication is a valuable source of data for researchers interested in distributions and the boundary values of analytic functions.

  • Advanced Calculus with Linear Analysis

    • 1st Edition
    • Joseph R. Lee
    • English
    Advanced Calculus with Linear Analysis provides information pertinent to the fundamental aspects of advanced calculus from the point of view of linear spaces. This book covers a variety of topics, including function spaces, infinite series, real number system, sequence spaces, power series, partial differentiation, uniform continuity, and the class of measurable sets. Organized into nine chapters, this book begins with an overview of the concept of a single-valued function, consisting of a rule, a domain, and a range. This text then describes an infinite sequence as an ordered set of elements that can be put into a one-to-one correspondence with the positive integers. Other chapters consider a normed linear space, which is complete if and only if every Cauchy sequence converges to an element in the space. This book discusses as well the convergence of an infinite series, which is determined by the convergence of the infinite sequence of partial sums. This book is a valuable resource for students.

  • 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.

  • Linear Algebra

    • 1st Edition
    • R. R. Stoll + 1 more
    • English
    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understanding some of the examples and exercises. This book sets itself apart from other similar textbooks through its dedication to the principle that, whenever possible, definitions and theorems should be stated in a form which is independent of the notion of the dimension of a vector space. A second feature of this book which is worthy of mention is the early introduction of inner product spaces and the associated metric concepts. Students soon feel at ease with this class of spaces because they share so many properties with physical space when equipped with a rectangular coordinate system. Finally, the book includes a chapter concerned with several applications to other fields of the theory that have been developed.

  • Intermediate Algebra & Analytic Geometry

    • 1st Edition
    • William R. Gondin + 1 more
    • English
    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, systems involving quadratics, and determinants. Topics include determinants of higher order, application of Cramer's rule, second-order determinants, systems linear in quadratic terms, systems treatable by substitution, systems with a linear equation, and other systems treated by comparison. The manuscript ponders on trigonometric functions and equations, straight lines, and points, distances, and slopes, including intersection points of lines, perpendicular distances, angles between lines, positions of points, inverse trigonometric functions, and trigonometric equations. The publication is a valuable source of data for readers interested in intermediate algebra and analytic geometry.

  • Algebraic Methods of Mathematical Logic

    • 1st Edition
    • Ladislav Rieger
    • English
    Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-math... parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semant... rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.

  • On Applications and Theory of Functional Equations

    • 1st Edition
    • J. Aczél
    • English
    On Applications and Theory of Functional Equations focuses on the principles and advancement of numerical approaches used in functional equations. The publication first offers information on the history of functional equations, noting that the research on functional equations originated in problems related to applied mathematics. The text also highlights the influence of J. d'Alembert, S. D. Poisson, E. Picard, and A. L. Cauchy in promoting the processes of numerical analyses involving functional equations. The role of vectors in solving functional equations is also noted. The book ponders on the international Fifth Annual Meeting on Functional Equations, held in Waterloo, Ontario, Canada on April 24-30, 1967. The meeting gathered participants from America, Asia, Australia, and Europe. One of the topics presented at the meeting focuses on the survey of materials dealing with the progress of approaches in the processes and methodologies involved in solving problems dealing with functional equations. The influence, works, and contributions of A. L. Cauchy, G. Darboux, and G. S. Young to the field are also underscored. The publication is a valuable reference for readers interested in functional equations.

  • Microprocessor Architectures and Systems

    RISC, CISC and DSP
    • 1st Edition
    • Steve Heath
    • English
    Microprocessor Architectures and Systems: RISC, CISC, and DSP focuses on the developments of Motorola's CISC, RISC, and DSP processors and the advancements of the design, functions, and architecture of microprocessors. The publication first ponders on complex instruction set computers and 32-bit CISC processors. Discussions focus on MC68881 and MC68882 floating point coprocessors, debugging support, MC68020 32-bit performance standard, bus interfaces, MC68010 SUPERVISOR resource, and high-level language support. The manuscript then covers the RISC challenge, digital signal processing, and memory management and caches. Topics include implementing memory systems, multitasking and user/supervisor conflicts, partitioning the system, cache size and organization, DSP56000 family, MC88100 programming model, M88000 family, and the 80/20 rule. The text examines the selection of a microprocessor architecture, changing design cycle, semiconductor technology, multiprocessing, and real-time software, interrupts, and exceptions. Concerns include locating associated tasks, MC88100 interrupt service routines, single- and multiple-threaded operating systems, and the MC68300 family. The publication is a valuable reference for computer engineers and researchers interested in microprocessor architectures and systems.

  • 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.

  • Symposia Mathematica

    • 1st Edition
    • Sam Stuart
    • English
    Symposia Mathematica, Volume I focuses on research in the field of mathematics and its applications. This book discusses the definition of S-semigroup, extensions of R modules, structure of H, laws of conservation and equations of motion, and measures of strain. The basic equations for continua with internal rotations, general concepts of the discrete particle mechanics of matter, and implications of the first law of thermodynamics are also elaborated. This text likewise covers the homomorphism theorem, magneto-elastic interactions, transition from discrete particle mechanics to continuum mechanics, and passage to the continuum. This publication is suitable for mathematicians, specialists, and students interested in mathematical structures.

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