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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.

  • Applications of Number Theory to Numerical Analysis

    • 1st Edition
    • S. K. Zaremba
    • English
    Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.

  • Optimal Control of Differential and Functional Equations

    • 1st Edition
    • J. Warga
    • English
    Optimal Control of Differential and Functional Equations presents a mathematical theory of deterministic optimal control, with emphasis on problems involving functional-integral equations and functional restrictions. The book reviews analytical foundations, and discusses deterministic optimal control problems requiring original, approximate, or relaxed solutions. Original solutions involve mathematicians, and approximate solutions concern engineers. Relaxed solutions yield a complete theory that encompasses both existence theorems and necessary conditions. The text also presents general optimal control problems, optimal control of ordinary differential equations, and different types of functional-integral equations. The book discusses control problems defined by equations in Banach spaces, the convex cost functionals, and the weak necessary conditions for an original minimum. The text illustrates a class of ordinary differential problems with examples, and explains some conflicting control problems with relaxed adverse controls, as well as conflicting control problems with hyper-relaxed adverse controls. The book is intended for mature mathematicians, graduate students in analysis, and practitioners of optimal control whose primary interests and training are in science or engineering.

  • Multivariable Calculus with Linear Algebra and Series

    • 1st Edition
    • William F. Trench + 1 more
    • English
    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.

  • Topics in Multivariate Approximation

    • 1st Edition
    • C. K. Chui + 2 more
    • English
    Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.

  • 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.

  • Stochastic Economics

    Stochastic Processes, Control, and Programming
    • 1st Edition
    • Gerhard Tintner + 1 more
    • English
    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.

  • Stochastic Modelling of Social Processes

    • 1st Edition
    • Andreas Diekmann + 1 more
    • English
    Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians.

  • Pascal-SC

    A Computer Language for Scientific Computation
    • 1st Edition
    • Gerd Bohlender + 2 more
    • Werner Rheinboldt + 1 more
    • English
    Perspectives in Computing, Vol. 17: Pascal-SC: A Computer Language for Scientific Computation focuses on the application of Pascal-SC, a programming language developed as an extension of standard Pascal, in scientific computation. The publication first elaborates on the introduction to Pascal-SC, a review of standard Pascal, and real floating-point arithmetic. Discussions focus on optimal scalar product, standard functions, real expressions, program structure, simple extensions, real floating-point arithmetic, vector and matrix arithmetic, and dynamic arrays. The text then examines functions and operators with arbitrary result types and solving problems with Pascal-SC. The book ponders on strings and text processing, dynamic arrays, and modules. Topics include declaration and use of modules, compatibility of static and dynamic arrays, dynamic result types of functions and operators, strings in procedures, functions, and operators, and declaration of string variables. The publication is a dependable reference for computer science experts and researchers interested in the application of Pascal-SC in scientific computation.

  • Theory and Application of Special Functions

    Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31-April 2, 1975
    • 1st Edition
    • Richard Askey
    • English
    Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.

  • 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.

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