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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.

  • Handbook of Differential Equations

    • 2nd Edition
    • Daniel Zwillinger
    • English
    Handbook of Differential Equations, Second Edition is a handy reference to many popular techniques for solving and approximating differential equations, including numerical methods and exact and approximate analytical methods. Topics covered range from transformations and constant coefficient linear equations to Picard iteration, along with conformal mappings and inverse scattering. Comprised of 192 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques needed to determine if a partial differential equation is well-posed or what the "natural" boundary conditions are. Subsequent sections focus on exact and approximate analytical solution techniques for differential equations, along with numerical methods for ordinary and partial differential equations. This monograph is intended for students taking courses in differential equations at either the undergraduate or graduate level, and should also be useful for practicing engineers or scientists who solve differential equations on an occasional basis.

  • Uncertainty in Artificial Intelligence

    Proceedings of the Eighth Conference (1992), July 17–19, 1992, Eighth Conference on Uncertainty in Artificial Intelligence, Stanford University
    • 1st Edition
    • Didier J. Dubois + 2 more
    • English
    Uncertainty in Artificial Intelligence: Proceedings of the Eighth Conference (1992) covers the papers presented at the Eighth Conference on Uncertainty in Artificial Intelligence, held at Stanford University on July 17-19, 1992. The book focuses on the processes, methodologies, technologies, and approaches involved in artificial intelligence. The selection first offers information on Relative Evidential Support (RES), modal logics for qualitative possibility and beliefs, and optimizing causal orderings for generating DAGs from data. Discussions focus on reversal, swap, and unclique operators, modal representation of possibility, and beliefs and conditionals. The text then examines structural controllability and observability in influence diagrams, lattice-based graded logic, and dynamic network models for forecasting. The manuscript takes a look at reformulating inference problems through selective conditioning, entropy and belief networks, parallelizing probabilistic inference, and a symbolic approach to reasoning with linguistic quantifiers. The text also ponders on sidestepping the triangulation problem in Bayesian net computations; exploring localization in Bayesian networks for large expert systems; and expressing relational and temporal knowledge in visual probabilistic networks. The selection is a valuable reference for researchers interested in artificial intelligence.

  • An Architecture for Combinator Graph Reduction

    • 1st Edition
    • Philip John Koopman
    • English
    An Architecture for Combinator Graph Reduction examines existing methods of evaluating lazy functional programs using combinator reduction techniques, implementation, and characterization of a means for accomplishing graph reduction on uniprocessors, and analysis of the potential for special-purpose hardware implementations. Comprised of eight chapters, the book begins by providing a background on functional programming languages and existing implementation technology. Subsequent chapters discuss the TIGRE (Threaded Interpretive Graph Reduction Engine) methodology for implementing combinator graph reduction; the TIGRE abstract machine, which is used to implement the graph reduction methodology; the results of performance measurements of TIGRE on a variety of platforms; architectural metrics for TIGRE executing on the MIPS R2000 processor; and the potential for special-purpose hardware to yield further speed improvements. The final chapter summarizes the results of the research, and suggests areas for further investigation. Computer engineers, programmers, and computer scientists will find the book interesting.

  • Theoretical Aspects of Reasoning About Knowledge

    Proceedings of the Fifth Conference (TARK 1994)
    • 1st Edition
    • Ronald Fagin
    • English
    Theoretical Aspects of Reasoning About Knowledge contains the proceedings of the Fifth Conference on Theoretical Aspects of Reasoning About Knowledge (TARK 1994) held in Pacific Grove, California, on March 13-16, 1994. The conference provided a forum for discussing the theoretical aspects of reasoning about knowledge and tackled topics ranging from the logic of iterated belief revision and backwards forward induction to information acquisition from multi-agent resources, infinitely epistemic logic, and coherent belief revision in games. Comprised of 23 chapters, this book begins with a review of situation calculus and a solution to the frame problem, along with the use of a regression method for reasoning about the effect of actions. A novel programming language for high-level robotic control is described, along with a knowledge-based framework for belief change. Subsequent chapters deal with consistent belief reasoning in the presence of inconsistency; an epistemic logic of situations; an axiomatic approach to the logical omniscience problem; and an epistemic proof system for parallel processes. Inductive learning, knowledge asymmetries, and convention are also examined. This monograph will be of interest to both students and practitioners in the fields of artificial intelligence and computer science.

  • Computing for Calculus

    • 1st Edition
    • Mark J. Christensen
    • English
    Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems. This book discusses the input statement for numeric variables, advanced intrinsic functions, numerical estimation of limits, and linear approximations and tangents. The elementary estimation of areas, numerical and string arrays, line drawing algorithms, and bisection and secant method are also elaborated. This text likewise covers the implicit functions and differentiation, upper and lower rectangular estimates, Simpson's rule and parabolic approximation, and interpolating polynomials. Other topics include the Taylor polynomials, estimating the limit of a sequence, infinite series, and level curves and central projection of surfaces. This publication is beneficial to math students and specialists who use computer languages for educational purposes.

  • Object-Oriented Graphics Programming in C++

    • 1st Edition
    • Roger T. Stevens
    • English
    Object-Oriented Graphics Programming in C++ provides programmers with the information needed to produce realistic pictures on a PC monitor screen. The book is comprised of 20 chapters that discuss the aspects of graphics programming in C++. The book starts with a short introduction discussing the purpose of the book. It also includes the basic concepts of programming in C++ and the basic hardware requirement. Subsequent chapters cover related topics in C++ programming such as the various display modes; displaying TGA files, and the vector class. The text also tackles subjects on the processing of objects; how the ray tracing process works; how to put the program together and compile and run it; and animation. Computer programmers will find the book very useful.

  • Instructor's Manual to Accompany CALCULUS WITH ANALYTIC GEOMETRY

    • 1st Edition
    • Sam Stuart
    • English
    Instructor's Manual to Accompany Calculus with Analytic Geometry is an instructor's manual on calculus with analytic geometry. It contains answers to even-numbered exercises and solutions of selected even- and odd-numbered exercises. Comments on selected exercises are included. Comprised of 18 chapters, this book first presents answers and solutions to exercises relating to functions and graphs. The next chapter is about derivatives and covers topics ranging from the slope problem to limits, sums and products, and quotients and square roots, along with limits and continuity. Subsequent chapters deal with applications of differentiation; exponential and trigonometric functions; techniques and applications of integration; inverse functions; and plane analytic geometry. The rest of the book focuses on approximation and convergence; power series; space geometry and vectors; vector functions and curves; higher partials and their applications; and double and multiple integrals. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

  • Business Mathematics

    • 1st Edition
    • Michael Sentlowitz
    • English
    Business Mathematics deals with the concepts and problem-solving techniques used in business mathematics. Learning objectives are included at the beginning of each chapter to give the student an overview of the skills they can expect to master after completing the chapter, along with worked-out examples and practice exercises; drill problems and word problems; and post-tests that let students measure their problem-solving skills. Topics covered in this book include operations with whole numbers, decimals, fractions, and percent; sales and inventory; finance; business and personal expenses; borrowing and investing; and data analysis. Starting with the fourth chapter, a case study is included at the end of each chapter for an in-depth analysis and discussion of a hypothetical business-related situation. Optional subsections in each chapter deal with mental arithmetic skills. Step-by-step problem-solving procedures are translated into written formulas, located in easy-to-find boxes for quick reference. A chapter glossary includes definitions for all key terms introduced in the chapter. The answer key at the end of the text includes all the answers for the pretests and post-tests, plus the answers to odd-numbered exercises. This monograph is intended for instructors of business mathematics and for their students who want to understand the concepts and master the problem-solving techniques of business mathematics.

  • Quick Reference to Computer Graphics Terms

    • 1st Edition
    • Roger T. Stevens
    • English
    Quick Reference to Computer Graphics Terms is a collection of technical terms used in computer graphics in a compact and convenient reference volume. The book lists a number of acronyms, phrases, and words that have specialized meanings in the field of computer graphics. The definitions provided are simple and easily understood. The author attempts to present, as much as possible, words and phrases that are widely used during the publication of the volume. Any terms not found in the book may be included in the next edition. Users of computers graphics and students will find the book useful.

  • Elementary Differential Equations with Linear Algebra

    • 3rd Edition
    • Albert L. Rabenstein
    • English
    Elementary Differential Equations with Linear Algebra, Third Edition provides an introduction to differential equation and linear algebra. This book includes topics on numerical methods and Laplace transforms. Organized into nine chapters, this edition begins with an overview of an equation that involves a single unknown function of a single variable and some finite number of its derivatives. This text then examines a linear system of two equations with two unknowns. Other chapters consider a class of linear transformations that are defined on spaces of functions wherein these transformations are essential in the study of linear differential equations. This book discusses as well the linear differential equations whose coefficients are constant functions. The final chapter deals with the properties of Laplace transform in detail and examine as well the applications of Laplace transforms to differential equations. This book is a valuable resource for mathematicians, students, and research workers.

  • An Introduction to Algebraic and Combinatorial Coding Theory

    • 1st Edition
    • Ian F. Blake + 1 more
    • English
    An Introduction to Algebraic and Combinatorial Coding Theory focuses on the principles, operations, and approaches involved in the combinatorial coding theory, including linear transformations, chain groups, vector spaces, and combinatorial constructions. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on quadratic residues and codes, self-dual and quasicyclic codes, balanced incomplete block designs and codes, polynomial approach to coding, and linear transformations of vector spaces over finite fields. The text then examines coding and combinatorics, including chains and chain groups, equidistant codes, matroids, graphs, and coding, matroids, and dual chain groups. The manuscript also ponders on Möbius inversion formula, Lucas's theorem, and Mathieu groups. The publication is a valuable source of information for mathematicians and researchers interested in the combinatorial coding theory.

  • Programming for the Newton®

    Software Development with Newtonscript™
    • 1st Edition
    • Julie McKeehan + 1 more
    • English
    Programming for the Newton: Software Development with NewtonScript focuses on the processes, approaches, operations, and principles involved in software development with NewtonScript. The publication first elaborates on Newton application design, views on the Newton, and protos. Discussions focus on system protos, creating and using user protos, linking and naming templates, creating the views of WaiterHelper, Newton application designs, and life cycle of an application. The text then elaborates on the fundamentals of NewtonScript, inheritance in NewtonScript, and view system and messages. Topics include InstallScript and RemoveScript, adding code to WaiterHelper, proto and parent inheritance, combining proto and parent inheritance, frames, arrays, and symbols and path expressions. The book ponders on debugging and Newton data storage, including description of methods and functions, handling soups in application, printing, tracking, and debugging functions. The publication is a vital reference for computer programmers and researchers interested in NewtonScript.

  • Mathematical Tools for Applied Multivariate Analysis

    • 1st Edition
    • Paul E. Green
    • English
    Mathematical Tools for Applied Multivariate Analysis provides information pertinent to the aspects of transformational geometry, matrix algebra, and the calculus that are most relevant for the study of multivariate analysis. This book discusses the mathematical foundations of applied multivariate analysis. Organized into six chapters, this book begins with an overview of the three problems in multiple regression, principal components analysis, and multiple discriminant analysis. This text then presents a standard treatment of the mechanics of matrix algebra, including definitions and operations on matrices, vectors, and determinants. Other chapters consider the topics of eigenstructures and linear transformations that are important to the understanding of multivariate techniques. This book discusses as well the eigenstructures and quadratic forms. The final chapter deals with the geometric aspects of linear transformations. This book is a valuable resource for students.

  • Handbook of Networking & Connectivity

    • 1st Edition
    • Gary R. McClain
    • English
    Handbook of Networking & Connectivity focuses on connectivity standards in use, including hardware and software options. The book serves as a guide for solving specific problems that arise in designing and maintaining organizational networks. The selection first tackles open systems interconnection, guide to digital communications, and implementing TCP/IP in an SNA environment. Discussions focus on elimination of the SNA backbone, routing SNA over internets, connectionless versus connection-oriented networks, internet concepts, application program interfaces, basic principles of layering, protocols and services, application layer, and conformance testing. The book then takes a look at integrated services digital network, an overview of the synchronous optical network, and X.25 and worldwide networking. The publication ponders on Metropolitan Area Networks (MAN), an overview of the switched multimegabit data service, and Ethernet/802.3 and Token Ring/802.5. Topics include Ethernet versus token ring, Ethernet/802.3, customer network management, MAN conception and technology, and SMDS specifications and sources and interface protocol. The selection is a vital source of data for systems professionals and researchers interested in networking and connectivity.

  • Calculus Using Mathematica

    Scientific Projects and Mathematical Background
    • 1st Edition
    • K.D. Stroyan
    • English
    Calculus Using Mathematica: Scientific Projects and Mathematical Background is a companion to the core text, Calculus Using Mathematica. The book contains projects that illustrate applications of calculus to a variety of practical situations. The text consists of 14 chapters of various projects on how to apply the concepts and methodologies of calculus. Chapters are devoted to epidemiological applications; log and exponential functions in science; applications to mechanics, optics, economics, and ecology. Applications of linear differential equations; forced linear equations; differential equations from vector geometry; and to chemical reactions are presented as well. College students of calculus will find this book very helpful.

  • Computers and Data Processing

    International Edition
    • 1st Edition
    • Harvey M. Deitel + 1 more
    • English
    Computers and Data Processing provides information pertinent to the advances in the computer field. This book covers a variety of topics, including the computer hardware, computer programs or software, and computer applications systems. Organized into five parts encompassing 19 chapters, this book begins with an overview of some of the fundamental computing concepts. This text then explores the evolution of modern computing systems from the earliest mechanical calculating devices to microchips. Other chapters consider how computers present their results and explain the storage and retrieval of massive amounts of computer-accessible information from secondary storage devices. This book discusses as well the development installation, evaluation, and control of computer systems. The final chapter discusses the use of computers in the transportation systems and the ways in which they make possible other innovations in transportation. This book is a valuable resource for computer scientists, systems analysts, computer programmers, mathematicians, and computer specialists.

  • Stories About Sets

    • 1st Edition
    • N. Ya. Vilenkin
    • D. Allan Bromley + 2 more
    • English
    Stories About Sets discusses the cardinality of sets and mathematical concepts, such as function, curve, surface, dimensions, and the paradoxical properties of curves and surfaces. The book reviews sets, operations on sets, the empty set, subsets, the universal sets, intersection of sets, union of sets, partitioning of sets, and boolean algebras. The text also discusses the cardinality of sets, including equality between sets, countable sets, unequal sets, the uncountability of the continuum, the existence of transcendental numbers, and the enigmatic axiom. The book analyzes if a part can be equal to the whole (which turns out to be true if it is applied to infinite sets). The text also discusses the arithmetic of the infinite such as involving the multiplication of infinite cardinalities. The book explains some remarkable functions and curves, the Dirichlet's function, Cantor's set, points of fracture, and continuous functions whose graphs possess a tangent at no point. The text shows how to construct a closed curve of infinite length or a curve passing through all the points of a square. The book can prove interesting and highly educational for students with mathematic or algebra subjects, as well as for academicians involved in teaching statistics or mathematics.

  • Open Client/Server Computing and Middleware

    • 1st Edition
    • Alan R. Simon + 1 more
    • English
    Open Client/Server Computing and Middleware provides a tutorial-oriented overview of open client/server development environments and how client/server computing is being done. This book analyzes an in-depth set of case studies about two different open client/server development environments—Microso... Windows and UNIX, describing the architectures, various product components, and how these environments interrelate. Topics include the open systems and client/server computing, next-generation client/server architectures, principles of middleware, and overview of ProtoGen+. The ViewPaint environment, ProtoView screen manager, SQLView visual database access, and ProtoView WinControl library are also elaborated. This text likewise covers the interaction with db-UIM/X, widgets and building interfaces, network object toolkit, and integration of cross-platform components. This publication is suitable for computing professionals and researchers interested in open client/server computing.

  • Capacity Planning for Computer Systems

    • 1st Edition
    • Tim Browning
    • English
    Capacity Planning for Computer Systems covers the principles, concepts, and practical application of capacity planning to computer systems. This book is divided into nine chapters and begins with an introduction to the foundation and metrics of capacity planning. The subsequent chapters deal with the business elements, service levels, forecasting, and predictions of capacity planning, along with the regression techniques, forecast monitoring, and revision for the field. The remaining chapters highlight the applications of capacity planning, including in systems optimization, computer disk, tape, and tape drive. These chapters also provide the charting and graphics presentations for capacity planning. This book will be of value to computer scientists and researchers.

  • Efficient C/C++ Programming

    Smaller, Faster, Better
    • 2nd Edition
    • Steve Heller
    • English
    Efficient C/C++ Programming describes a practical, real-world approach to efficient C/C++ programming. Topics covered range from how to save storage using a restricted character set and how to speed up access to records by employing hash coding and caching. A selective mailing list system is used to illustrate rapid access to and rearrangement of information selected by criteria specified at runtime. Comprised of eight chapters, this book begins by discussing factors to consider when deciding whether a program needs optimization. In the next chapter, a supermarket price lookup system is used to illustrate how to save storage by using a restricted character set and how to speed up access to records with the aid of hash coding and caching. Attention is paid to rapid retrieval of prices. A selective mailing list system is then used to illustrate rapid access to and rearrangement of information selected by criteria specified at runtime. The book also considers the Huffman coding and arithmetic coding methods of data compression; a token-threaded interpreter whose code can run faster than equivalent compiled C code, due to its greater code density; a customer database program with variable-length records; and index and key access to variable-length records. The final chapter summarizes the characteristics of the algorithms encountered in previous chapters, as well as the future of the art of optimization. This monograph will be a useful resource for practicing computer programmers and those who intend to be working programmers.

  • Test Bank to Accompany Computers Data and Processing

    • 1st Edition
    • Harvey M. Deitel + 1 more
    • English
    Test Bank to Accompany Computers and Data Processing provides a variety of questions from which instructors can easily custom tailor exams appropriate for their particular courses. This book contains over 4000 short-answer questions that span the full range of topics for introductory computing course. This book is organized into five parts encompassing 19 chapters. This text provides a very large number of questions so that instructors can produce different exam testing essentially the same topics in succeeding semesters. Three types of questions are included in this book, including multiple choices, true/false, and fill-in-the-blanks. The answers are provided side-by-side with the questions so that instructors can easily locate questions that are unambiguous and appropriate in the context of their courses.This book covers a variety of topics, including evolution of computers, computer processor, input, output, software, programming languages, and data communications. This book is a valuable resource for students and instructors in introductory computing course.

  • Fuzzy Logic

    A Practical Approach
    • 1st Edition
    • F. Martin McNeill + 1 more
    • English
    Fuzzy Logic: A Practical Approach focuses on the processes and approaches involved in fuzzy logic, including fuzzy sets, numbers, and decisions. The book first elaborates on fuzzy numbers and logic, fuzzy systems on the job, and Fuzzy Knowledge Builder. Discussions focus on formatting the knowledge base for an inference engine, personnel detection system, using a knowledge base in an inference engine, fuzzy business systems, industrial fuzzy systems, fuzzy sets and numbers, and quantifying word-based rules. The text then elaborates on designing a fuzzy decision and Fuzzy Thought Amplifier for complex situations. Topics include origins of cognitive maps, Fuzzy Thought Amplifier, training a map to predict the future, introducing the Fuzzy Decision Maker, and merging interests. The publication takes a look at fuzzy associative memory, fuzzy sets as hypercube points, and disk files and descriptions, including Fuzzy Thought Amplifier, Fuzzy Decision Maker, and composing and creating a memory. The text is a valuable source of data for researchers interested in fuzzy logic.

  • Algebra and Trigonometry

    • 1st Edition
    • Harley Flanders + 1 more
    • English
    Algebra and Trigonometry presents the essentials of algebra and trigonometry with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered. Comprised of 11 chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities. Subsequent chapters deal with the most basic functions: polynomial, rational, exponential, logarithm, and trigonometric. Trigonometry and the inverse trigonometric functions and identities are also presented. The book concludes with a review of progressions, permutations, combinations, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

  • Measure, Integration, and Functional Analysis

    • 1st Edition
    • Robert B. Ash
    • English
    Measure, Integration, and Functional Analysis deals with the mathematical concepts of measure, integration, and functional analysis. The fundamentals of measure and integration theory are discussed, along with the interplay between measure theory and topology. Comprised of four chapters, this book begins with an overview of the basic concepts of the theory of measure and integration as a prelude to the study of probability, harmonic analysis, linear space theory, and other areas of mathematics. The reader is then introduced to a variety of applications of the basic integration theory developed in the previous chapter, with particular reference to the Radon-Nikodym theorem. The third chapter is devoted to functional analysis, with emphasis on various structures that can be defined on vector spaces. The final chapter considers the connection between measure theory and topology and looks at a result that is a companion to the monotone class theorem, together with the Daniell integral and measures on topological spaces. The book concludes with an assessment of measures on uncountably infinite product spaces and the weak convergence of measures. This book is intended for mathematics majors, most likely seniors or beginning graduate students, and students of engineering and physics who use measure theory or functional analysis in their work.

  • Random Polynomials

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • A. T. Bharucha-Reid + 1 more
    • Z. W. Brinbaum + 1 more
    • English
    Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Random Polynomials focuses on a comprehensive treatment of random algebraic, orthogonal, and trigonometric polynomials. The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials. The text then elaborates on the number and expected number of real zeros of random algebraic polynomials; number and expected number of real zeros of other random polynomials; and variance of the number of real zeros of random algebraic polynomials. Topics include the expected number of real zeros of random orthogonal polynomials and the number and expected number of real zeros of trigonometric polynomials. The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials. The publication is a dependable reference for probabilists, statisticians, physicists, engineers, and economists.

  • Asymptotic Approximations of Integrals

    Computer Science and Scientific Computing
    • 1st Edition
    • R. Wong
    • Werner Rheinboldt + 1 more
    • English
    Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

  • Computer Arithmetic and Self-Validating Numerical Methods

    • 1st Edition
    • Christian Ullrich
    • English
    Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods,” held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.

  • The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

    • 1st Edition
    • A. K. Aziz
    • English
    The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.

  • Weak Convergence of Measures

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • Harald Bergström
    • Z. W. Birnbaum + 1 more
    • English
    Weak Convergence of Measures provides information pertinent to the fundamental aspects of weak convergence in probability theory. This book covers a variety of topics, including random variables, Hilbert spaces, Gaussian transforms, probability spaces, and random variables. Organized into six chapters, this book begins with an overview of elementary fundamental notions, including sets, different classes of sets, different topological spaces, and different classes of functions and measures. This text then provides the connection between functionals and measures by providing a detailed introduction of the abstract integral as a bounded, linear functional. Other chapters consider weak convergence of sequences of measures, such as convergence of sequences of bounded, linear functionals. This book discusses as well the weak convergence in the C- and D-spaces, which is reduced to limit problems. The final chapter deals with weak convergence in separable Hilbert spaces. This book is a valuable resource for mathematicians.

  • Numerical Solution of Partial Differential Equations—II, Synspade 1970

    Proceedings of the Second Symposium on the Numerical Solution of Partial Differential Equations, SYNSPADE 1970, Held at the University of Maryland, College Park, Maryland, May 11-15, 1970
    • 1st Edition
    • Bert Hubbard
    • English
    Numerical Solution of Partial Differential Equations—II: Synspade 1970 provides information pertinent to the fundamental aspects of partial differential equations. This book covers a variety of topics that range from mathematical numerical analysis to numerical methods applied to problems in mechanics, meteorology, and fluid dynamics. Organized into 18 chapters, this book begins with an overview of the methods of the Rayleigh–Ritz–Galerk... type for the approximation of boundary value problems using spline basis functions and Sobolev spaces. This text then analyzes a special approach aimed at solving elliptical equations. Other chapters consider the approximation theoretic study of special sets of approximating functions. This book discusses as well combining the alternating-directio... methods with Galerkin methods to obtain highly efficient procedures for the numerical solution of second order parabolic and hyperbolic problems. The final chapter deals with the results concerning Chebyshev rational approximations of reciprocals of certain entire functions. This book is a valuable resource for mathematicians.

  • Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series

    • 1st Edition
    • William F. Trench + 1 more
    • English
    Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples. The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eigenvalues and eigenvectors; vector analysis and analytic geometry in R3; curves and surfaces; the differential calculus of real-valued functions of n variables; and vector-valued functions as ordered m-tuples of real-valued functions. Integration (line, surface, and multiple integrals) is also covered, together with Green's and Stokes's theorems and the divergence theorem. The final chapter is devoted to infinite sequences, infinite series, and power series in one variable. This monograph is intended for students majoring in science, engineering, or mathematics.

  • Numerical Solution of Differential Equations

    • 1st Edition
    • Isaac Fried
    • Werner Rheinboldt
    • English
    Numerical Solution of Differential Equations is a 10-chapter text that provides the numerical solution and practical aspects of differential equations. After a brief overview of the fundamentals of differential equations, this book goes on presenting the principal useful discretization techniques and their theoretical aspects, along with geometrical and physical examples, mainly from continuum mechanics. Considerable chapters are devoted to the development of the techniques of the numerical solution of differential equations and their analysis. The remaining chapters explore the influential invention in computational mechanics-finite elements. Each chapter emphasizes the relationship among the analytic formulation of the physical event, the discretization techniques applied to it, the algebraic properties of the discrete systems created, and the properties of the digital computer. This book will be of great value to undergraduate and graduate mathematics and physics students.

  • Study Guide for College Algebra and Trigonometry

    • 1st Edition
    • James W. Snow + 2 more
    • English
    Study Guide for College Algebra and Trigonometry is a supplement material to the basic text, College Algebra and Trigonometry. It is written to assist the student in learning mathematics effectively. The book provides detailed solutions to exercises found in the text. Students are encouraged to use these solutions to find a way to approach a problem. The Study Guide and Solutions Manual consists of four major components: basic concepts that should be learned from each unit, what was learned upon completion of each unit, solutions to selected problems, and a short chapter quiz, including the answers, covering the concepts and problem types. Students of algebra and trigonometry in the college level will find the book very useful.

  • Introduction to Abstract Mathematics

    • 1st Edition
    • T. A. Bick
    • English
    Introduction to Abstract Mathematics focuses on the principles, approaches, and operations involved in abstract mathematics, including metric spaces, sets, axiom systems, and open sentences. The book first offers information on logic and set theory, natural numbers, and integers and rational numbers. Discussions focus on rational numbers and ordered fields, ordering, arithmetic, axiom systems and methods of proof, functions of kindred matters, ordered pairs and relations, sets, and statements and open sentences. The text then examines real and complex numbers, metric spaces, and limits. Topics include generalized limits, continuous functions, openness, closedness, and neighborhood systems, definition and basic properties, and construction of R. The publication is a vital reference for mathematicians and students interested in abstract mathematics.

  • Introduction to Combinatorics

    • 1st Edition
    • Gerald Berman + 1 more
    • English
    Introduction to Combinatorics focuses on the applications, processes, methodologies, and approaches involved in combinatorics or discrete mathematics. The book first offers information on introductory examples, permutations and combinations, and the inclusion-exclusion principle. Discussions focus on some applications of the inclusion-exclusion principle, derangements, calculus of sets, permutations, combinations, Stirling's formula, binomial theorem, regions of a plane, chromatic polynomials, and a random walk. The text then examines linear equations with unit coefficients, recurrence relations, and generating functions. Topics include derivatives and differential equations, solution of difference equations by means of generating functions, recurrence relations, summation method, difference methods, combinations with repetitions, solutions bounded below, and solutions bounded above and below. The publication takes a look at generating functions and difference equations, ramifications of the binomial theorem, finite structures, coloring problems, maps on a sphere, and geometry of the plane. The manuscript is a valuable reference for researchers interested in combinatorics.

  • Applied Finite Mathematics

    • 1st Edition
    • Howard Anton + 1 more
    • English
    Applied Finite Mathematics presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications. Applications in fields such as business, biology, behavioral sciences, and social sciences are included. Comprised of nine chapters, this book begins with an introduction to set theory, explaining concepts such as sets and union and intersection of sets as well as counting elements in sets. The next chapter deals with coordinate systems and graphs, along with applications of linear equations and graphs of linear inequalities. The discussion then turns to linear programming; matrices and linear systems; probability; and statistics. Examples of applications are given, including those of game theory, Markov chains, and probability. The final chapter is devoted to computers and programming languages such as FORTRAN. This monograph is intended for students and instructors of applied mathematics.

  • An Introduction to Analytic Geometry and Calculus

    • 1st Edition
    • A. C. Burdette
    • English
    An Introduction to Analytic Geometry and Calculus covers the basic concepts of analytic geometry and the elementary operations of calculus. This book is composed of 14 chapters and begins with an overview of the fundamental relations of the coordinate system. The next chapters deal with the fundamentals of straight line, nonlinear equations and graphs, functions and limits, and derivatives. These topics are followed by a discussion of some applications of previously covered mathematical subjects. This text also considers the fundamentals of the integrals, trigonometric functions, exponential and logarithm functions, and methods of integration. The final chapters look into the concepts of parametric equations, polar coordinates, and infinite series. This book will prove useful to mathematicians and undergraduate and graduate mathematics students.

  • The Numerical Solution of Ordinary and Partial Differential Equations

    • 1st Edition
    • Granville Sewell
    • English
    The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.

  • Matrix Methods

    An Introduction
    • 1st Edition
    • Richard Bronson
    • English
    Matrix Methods: An Introduction is a nine-chapter text that emphasizes the methodological aspects of mathematical matrices. This book is intended for an introductory course in matrices similar to those given to sophomore and junior engineering students at Fairleigh Dickinson University. The first five chapters deal with the elementary aspects of matrices, including their definition, determinants, method of inversion, simultaneous linear equations, eigenvalues, and eigenvectors. The remaining chapters explore the materials of fundamental importance to both engineers and scientists. These chapters discuss the principles of matrix calculus, linear differential equations, Jordan canonical forms, and special matrices. A set of exercises is provided at the end of each section, which is basically routine in nature and serves primarily to enhance the reader's ability to use the methods just presented. On occasion, problems are assigned that will extend or complete topics previously introduced. This book is intended primarily for science, engineering, and applied mathematics students.

  • Elementary Functions and Analytic Geometry

    • 1st Edition
    • Harley Flanders
    • English
    Elementary Functions and Analytic Geometry is an introduction to college mathematics, with emphasis on elementary functions and analytic geometry. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; and complex numbers, mathematical induction, and the binomial theorem. Comprised of 13 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors, and trigonometry are also explored, together with complex numbers and solid analytic geometry. The book concludes by considering mathematical induction, binomial coefficients, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

  • Applied Fuzzy Systems

    • 1st Edition
    • Toshiro Terano + 2 more
    • English
    Applied Fuzzy Systems provides information pertinent to the fundamental aspects of fuzzy systems theory and its application. This book discusses the development of high-level artificial intelligence and information processing systems, as well as the realization of fuzzy computers. Organized into six chapters, this book begins with an overview of the fundamental problems addressed by fuzzy systems. This text then reviews standard computer logic or two-valued Boolean algebra. Other chapters consider bus scheduling, evaluation of structural reliability, applications of schema systems for decision-making, and processing of natural-language information and systems for medical diagnosis as examples of fuzzy expert systems. This book discusses as well a practical fuzzy expert system for durability evaluations of reinforced concrete slabs for bridges, along with an example of application. The final chapter deals with the important parts of the construction of fuzzy computers, their architecture, and the outlook for the future. This book is a valuable resource for engineers, mathematicians, technicians, and research workers.

  • Introductory Calculus

    With Analytic Geometry and Linear Algebra
    • 2nd Edition
    • A. Wayne Roberts
    • English
    Introductory Calculus: Second Edition, with Analytic Geometry and Linear Algebra is an introductory text on calculus and includes topics related to analytic geometry and linear algebra. Functions and graphs are discussed, along with derivatives and antiderivatives, curves in the plane, infinite series, and differential equations. Comprised of 15 chapters, this book begins by considering vectors in the plane, the straight line, and conic sections. The next chapter presents some of the basic facts about functions, the formal definition of a function, and the notion of a graph of a function. Subsequent chapters examine the derivative as a linear transformation; higher derivatives and the mean value theorem; applications of graphs; and the definite integral. Transcendental functions and how to find an antiderivative are also discussed, together with the use of parametric equations to determine the curve in a plane; how to solve linear equations; functions of several variables and the derivative and integration of these functions; and problems that lead to differential equations. This monograph is intended for students taking a two- or three-semester course in introductory calculus.

  • Metric Affine Geometry

    • 1st Edition
    • Ernst Snapper + 1 more
    • English
    Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.

  • Theory of Machines and Computations

    Proceedings of an International Symposium on the Theory of Machines and Computations Held at Technion in Haifa, Israel, on August 16–19, 1971
    • 1st Edition
    • Zvi Kohavi + 1 more
    • English
    Theory of Machines and Computations consists of papers presented at the International Symposium on the Theory of Machines and Computations, held at Technion-Israel Institute of Technology in Haifa, Israel, in August 1971. This book is organized into five main sections—computabili... theory, formal and stochastic languages, finite automata, fault-detection experiments, and switching theory. In these sections, this compilation specifically discusses the computationally complex and pseudo-random zero-one valued functions and rate of convergence of local iterative schemes. The simple syntactic operators on full semiAFLs, whirl decomposition of stochastic systems, and existence of a periodic analogue of a finite automaton are also elaborated. This text likewise covers the theorems on additive automata, fault location in iterative logic arrays, and tree-threshold-synth... of ternary functions. This publication is useful to practitioners and specialists interested in the theory of machines and computations.

  • Test Bank for Precalculus

    Functions & Graphs
    • 1st Edition
    • Bernard Kolman + 2 more
    • English
    Test Bank for Precalculus: Functions & Graphs is a supplementary material for the text, Precalculus: Functions & Graphs. The book is intended for use by mathematics teachers. The book contains standard tests for each chapter in the textbook. Each set of test focuses on gauging the level of knowledge the student has achieved during the course. The answers for each chapter test and the final exam are found at the end of the book. Mathematics teachers teaching calculus will find the book extremely useful.

  • Introductory Complex and Analysis Applications

    • 1st Edition
    • William R. Derrick
    • English
    Introductory Complex and Analysis Applications provides an introduction to the functions of a complex variable, emphasizing applications. This book covers a variety of topics, including integral transforms, asymptotic expansions, harmonic functions, Fourier transformation, and infinite series. Organized into eight chapters, this book begins with an overview of the theory of functions of a complex variable. This text then examines the properties of analytical functions, which are all consequences of the differentiability of the function. Other chapters consider the converse of Taylor's Theorem, namely that convergent power series are analytical functions in their domain of convergence. This book discusses as well the Residue Theorem, which is of fundamental significance in complex analysis and is the core concept in the development of the techniques. The final chapter deals with the method of steepest descent, which is useful in determining the asymptotic behavior of integral representations of analytic functions. This book is a valuable resource for undergraduate students in engineering and mathematics.

  • Linear Integral Equations

    Theory and Technique
    • 1st Edition
    • Ram P. Kanwal
    • English
    Linear Integral Equations: Theory and Technique is an 11-chapter text that covers the theoretical and methodological aspects of linear integral equations. After a brief overview of the fundamentals of the equations, this book goes on dealing with specific integral equations with separable kernels and a method of successive approximations. The next chapters explore the properties of classical Fredholm theory and the applications of linear integral equations to ordinary and partial differential equations. These topics are followed by discussions of the symmetric kernels, singular integral equations, and the integral transform methods. The final chapters consider the applications of linear integral equations to mixed boundary value problems. These chapters also look into the integral equation perturbation methods. This book will be of value to undergraduate and graduate students in applied mathematics, theoretical mechanics, and mathematical physics.

  • Elementary Linear Algebra

    • 1st Edition
    • Richard O. Hill
    • English
    Elementary Linear Algebra reviews the elementary foundations of linear algebra in a student-oriented, highly readable way. The many examples and large number and variety of exercises in each section help the student learn and understand the material. The instructor is also given flexibility by allowing the presentation of a traditional introductory linear algebra course with varying emphasis on applications or numerical considerations. In addition, the instructor can tailor coverage of several topics. Comprised of six chapters, this book first discusses Gaussian elimination and the algebra of matrices. Applications are interspersed throughout, and the problem of solving AX = B, where A is square and invertible, is tackled. The reader is then introduced to vector spaces and subspaces, linear independences, and dimension, along with rank, determinants, and the concept of inner product spaces. The final chapter deals with various topics that highlight the interaction between linear algebra and all the other branches of mathematics, including function theory, analysis, and the singular value decomposition and generalized inverses. This monograph will be a useful resource for practitioners, instructors, and students taking elementary linear algebra.

  • Ordinary Differential Equations

    • 1st Edition
    • Richard K Miller + 1 more
    • English
    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity, prerequisites have been kept to a minimum and the material is covered in such a way as to be appealing to a wide audience. The book contains eight chapters and begins with an introduction the subject and a discussion of some important examples of differential equations that arise in science and engineering. Separate chapters follow on the fundamental theory of linear and nonlinear differential equations; linear boundary value problems; Lyapunov stability theory; and perturbations of linear systems. Subsequent chapters deal with the Poincare-Bendixson theory and with two-dimensional van der Pol type equations; and periodic solutions of general order systems.

  • On the Cauchy Problem

    • 1st Edition
    • Sigeru Mizohata
    • William F. Ames
    • English
    Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems. The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations. The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.

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