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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 VLSI Chip Design and Expert Systems

    • 1st Edition
    • A. F. Schwarz
    • English
    Handbook of VLSI Chip Design and Expert Systems provides information pertinent to the fundamental aspects of expert systems, which provides a knowledge-based approach to problem solving. This book discusses the use of expert systems in every possible subtask of VLSI chip design as well as in the interrelations between the subtasks. Organized into nine chapters, this book begins with an overview of design automation, which can be identified as Computer-Aided Design of Circuits and Systems (CADCAS). This text then presents the progress in artificial intelligence, with emphasis on expert systems. Other chapters consider the impact of design automation, which exploits the basic capabilities of computers to perform complex calculations and to handle huge amounts of data with a high speed and accuracy. This book discusses as well the characterization of microprocessors. The final chapter deals with interactive I/O devices. This book is a valuable resource for system design experts, circuit analysts and designers, logic designers, device engineers, technologists, and application-specific designers.

  • Introduction to Group Theory with Applications

    Materials Science and Technology
    • 1st Edition
    • Gerald Burns
    • Allen M. Alper + 1 more
    • English
    Introduction to Group Theory with Applications covers the basic principles, concepts, mathematical proofs, and applications of group theory. This book is divided into 13 chapters and begins with discussions of the elementary topics related to the subject, including symmetry operations and group concepts. The succeeding chapters deal with the properties of matrix representations of finite groups, the vibrations of molecular and crystals, vibrational wave function, selection rules, and molecular approximations. These topics are followed by reviews of the basic of quantum mechanics, crystal field theory, atomic physics, hybrid functions, and molecular orbital theory. The last chapters describe the symmetry of crystal lattices, the band theory of solids, and the full rotation group. This book will be of value to undergraduate mathematics and physics students.

  • Large Scale Scientific Computation

    Proceedings of a Conference Conducted by the Mathematics Research Center, the University of Wisconsin - Madison, May 17-19, 1983
    • 1st Edition
    • Seymour V. Parter
    • English
    Large Scale Scientific Computation is a collection of papers that deals with specialized architectural considerations, efficient use of existing computers, software developments, large scale projects in diverse disciplines, and mathematical approaches to basic algorithmic problems. One paper describes numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques applied in many institutions such as in Laboratoire Central des Ponts et Chaussees, Avions Marcel Dassault et Breguet Aviation. Another paper discusses computer-structured design techniques to improve the reliability, efficiency, and accuracy of future production codes. Computer modelling is a potent tool in numerical weather prediction relying on observation, analysis, initialization, and model development. One paper illustrates a systolic algorithm for matrix triangulation, as well as its uses in the Cholesky decomposition of covariance matrices. Another paper describes the Transient Reactor Analysis Code (TRAC) designed to deal with internal flow problems of nuclear reactors. One paper explains the application of large-scale aerodynamic simulation where the programmer can use finite difference techniques in which a large number of mesh points are strategically and orderly placed in the domain of the flow field. The collection is intended for undergraduates in mathematics, programming, computer science, or engineering courses, and designers or researchers involved in industrial facilities, aeronautics, and nuclear design.

  • Iterative Solution of Nonlinear Equations in Several Variables

    • 1st Edition
    • J. M. Ortega + 1 more
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution. This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods. This publication is a good reference for specialists and readers with an extensive functional analysis background.

  • Mastering C Pointers

    Tools for Programming Power
    • 1st Edition
    • Robert J. Traister
    • English
    Mastering C Pointers: Tools for Programming Power focuses on the pointer operations of the C programming language, explaining exactly what pointers are and how to master them through easy-to-understand phrasing and by presenting many simple program examples. The functions of pointers with respect to memory access and memory allocation are also discussed. Comprised of 10 chapters, this book begins with the author's personal reflection on his first encounters with the C programming language and its pointers. The next two chapters presents steps to learning pointers, with emphasis on the essential processes that occur (invisibly and internally) when declaring standard numeric variables in C language and how to deal with C language character arrays and C strings. The reader is then introduced to string pointers and declared pointers of numeric types; the use of C language pointers and the memory allocation functions; and C language functions. The book also explores some of the other "entities" that pointers are used to access, including structures and unions, before concluding with an examination of the source code format of C language. This monograph is intended for both beginning and experienced C language programmers.

  • Generatingfunctionology

    • 1st Edition
    • Herbert S. Wilf
    • English
    Generatingfunctionol... provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

  • The Mathematical Structure of Raster Graphics

    • 1st Edition
    • Eugene L. Fiume
    • English
    The Mathematical Structure of Raster Graphics presents a mathematical characterization of the structure of raster graphics, a popular and diverse form of computer graphics. The semantics and theory of the mathematical structure of raster graphics are discussed. Notations that help to clarify some of the concepts generally considered to be fundamental to computer graphics are included. Comprised of seven chapters, this book begins with a description of a general framework for specifying and manipulating scenes. Basic graphic entities, called primitive graphic objects, are defined using a simple notation over a Euclidean space. The reader is then introduced to a semantics of visibility; a mathematical semantics of rendering, developed using the very basic notion of measure; and a mathematical formalization of bit-mapped graphics. A framework for specifying illumination models is also described, along with the complexity of abstract ray tracing. This monograph will be a useful resource for undergraduate and graduate students, researchers, and practitioners in the fields of mathematics and computer graphics, and to those with some basic computer graphics background.

  • Introduction to Ordinary Differential Equations

    Second Enlarged Edition with Applications
    • 2nd Edition
    • Albert L. Rabenstein
    • English
    Introduction to Ordinary Differential Equations, Second Edition provides an introduction to differential equations. This book presents the application and includes problems in chemistry, biology, economics, mechanics, and electric circuits. Organized into 12 chapters, this edition begins with an overview of the methods for solving single differential equations. This text then describes the important basic properties of solutions of linear differential equations and explains higher-order linear equations. Other chapters consider the possibility of representing the solutions of certain linear differential equations in terms of power series. This book discusses as well the important properties of the gamma function and explains the stability of solutions and the existence of periodic solutions. The final chapter deals with the method for the construction of a solution of the integral equation and explains how to establish the existence of a solution of the initial value system. This book is a valuable resource for mathematicians, students, and research workers.

  • 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.

  • 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.

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