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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.

  • A Course of Higher Mathematics

    Adiwes International Series in Mathematics, Volume 2
    • 1st Edition
    • V. I. Smirnov
    • A. J. Lohwater
    • English
    A Course of Higher Mathematics, Volume II: Advanced Calculus covers the theory of functions of real variable in advanced calculus. This volume is divided into seven chapters and begins with a full discussion of the solution of ordinary differential equations with many applications to the treatment of physical problems. This topic is followed by an account of the properties of multiple integrals and of line integrals, with a valuable section on the theory of measurable sets and of multiple integrals. The subsequent chapters deal with the mathematics necessary to the examination of problems in classical field theories in vector algebra and vector analysis and the elements of differential geometry in three-dimensional space. The final chapters explore the Fourier series and the solution of the partial differential equations of classical mathematical physics. This book will prove useful to advanced mathematics students, engineers, and physicists.

  • Programming — ALGOL

    • 1st Edition
    • D. J. Malcolme-Lawes
    • English
    Programming — ALGOL describes the basics of computer programming using Algol. Commands that could be added to Algol and could increase its scope are described, including multiplication and division and the use of brackets. The idea of labeling or naming a command is also explained, along with a command allowing two alternative results. Most of the important features of Algol syntax are discussed, and examples of compound statements (that is, sets of commands enclosed by a begin ... end command) are given. Comprised of 11 chapters, this book begins with an introduction to the digital computer and how it works using a list of instructions known as a program. The "punched-tape" method of feeding information into a computer is described together with the flexowriter. The next chapter provides an overview of Algol by studying a very simple program and comparing it with the same sequence of instructions written in normal English. The third chapter is about building a program, first by increasing the complexity of the actual computation and then economizing on memory stores. Subsequent chapters focus on how computer programs can be built up of simple commands; labeling or naming a command; facilities in the Algol language which allow the addition of a second alternative command to an if ... then statement; and the use of a flow diagram to translate a problem into Algol. The final chapter examines the method of running a program on a computer. This monograph will be of interest to computer programmers.

  • Linear Associative Algebras

    • 1st Edition
    • Alexander Abian
    • English
    Linear Associative Algebras focuses on finite dimensional linear associative algebras and the Wedderburn structure theorems. The publication first elaborates on semigroups and groups, rings and fields, direct sum and tensor product of rings, and polynomial and matrix rings. The text then ponders on vector spaces, including finite dimensional vector spaces and matrix representation of vectors. The book takes a look at linear associative algebras, as well as the idempotent and nilpotent elements of an algebra, ideals of an algebra, total matrix algebras and the canonical forms of matrices, matrix representation of algebras, and division of algebras. The manuscript also tackles the Wedderburn structure theorems, including direct sum and tensor product decomposition of algebras, nilpotent algebras and the radical of an algebra, and structure of simple and semi-simple algebras. The publication is highly recommended for mathematicians and students interested in the Wedderburn structure theorems and finite dimensional linear associative algebras.

  • A Guide to Mathematical Tables

    Supplement No. 1
    • 1st Edition
    • N. M. Burunova + 2 more
    • English
    A Guide to Mathematical Tables is a supplement to the Guide to Mathematical Tables published by the U.S.S.R. Academy of Sciences in 1956. The tables contain information on subjects such as powers, rational and algebraic functions, and trigonometric functions, as well as logarithms and polynomials and Legendre functions. An index listing all functions included in both the Guide and the Supplement is included. Comprised of 15 chapters, this supplement first describes mathematical tables in the following order: the accuracy of the table (that is, the number of decimal places or significant figures); the limits of variation of the argument and the interval of the table; and the serial number of the book or journal in the reference material. The second part gives the author, title, publishing house, and date and place of publication for books, and the name of the journal, year of publication, series, volume and number, page and author and title of the article cited for journals. Topics range from exponential and hyperbolic functions to factorials, Euler integrals, and related functions. Sums and quantities related to finite differences are also tabulated. This book will be of interest to mathematicians and mathematics students.

  • Mathematical Tables

    Tables of in G [z] for Complex Argument
    • 1st Edition
    • A. A. Abramov
    • English
    Mathematical Tables of In ? (z) for Complex Argument is a compilation of tables of In ? (z), z = x + iy, calculated for steps in x and y of 0.01 and with an accuracy of one unit in the last (the sixth) decimal place. Interpolation is used to calculate In ? (z) for intermediate values and is carried out separately for the real and imaginary parts of In ? (z). Six places are retained in interpolation. This book first explains how the values of In ? (z) are calculated using the asymptotic formula in a wide lattice with step h = 0.16, and how the tables and the nomograph are used. The values in the lattice are interpolated successively at the centers of various symmetric figures. The calculation of In ? (z) outside the quadrangle is also considered. Formulas for the calculation of In ? (z) outside the given rectangle are listed. The nomograph is intended to facilitate the interpolation procedure. Some of the calculations (including the rounding off of the results to the sixth place and the calculation of second differences) are carried out with the aid of analytical computers. This monograph will be of interest to mathematicians and mathematics students.

  • Some Modern Mathematics for Physicists and Other Outsiders

    An Introduction to Algebra, Topology, and Functional Analysis
    • 1st Edition
    • Paul Roman
    • English
    Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis, Volume 1 focuses on the operations, principles, methodologies, and approaches employed in algebra, topology, and functional analysis. The publication first offers information on sets, maps, and algebraic composition laws and systems. Discussions focus on morphisms of algebraic systems, sequences and families, cardinal numbers, ordered sets and maps, equivalence relations and maps, composite functions and inverses, operations with sets, and relations in sets. The text then ponders on special algebraic systems, topological spaces, and topological spaces with special properties. Topics include complete metric spaces, compact spaces, separable and connected spaces, homeomorphism and isometry, convergence, continuity, general structure of topological spaces, rings and fields, linear spaces, linear algebras, and nonassociative algebras. The book elaborates on the theory of integration and measure spaces, including measurable spaces, general properties of the integral, and measureable functions. The publication is a valuable reference for theoretical physicists, research engineers, and scientists who are concerned with structural problems.

  • Economics and Artificial Intelligence

    Proceedings of the IFAC/IFORS/IFIP/IASC/AFCET Conference, Aix-en-Provence, France, 2—4 September 1986
    • 1st Edition
    • Jean-Louis Roos
    • English
    Economics and Artificial Intelligence documents the proceedings of the IFAC/IFORS/IFIP/IASC... Conference held in Aix-en-Provence, France on September 2-4, 1986. This book discusses the design of intelligent dialogue in D.S.S. qualitative modeling of economic studies; basic propositions for intelligent systems design methods; and expert systems for confirmatory data analysis. The artificial intelligence for transaction cost economizing; knowledge-based evaluation of strategic investments; and reasoning system for the guidance of technological transfer are also elaborated. This text likewise covers the A.I. impacts on the process of the division of labor; using automated techniques to generate expert systems for R&D project monitoring; and intelligent support to decision making process. This compilation is a good reference for students and researchers conducting work on the nature of economics and artificial intelligence.

  • Homotopy Theory

    The Mathematical Works of J. H. C. Whitehead
    • 1st Edition
    • I. M. James
    • English
    Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes. This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are followed by reviews of other homotopy types, such as group extensions with homotopy operators, cohomology systems, secondary boundary operator, algebraic homotopy, and the G-dual of a semi-exact couple. The last chapters examine the connected complex homotopy types and the second non-vanishing homotopy groups. This book will be of great value to mathematicians.

  • Minicomputer Research and Applications

    Proceedings of the First Conference of the HP/1000 International Users Group
    • 1st Edition
    • Helen K. Brown
    • English
    Minicomputer Research and Applications covers the proceedings of the First Conference of the HP/1000 International Users Group, held on August 25-27, 1980 in San Jose, California. The book focuses on the operations, applications, and functions of the HP/1000 computer driver. The selection first underscores an interactive color display station for IC layout and computer aided design in automatic control and logical automata. Discussions focus on automatic control, logical automata, organization of sirena, hardware and software configurations, interactive input support, and display processing. The text then examines a mini-based sculptured surface system and real-time performance analysis system for computers. The publication ponders on variations on a theme (RTE) by Hewlett-Packard, circumventing RTE system memory and disc restrictions, and the Gerber data management system. Topics include user interface, system security, command file, implementation of shared-EMA, and real-time executive modifications. The manuscript also elaborates on ultra low level programming using a high level language and future directions of the HP/1000. The selection is a dependable reference for readers interested in the HP/1000 computer driver.

  • Algebraical and Topological Foundations of Geometry

    Proceedings of a Colloquium Held in Utrecht, August 1959
    • 1st Edition
    • Hans Freudenthal
    • English
    Algebraical and Topological Foundations of Geometry contains the proceedings of the Colloquium on Algebraic and Topological Foundations of Geometry, held in Utrecht, the Netherlands in August 1959. The papers review the algebraical and topological foundations of geometry and cover topics ranging from the geometric algebra of the Möbius plane to the theory of parallels with applications to closed geodesies. Groups of homeomorphisms and topological descriptive planes are also discussed. Comprised of 26 chapters, this book introduces the reader to the theory of parallels with applications to closed geodesies; groups of homeomorphisms; complemented modular lattices; and topological descriptive planes. Subsequent chapters focus on collineation groups; exceptional algebras and exceptional groups; the connection between algebra and constructions with ruler and compasses; and the use of differential geometry and analytic group theory methods in foundations of geometry. Von Staudt projectivities of Moufang planes are also considered, and an axiomatic treatment of polar geometry is presented. This monograph will be of interest to students of mathematics.

  • Linear Network Theory

    • 1st Edition
    • G. I. Atabekov
    • P. K. M'Pherson
    • English
    Linear Network Theory presents the problems of linear network analysis and synthesis. This book discusses the theory of linear electrical circuits, which is important for developing the scientific outlook of specialists in radio and electrical engineering. Organized into 13 chapters, this book begins with an overview of circuit theory that operates with electrical quantities, including voltage, charge, and current. This text then examines sinusoidal function as the predominant form of a periodic process in electrical circuits. Other chapters consider the reduction of a series–parallel network to single equivalent impedance, which is one of the main forms of converting circuit diagrams often used in practice. The final chapter deals with the Laplace transformation or operational calculus, which is a combination of methods of mathematical analysis. This book is intended to be suitable for students in the specialized branches of electrical and radio engineering, post-graduates, and engineers extending their theoretical knowledge.

  • Mathematica® by Example

    • 2nd Edition
    • Martha L Abell + 1 more
    • English
    Mathematica by Example, Revised Edition presents the commands and applications of Mathematica, a system for doing mathematics on a computer. This text serves as a guide to beginning users of Mathematica and users who do not intend to take advantage of the more specialized applications of Mathematica. The book combines symbolic manipulation, numerical mathematics, outstanding graphics, and a sophisticated programming language. It is comprised of 7 chapters. Chapter 1 gives a brief background of the software and how to install it in the computer. Chapter 2 introduces the essential commands of Mathematica. Basic operations on numbers, expressions, and functions are introduced and discussed. Chapter 3 provides Mathematica's built-in calculus commands. The fourth chapter presents elementary operations on lists and tables. This chapter is a prerequisite for Chapter 5 which discusses nested lists and tables in detail. The purpose of Chapter 6 is to illustrate various computations Mathematica can perform when solving differential equations. Chapter 7 discusses some of the more frequently used commands contained in various graphics packages available with Mathematica. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

  • Programmes for Animation

    A Handbook for Animation Technicians
    • 1st Edition
    • Brian Salt
    • English
    Programmes for Animation: A Handbook for Animation Technicians is a handbook on animation containing a list of 57 programs for use on a programmable calculator. Each program is preceded by explanations of how the necessary mathematical formulas were derived; each step of the program is also accompanied by a brief explanation. The programs are intended for the Hewlett-Packard HP-97 calculator, and can also be used on the HP-67 pocket calculator. Comprised of 17 chapters, this book begins by giving sufficient information about the functions of the keys of the calculator. The discussion then turns to field widths and zoom counter readings; the field chart and coordinate systems; and lens and table off-sets. Subsequent chapters deal with linear movements and fairings; exponential movements; middle fairings and co-fairings; rotations and circular pans; and simple harmonic motion. Exposures at different field widths are also explained, along with zooms using several pieces of artwork and movements along a curve. The book concludes by describing two-lens aerial image projection. This monograph was written specifically for animation technicians.

  • Annual Review in Automatic Programming

    International Tracts in Computer Science and Technology and Their Application
    • 1st Edition
    • Richard Goodman
    • English
    Annual Review in Automatic Programming focuses on the techniques of automatic programming used with digital computers. Topics covered range from the design of machine-independent programming languages to the use of recursive procedures in ALGOL 60. A multi-pass translation scheme for ALGOL 60 is described, along with some commercial source languages. The structure and use of the syntax-directed compiler is also considered. Comprised of 12 chapters, this volume begins with a discussion on the basic ideas involved in the description of a computing process as a program for a computer, expressed in a formal symbolic language such as ALGOL 60. The emphasis is on the information conveyed by the program constituents (semantics), rather than the particular form used (syntax). Subsequent chapters focus on generalized ALGOL; the design of machine-independent programming languages; JOVIAL, a programming language for real-time command systems; and a complete ALGOL translator, expressed in ALGOL itself. A detailed description of the compiler compiler is also presented, together with the Rapidwrite program. The final chapter is devoted to file processing in SEAL (Standard Electronic Accounting Language). This monograph will be of interest to computer programmers.

  • Mathematical Modelling in Science and Technology

    The Fourth International Conference, Zurich, Switzerland, August 1983
    • 1st Edition
    • Xavier J.R. Avula + 2 more
    • English
    Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.

  • Elements of Combinatorial Computing

    • 1st Edition
    • Mark B. Wells
    • English
    Elements of Combinatorial Computing focuses on the processes, principles, methodologies, and approaches involved in combinatorial computing. The publication first takes a look at a language for combinatorial computing, language implementation and program efficiency, and computer representation of mathematical objects. Discussions focus on geometric configurations, elementary combinatorial configurations, sets and vectors, natural numbers, program optimization, data representation, set manipulation, notation for iteration and recursion, and nested iteration and recursive programming. The text then takes a look at backtrack programming, generation of elementary configurations, and additional basic techniques and manipulations. Topics include isomorph rejection, transformations, finite set covering, sorting techniques, permutations with repeated objects, compositions, partitions, subsets and combinations, and basic backtracking and impasse detection. The book examines additional basic techniques and manipulations and applications of advanced algorithms. The publication is highly recommended for computer science experts and researchers interested in the elements in combinatorial computing.

  • Current Issues in Computer Simulation

    • 1st Edition
    • Nabil R. Adam + 1 more
    • English
    Current Issues in Computer Simulation is a collection of papers dealing with computer simulation languages, statistical aspects of simulation, linkage with optimization and analytical models, as well as theory and application of simulation methodology. Some papers explain the General Purpose Simulation System (GPSS), a programming package incorporating a language to simulate discrete systems; and the SIMSCRIPT, a general-purpose simulation language using English commands, for example, FORTRAN. Another simulation language is the General Activity Simulation Program (GASP), providing for an organizational structure to build models to simulate the dynamic performance of systems on a digital computer. Other papers discuss simulation models of real systems, including corporate simulation models, multistage consumer choice process, determination of maximum occupancy for hospital facilities, and the juvenile court system. Many computer simulations are statistical sampling experiments performed on a model of the system under investigation. Other papers discuss some of the variables involved in the statistical design and analysis of simulation experiments such as variance reduction techniques, generation of random variates, and experimental layout. For example, one application simulates inventory systems when many items are stocked in various locations. The collection is suitable for programmers, computer engineers, businessmen, hospital administrators, schools officials, and depositories of huge volumes of information or data.

  • The Application of Mathematical Statistics to Chemical Analysis

    • 1st Edition
    • V. V. Nalimov
    • M. Williams
    • English
    The Application of Mathematical Statistics to Chemical Analysis presents the methods of mathematical statistics as applied to problems connected with chemical analysis. This book is divided into nine chapters that particularly consider the principal theorems of mathematical statistics that are explained with examples taken from researchers associated with chemical analysis in laboratory work. This text deals first with the problems of mathematical statistics as a means to summarize information in chemical analysis. The next chapters examine the classification of errors, random variables and their characteristics, and the normal distribution in mathematical statistics. These topics are followed by surveys of the application of Poisson's and binomial distribution in radiochemical analysis; the estimation of chemical analytic results; and the principles and application of determination of experimental variance. The last chapters explore the determination of statistical parameters of linear relations and some working methods associated with the statistical design of an experiment. This book will be of great value to analytical chemists and mathematical statisticians.

  • Exploring University Mathematics 2

    Lectures Given at Bedford College, London
    • 1st Edition
    • D. M. Burley + 2 more
    • N. J. Hardiman
    • English
    Exploring University Mathematics 2 presents the mathematical concept that is fundamental to the treatment of numbers. This book discusses the positive integers as the basis of common knowledge. Organized into seven chapters, this book begins with an overview of the analytical proof of the essentially geometrical isoperimetric problem. This text then explains that the simple models can be constructed, which lead to sixth-form mathematics. Other chapters consider the important physical ideas in kinetic theory. This book discusses as well the graphical method for establishing the general properties of the solution of a differential equation and applied it to the familiar equation for the motion of a simple pendulum when the amplitude of the oscillation is not small. The final chapter deals with certain methods in the theory of differential equations that are of considerable importance and interest. This book is a valuable resource for students, teachers, and research workers.

  • Elementary Vectors

    The Commonwealth and International Library: Mathematics Division
    • 1st Edition
    • E. Œ. Wolstenholme
    • W. J. Langford + 1 more
    • English
    Elementary Vectors is an introductory course in vector analysis which is both rigorous and elementary, and demonstrates the elegance of vector methods in geometry and mechanics. Topics covered range from scalar and vector products of two vectors to differentiation and integration of vectors, as well as central forces and orbits. Comprised of seven chapters, this book begins with an introduction to relevant definitions; addition and subtraction of vectors; multiplication of a vector by a real number; position vectors and distance between two points; and direction cosines and direction ratios. The discussion then turns to scalar and vector products of two vectors; application of vector methods to simple kinematical and dynamical problems concerning the motion of a particle; and differentiation and integration of vectors. Central forces and orbits are also considered, along with the equation of a straight line and that of a plane. A parametric treatment of certain three-dimensional curves and curved surfaces, including the helix, is presented. This monograph will be of value to students, teachers, and practitioners of mathematics.

  • Arithmetic Applied Mathematics

    • 1st Edition
    • Donald Greenspan
    • V. Lakshmikantham + 1 more
    • English
    Arithmetic Applied Mathematics deals with concepts of arithmetic applied mathematics and uses a computer, rather than a continuum, approach to the deterministic theories of particle mechanics. Models of classical physical phenomena are formulated from both Newtonian and special relativistic mechanics using only arithmetic. Definitions of energy and momentum are presented that are identical to those of continuum mechanics. Comprised of nine chapters, this book begins by exploring discrete modeling as it relates to Newtonian mechanics and special relativistic mechanics, paying particular attention to gravity. The reader is then introduced to long-range forces such as gravitation and short-range forces such as molecular attraction and repulsion; the N-body problem; and conservative and non-conservative models of complex physical phenomena. Subsequent chapters focus on the foundational concepts of special relativity; arithmetic special relativistic mechanics in one space dimension and three space dimensions; and Lorentz invariant computations. This monograph will be of interest to students and practitioners in the fields of mathematics and physics.

  • Nonlinear Stochastic Operator Equations

    • 1st Edition
    • George Adomian
    • English
    Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science. This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology, medicine. This text discusses operator equations and the decomposition method. This book also explains the limitations, restrictions and assumptions made in differential equations involving stochastic process coefficients (the stochastic operator case), which yield results very different from the needs of the actual physical problem. Real-world application of mathematics to actual physical problems, requires making a reasonable model that is both realistic and solvable. The decomposition approach or model is an approximation method to solve a wide range of problems. This book explains an inherent feature of real systems—known as nonlinear behavior—that occurs frequently in nuclear reactors, in physiological systems, or in cellular growth. This text also discusses stochastic operator equations with linear boundary conditions. This book is intended for students with a mathematics background, particularly senior undergraduate and graduate students of advanced mathematics, of the physical or engineering sciences.

  • Statistics for Experimentalists

    • 1st Edition
    • B. E. Cooper
    • English
    Statistics for Experimentalists aims to provide experimental scientists with a working knowledge of statistical methods and search approaches to the analysis of data. The book first elaborates on probability and continuous probability distributions. Discussions focus on properties of continuous random variables and normal variables, independence of two random variables, central moments of a continuous distribution, prediction from a normal distribution, binomial probabilities, and multiplication of probabilities and independence. The text then examines estimation and tests of significance. Topics include estimators and estimates, expected values, minimum variance linear unbiased estimators, sufficient estimators, methods of maximum likelihood and least squares, and the test of significance method. The manuscript ponders on distribution-free tests, Poisson process and counting problems, correlation and function fitting, balanced incomplete randomized block designs and the analysis of covariance, and experimental design. The publication is a valuable reference for statisticians and researchers interested in the use of statistical methods.

  • Algebraic and Classical Topology

    The Mathematical Works of J. H. C. Whitehead
    • 1st Edition
    • I. M. James
    • English
    Algebraic and Classical Topology contains all the published mathematical work of J. H. C. Whitehead, written between 1952 and 1960. This volume is composed of 21 chapters, which represent two groups of papers. The first group, written between 1952 and 1957, is principally concerned with fiber spaces and the Spanier-Whitehead S-theory. In the second group, written between 1957 and 1960, Whitehead returns to classical topology after a long interval, and participates in the renewed assault on the problems which fascinated him most. This book will prove useful to mathematicians.

  • Vectors and Matrices

    • 1st Edition
    • Pamela Liebeck
    • C. Plumpton
    • English
    Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

  • Differential Equations with Maple V®

    • 1st Edition
    • Martha L Abell + 1 more
    • English
    Differential Equations with Maple V provides an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as some supplementary topics such as Laplace transforms, Fourier series, and partial differential equations. It also illustrates how Maple V is used to enhance the study of differential equations not only by eliminating the computational difficulties, but also by overcoming the visual limitations associated with the solutions of differential equations. The book contains chapters that present differential equations and illustrate how Maple V can be used to solve some typical problems. The text covers topics on differential equations such as first-order ordinary differential equations, higher order differential equations, power series solutions of ordinary differential equations, the Laplace Transform, systems of ordinary differential equations, and Fourier Series and applications to partial differential equations. Applications of these topics are also provided. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

  • Sets: Naïve, Axiomatic and Applied

    A Basic Compendium with Exercises for Use in Set Theory for Non Logicians, Working and Teaching Mathematicians and Students
    • 1st Edition
    • D. Van Dalen + 2 more
    • I. N. Sneddon
    • English
    Sets: Naïve, Axiomatic and Applied is a basic compendium on naïve, axiomatic, and applied set theory and covers topics ranging from Boolean operations to union, intersection, and relative complement as well as the reflection principle, measurable cardinals, and models of set theory. Applications of the axiom of choice are also discussed, along with infinite games and the axiom of determinateness. Comprised of three chapters, this volume begins with an overview of naïve set theory and some important sets and notations. The equality of sets, subsets, and ordered pairs are considered, together with equivalence relations and real numbers. The next chapter is devoted to axiomatic set theory and discusses the axiom of regularity, induction and recursion, and ordinal and cardinal numbers. In the final chapter, applications of set theory are reviewed, paying particular attention to filters, Boolean algebra, and inductive definitions together with trees and the Borel hierarchy. This book is intended for non-logicians, students, and working and teaching mathematicians.

  • Applied Stochastic Processes

    • 1st Edition
    • G. Adomian
    • English
    Applied Stochastic Processes is a collection of papers dealing with stochastic processes, stochastic equations, and their applications in many fields of science. One paper discusses stochastic systems involving randomness in the system itself that can be a large dynamical multi-input, multi-output system. Examples of a large system are the national economy of a major country or when an acoustic wave is propagating as in the atmosphere, ocean, or sea. Another paper proves that only the average properties of the molecules of biology can be measured with precision in the test tube; and disputes a "simplistic" model of the cell as defined by a miniature Laplaces' universe. The paper notes that the way existing cells are constructed implies that quantum mechanical principles lead to certain questions (about simple experiments) having only statistical answers. Another paper addresses the detection of distributed, fluctuating targets in a reverberation limited, randomly time, and space varying transmission media. This approach is done by using the concepts of "random Green's functions" and the "stochastic Green's function." The collection will prove useful for cellular researchers, mathematicians, physicist, engineers, and academicians in the field of applied mathematics, statistics, and chemistry.

  • Mathematics with Understanding

    • 1st Edition
    • Harold Fletcher + 1 more
    • C. Plumpton
    • English
    Mathematics with Understanding, Book 1 provides a guide for teaching primary mathematics. This book consists of nine main topics–aims of a modern approach; language of sets; relations and sorting; recording of number and use of different bases; open sentences, number facts and pictorial representation; natural numbers and addition; subtraction; multiplication; and division. In these topics, this text specifically discusses the union and intersection of two sets, Cardinal number of a set, and recording by means of a mapping. The collection of data, fundamental operations for natural numbers, and subtraction algorithm are also deliberated. This compilation likewise covers the Cartesian product of two sets and properties of division. This publication is recommended for math teachers intending to acquire a deeper understanding of the structure behind many mathematical ideas and processes.

  • An Introduction to Measure-Theoretic Probability

    • 2nd Edition
    • George G. Roussas
    • English
    An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching the basics of measure theoretic probability. This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics, probability and other related areas should be equipped with. This edition requires no prior knowledge of measure theory, covers all its topics in great detail, and includes one chapter on the basics of ergodic theory and one chapter on two cases of statistical estimation. Topics range from the basic properties of a measure to modes of convergence of a sequence of random variables and their relationships; the integral of a random variable and its basic properties; standard convergence theorems; standard moment and probability inequalities; the Hahn-Jordan Decomposition Theorem; the Lebesgue Decomposition T; conditional expectation and conditional probability; theory of characteristic functions; sequences of independent random variables; and ergodic theory. There is a considerable bend toward the way probability is actually used in statistical research, finance, and other academic and nonacademic applied pursuits. Extensive exercises and practical examples are included, and all proofs are presented in full detail. Complete and detailed solutions to all exercises are available to the instructors on the book companion site. This text will be a valuable resource for graduate students primarily in statistics, mathematics, electrical and computer engineering or other information sciences, as well as for those in mathematical economics/finance in the departments of economics.

  • Mathematical Analysis Fundamentals

    • 1st Edition
    • Agamirza Bashirov
    • English
    The author’s goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric options.

  • Effective Dynamics of Stochastic Partial Differential Equations

    • 1st Edition
    • Jinqiao Duan + 1 more
    • English
    Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension.

  • Advances in Computers

    • 1st Edition
    • Volume 93
    • English
    Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.

  • Differential Forms

    Theory and Practice
    • 2nd Edition
    • Steven H. Weintraub
    • English
    Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications. They both unify and simplify results in concrete settings, and allow them to be clearly and effectively generalized to more abstract settings. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems. Differential Forms, Second Edition, is a solid resource for students and professionals needing a general understanding of the mathematical theory and to be able to apply that theory into practice.

  • Advances in Computers

    • 1st Edition
    • Volume 92
    • English
    Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.

  • Introduction to Probability Models

    • 11th Edition
    • Sheldon M. Ross
    • English
    Introduction to Probability Models, Eleventh Edition is the latest version of Sheldon Ross's classic bestseller, used extensively by professionals and as the primary text for a first undergraduate course in applied probability. The book introduces the reader to elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research. The hallmark features of this text have been retained in this eleventh edition: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topic; and real-world applications in engineering, science, business and economics. The 65% new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data. The book contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new exams. It also presents new applications of probability models in biology and new material on Point Processes, including the Hawkes process. There is a list of commonly used notations and equations, along with an instructor's solutions manual. This text will be a helpful resource for professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.

  • An Introduction to the Mathematics of Financial Derivatives

    • 3rd Edition
    • Ali Hirsa + 1 more
    • English
    An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems.

  • Hypersingular Integral Equations in Fracture Analysis

    • 1st Edition
    • Whye-Teong Ang
    • English
    Hypersingular Integral Equations in Fracture Analysis explains how plane elastostatic crack problems may be formulated and solved in terms of hypersingular integral equations. The unknown functions in the hypersingular integral equations are the crack opening displacements. Once the hypersingular integral equations are solved, the crack tip stress intensity factors, which play an important role in fracture analysis, may be easily computed. This title consists of six chapters: Elastic crack problems, fracture mechanics, equations of elasticity and finite-part integrals; Hypersingular integral equations for coplanar cracks in anisotropic elastic media; Numerical methods for solving hypersingular integral equations; Hypersingular boundary integral equation method for planar cracks in an anisotropic elastic body; A numerical Green's function boundary integral approach for crack problems; and Edge and curved cracks and piezoelectric cracks. This book provides a clear account of the hypersingular integral approach for fracture analysis, gives in complete form the hypersingular integral equations for selected crack problems, and lists FORTRAN programs of numerical methods for solving hypersingular integral equations.

  • Explorations in Topology

    Map Coloring, Surfaces and Knots
    • 2nd Edition
    • David Gay
    • English
    Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology.

  • Introduction to Probability

    • 2nd Edition
    • George G. Roussas
    • English
    Introduction to Probability, Second Edition, discusses probability theory in a mathematically rigorous, yet accessible way. This one-semester basic probability textbook explains important concepts of probability while providing useful exercises and examples of real world applications for students to consider. This edition demonstrates the applicability of probability to many human activities with examples and illustrations. After introducing fundamental probability concepts, the book proceeds to topics including conditional probability and independence; numerical characteristics of a random variable; special distributions; joint probability density function of two random variables and related quantities; joint moment generating function, covariance and correlation coefficient of two random variables; transformation of random variables; the Weak Law of Large Numbers; the Central Limit Theorem; and statistical inference. Each section provides relevant proofs, followed by exercises and useful hints. Answers to even-numbered exercises are given and detailed answers to all exercises are available to instructors on the book companion site. This book will be of interest to upper level undergraduate students and graduate level students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences.

  • An Introduction to Nonsmooth Analysis

    • 1st Edition
    • Juan Ferrera
    • English
    Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail.

  • Computer-Aided Design International Yearbook 1985

    • 1st Edition
    • Alison Smith
    • English
    Computer-Aided Design International Yearbook 1985 covers developments and trends in computer-aided design. This book examines the role of the computer in making design decisions and surveys the CAD industry. This text also presents a run-down of the latest acquisitions of companies in the field and a survey of the major firms working in CAD. The main part of this yearbook is taken up by a directory of products and vendors and manufacturers of CAD equipment. This yearbook consists of 13 chapters and begins with a discussion on the importance of computers in design decision-making, as well as historical precedents in the evolutionary stages in the development of human's control over his environment. The next chapter presents an overview of the status of the CAD industry. After providing a profile of Scottish company Lattice Logic, this book turns to Plessey Airports of the UK and its investment in CAD. A directory of products and manufacturers of CAD equipment follows. Entries are organized alphabetically by vendor and are grouped under four headings: turnkey systems, software, system components, and services. This book also provides lists of useful addresses and product indexes. This monograph will be of interest to CAD users and vendors alike.

  • Evaluating Performance in Physical Education

    • 1st Edition
    • B. Don Franks + 1 more
    • English
    Evaluating Performance in Physical Education describes the tools and techniques that can be used by teachers to assess student performance, curriculum, and method of teaching. The book discusses conventional material in evaluating physical education performance through written, fitness tests, and elementary statistics. The text also explains nonparametric statistics, subjective evaluation, and a theoretical model for fitness and performance. The authors review the functions, evaluation, and administration of testing. The authors also explain in more detail subjective evaluation and offer three forms: 1) experience of the teacher; 2) skill to be rated; and 3) length of time for rating. In testing events, nonparametric statistical procedures show more reliability; parametric procedures are preferably to be used in established research stations. The authors also list some guidelines to be followed in evaluating the student such as objectives, assignment of grades, and acceptance of the grading plan. The book also discusses procedures when evaluation involves large groups. The text can assist physical education teachers, school administrators, and educators in evaluating their subject course or curricula.

  • Neural Modeling and Neural Networks

    • 1st Edition
    • F. Ventriglia
    • English
    Research in neural modeling and neural networks has escalated dramatically in the last decade, acquiring along the way terms and concepts, such as learning, memory, perception, recognition, which are the basis of neuropsychology. Nevertheless, for many, neural modeling remains controversial in its purported ability to describe brain activity. The difficulties in "modeling" are various, but arise principally in identifying those elements that are fundamental for the expression (and description) of superior neural activity. This is complicated by our incomplete knowledge of neural structures and functions, at the cellular and population levels. The first step towards enhanced appreciation of the value of neural modeling and neural networks is to be aware of what has been achieved in this multidisciplinary field of research. This book sets out to create such awareness. Leading experts develop in twelve chapters the key topics of neural structures and functions, dynamics of single neurons, oscillations in groups of neurons, randomness and chaos in neural activity, (statistical) dynamics of neural networks, learning, memory and pattern recognition.

  • An Introduction to Psychoanalytic Theory of Motivation

    • 1st Edition
    • Walter Toman
    • English
    An Introduction to Psychoanalytic Theory of Motivation details the fundamental concepts in applying the psychoanalytic theory in understanding motivation. The title addresses the short-comings of the psychoanalytic theory, particularly the lack of scientific literature. The first part of the text covers the critical concepts in psychoanalytic theory, such as the psychological forces, defense mechanisms, superego, and primal desires. In the second part, the selection details the theory at work; this part discusses the major stages of life from a psychoanalytic perspective. The text also talks about a system of psychopathology, along with the consideration to take in psychotherapy. The book will be of great interest to students, researchers, and practitioners of behavioral science.

  • Handbook of Automotive Design Analysis

    • 1st Edition
    • John Fenton
    • English
    Handbook of Automotive Design Analysis examines promising approaches to automotive design analysis. The discussions are organized based on the major “technological divisions” of motor vehicles: the transmission gearbox and drive line; steering and suspension; and the automobile structure. This handbook is comprised of three chapters; the first of which deals with transmission gearboxes and drive lines. This chapter describes manual-shift gearbox design, synchromesh mechanisms, hydrokinetic automatic gearboxes, drive-line main assemblies, and drive-line losses. The next chapter is about vehicle suspensions and optimum handling performance, with emphasis on two categories of handling of vehicles: steady-state turning (or cornering) and the transient state. The behavior of the steering system, ride parameters, and the design and installation of spring elements are discussed. The third and final chapter focuses on the application of structural design analysis to the automotive structure. After explaining the fundamentals of structural theory in car body design, this book presents the analysis of commercial vehicle body and chassis. Throughout the book, maximum use is made of line-drawings and concise textural presentation to provide the working designer with an easy assimilable account of automotive design analysis. This book will be useful to young automotive engineers and newcomers in automotive design.

  • Computers in the Service of Society

    • 1st Edition
    • Robert Lee Chartrand
    • English
    Computers in the Service of Society examines the role of computers in contemporary society. Based on a seminar series given in the spring of 1969 and co-sponsored by The American University, the book discusses the different societal problems that may be ameliorated by the application of computer technology. The focus of the book is on man’s response to computers, whether the multiple roles of the computer can be comprehended by the decision makers of our times, and whether the vast potential as well as limitations of automatic data processing can be conveyed to the public at large. The book consists of 10 chapters and begins with an overview of the evolution and impact of systems methodology and computer technology; their application to the management of information; and Congress’s increasing awareness of the potential of systems technology, especially the electronic computer. The text then turns its attention to the development of policies for national scientific and technical information systems; systems management in government; how computers help the government in serving society; and acceptance and use of computer technology by corporate management. The possibility of computer-utility services evolving as regulated services is also considered. The book concludes by assessing where the computer is likely to take us in the last third of the 20th century, paying particular attention to the possibility of applying computer technology to the operations of Congress and the legislative process. The text will be of interest to planners, decision makers, professionals, and students working in the field of computer technology.

  • Statistical Theory of Signal Detection

    International Series of Monographs in Electronics and Instrumentation
    • 2nd Edition
    • Carl W. Helstrom
    • D. W. Fry + 2 more
    • English
    Statistical Theory of Signal Detection, Second Edition provides an elementary introduction to the theory of statistical testing of hypotheses that is related to the detection of signals in radar and communications technology. This book presents a comprehensive survey of digital communication systems. Organized into 11 chapters, this edition begins with an overview of the theory of signal detection and the typical detection problem. This text then examines the goals of the detection system, which are defined through an analogy with the testing of statistical hypotheses. Other chapters consider the noise fluctuations in terms of probability distributions whereby the statistical information is used to design a receiver that attains the maximum rate of successful detections in a long series of trials. This book discusses as well the criteria of success and failure in statistical situations. The final chapter deals with the types of stochastic signals. This book is a valuable resource for mathematicians and engineers.

  • Computational Hydraulics

    • 1st Edition
    • C. A. Brebbia + 1 more
    • English
    Computational Hydraulics provides an introduction to computational techniques for hydraulic and fluid flow engineers. It combines classical hydraulics with new methods such as finite elements and boundary elements, which are both presented in a matrix formulation. The most interesting feature of the book is the integrated treatment given to the theoretical and computing aspects of numerical methods. The format presents a series of complete computer programs, for linear and non-linear pipe network analysis, depth flow computations, and finite and boundary elements for Laplace equations. The programs, which are written in standard FORTRAN, are self-contained and easy to implement in any computer. The book is the product of several years' experience in teaching and research at undergraduate and post-graduate level and can be used to offer a self-contained course on Computational Hydraulics for final year or M.Sc. Engineering students. The authors hope that this book will make practicing hydraulic engineers more aware of modern computer techniques and be useful in teaching them to the next generation.

  • Life Table Techniques and Their Applications

    • 1st Edition
    • Krishnan Namboodiri + 1 more
    • H. H. Winsborough
    • English
    This is the first volume to present a comprehensive treatment of the theory and application of life table techniques. The emphasis is placed on applications, and the theory is presented in such a way that individuals with minimal knowledge of calculus and matrix algebra can follow the argument.

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