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.

Books Journals

An Introduction to Stochastic Modeling

1st Edition
May 10, 2014
Howard M. Taylor + 1 more
English
eBook
9 7 8 1 4 8 3 2 2 0 4 4 4

An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Applied Fuzzy Systems

1st Edition
May 10, 2014
Toshiro Terano + 2 more
English
eBook
9 7 8 1 4 8 3 2 6 2 9 3 2

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.

Computer Methods in Operations Research

1st Edition
May 10, 2014
Arne Thesen
J. William Schmidt
English
eBook
9 7 8 1 4 8 3 2 6 0 7 4 7

Computer Methods in Operations Research focuses on the computational methods used in operations research. Topics covered range from list processing to sorting and searching, networks, and critical path methods. Resource-constrained scheduling methods and linear programming methods are also discussed, along with the branch and bound concept. Comprised of 11 chapters, this book begins with a review of some of the basic principles that make a software development effort successful, emphasizing the need to keep things simple and understandable. The reader is then introduced to the basic principles of list processing, searching, and sorting; the concept of networks and several matrix- and list-oriented methods for representing networks in the computer; and the critical path method. Subsequent chapters deal with more complex programs and algorithms to handle scheduling of activities under precedence and resource restrictions; the resource-constrained scheduling problem, formulated both in an exact (using integer programming) and in a heuristic manner; the design of algorithms for the solution of large linear programming problems; and the application of list processing concepts to the development of branch and bound algorithms for solution of combinatorial optimization problems. The book also considers the design of random number generators and discrete event simulation programming before concluding with a description of two programming languages, GPSS and WIDES, for use in simulation modeling. This monograph will be of value to students and practitioners of operations research and industrial engineering.

Stochastic Economics

1st Edition
May 10, 2014
Gerhard Tintner + 1 more
English
eBook
9 7 8 1 4 8 3 2 7 4 0 2 7

Stochastic Economics: Stochastic Processes, Control, and Programming presents some aspects of economics from a stochastic or probabilistic point of view. The application of stochastic processes to the theory of economic development, stochastic control theory, and various aspects of stochastic programming is discussed. Comprised of four chapters, this book begins with a short survey of the stochastic view in economics, followed by a discussion on discrete and continuous stochastic models of economic development. The next chapter focuses on methods of stochastic control and their application to dynamic economic models, with emphasis on those aspects connected especially with the theory of quantitative economic policy. Some basic operational problems of applying stochastic control, particularly in economic systems and organizations for problems such as dynamic resource allocation, growth planning, and economic coordination are considered. The last chapter is devoted to stochastic programming, paying particular attention to the decision rule theory of operations research under the chance-constrained model and a method of incorporating reliability measures into a systems reliability model. This book will be of interest to economists, statisticians, applied mathematicians, operations researchers, and systems engineers.

Numerical Analysis

1st Edition
May 10, 2014
John Todd
Ch. Blanc + 2 more
English
eBook
9 7 8 1 4 8 3 2 6 8 9 1 0

Basic Numerical Mathematics, Volume 1: Numerical Analysis focuses on numerical analysis, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The concepts of convergence and continuity are discussed, along with the rate of convergence, acceleration, and asymptotic series. The more traditional topics of interpolation, quadrature, and differential equations are also explored. Comprised of 10 chapters, this volume begins with an analysis of the algorithms of Gauss, Borchardt, and Carlson in relation to the rate of convergence. The reader is then introduced to orders of magnitude and rates of convergence; recurrence relations for powers; and the solution of equations. Subsequent chapters deal with uniform convergence and approximation; the acceleration processes of Aitken and Euler; asymptotic series; interpolation; and quadrature. The final chapter is devoted to linear difference equations with constant coefficients, along with differentiation and differential equations. This book will be of interest to mathematicians and students of mathematics.

Numerical Algebra

1st Edition
May 10, 2014
John Todd
Ch. Blanc + 2 more
English
eBook
9 7 8 1 4 8 3 2 6 9 4 1 2

Basic Numerical Mathematics, Volume II: Numerical Algebra focuses on numerical algebra, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The existence of an orthogonal matrix which diagonalizes a real symmetric matrix is highlighted, and partitioned or block matrices are discussed, along with induced norms and inversion problems. Comprised of 12 chapters, this volume begins with an overview of the manipulation of vectors and matrices, followed by an analysis of induced norms. The reader is then introduced to the direct solution of the inversion problem, first in the context of theoretical arithmetic (that is, when round-off is disregarded) and second in the context of practical computation. Various methods of handling the characteristic value problems are also considered, together with several iterative methods for the solution of a system of linear equations. Two applications are described: the solution of a two-point boundary value problem and the solution of least squares curve fitting. The book concludes with an account of the singular value decomposition and pseudo-inverses. This monograph will be of interest to mathematicians and students of mathematics.

Mastering C Pointers

1st Edition
May 10, 2014
Robert J. Traister
English
eBook
9 7 8 1 4 8 3 2 5 7 7 9 2

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.

Analytic Computational Complexity

1st Edition
May 10, 2014
J.F. Traub
English
eBook
9 7 8 1 4 8 3 2 5 7 8 9 1

Analytic Computational Complexity contains the proceedings of the Symposium on Analytic Computational Complexity held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7-8, 1975. The symposium provided a forum for assessing progress made in analytic computational complexity and covered topics ranging from strict lower and upper bounds on iterative computational complexity to numerical stability of iterations for solution of nonlinear equations and large linear systems. Comprised of 14 chapters, this book begins with an introduction to analytic computational complexity before turning to proof techniques used in analytic complexity. Subsequent chapters focus on the complexity of obtaining starting points for solving operator equations by Newton's method; maximal order of multipoint iterations using n evaluations; the use of integrals in the solution of nonlinear equations in N dimensions; and the complexity of differential equations. Algebraic constructions in an analytic setting are also discussed, along with the computational complexity of approximation operators. This monograph will be of interest to students and practitioners in the fields of applied mathematics and computer science.

Multivariable Calculus with Linear Algebra and Series

1st Edition
May 10, 2014
William F. Trench + 1 more
English
eBook
9 7 8 1 4 8 3 2 5 9 2 0 8

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

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

1st Edition
May 10, 2014
William F. Trench + 1 more
English
eBook
9 7 8 1 4 8 3 2 2 0 4 5 1

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.

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