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

Nonlinear Programming 4

1st Edition
May 10, 2014
Olvi L. Mangasarian + 2 more
English
eBook
9 7 8 1 4 8 3 2 6 0 1 7 4

Nonlinear Programming, 4 focuses on linear, quadratic, and nonlinear programming, unconstrained minimization, nonsmooth and discrete optimization, ellipsoidal methods, linear complementarity problems, and software evaluation. The selection first elaborates on an upper triangular matrix method for quadratic programming, solving quadratic programs by an exact penalty function, and QP-based methods for large-scale nonlinearly constrained optimization. Discussions focus on large-scale linearly constrained optimization, search direction for superbasic variables, finite convergence, basic properties, comparison of three active set methods, and QP-based methods for dense problems. The book then examines an iterative linear programming algorithm based on an augmented Lagrangian and iterative algorithms for singular minimization problems. The publication ponders on the derivation of symmetric positive definite secant updates, preconditioned conjugate gradient methods, and finding the global minimum of a function of one variable using the method of constant signed higher order derivatives. Topics include effects of calculation errors, application to polynomial minimization, using moderate additional storage, updating Cholesky factors, and utilizing sparse second order information. The selection is a valuable source of data for researchers interested in nonlinear programming.

The Theory of Eisenstein Systems

1st Edition
Volume 99
January 6, 1982
M. Scott Osborne + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 4 1 5 9

Elliptic Problem Solvers

1st Edition
May 10, 2014
Martin H. Schultz
English
eBook
9 7 8 1 4 8 3 2 5 9 1 2 3

Elliptic Problem Solvers provides information pertinent to some aspects of the numerical solution of elliptic partial differential equations. This book presents the advances in developing elliptic problem solvers and analyzes their performance. Organized into 40 chapters, this book begins with an overview of the approximate solution of using a standard Galerkin method employing piecewise linear triangular finite elements. This text then defines the types of vector architecture and discusses the variation in performance that can occur on a vector processor as a function of algorithm and implementation. Other chapters consider the implementation of techniques for elliptical problems. This book discusses as well the six techniques for the solution of nonsymmetric linear systems arising from finite difference discretization of the convection-diffusion equation. The final chapter deals with the basic semiconductor device equations. This book is a valuable resource for electrical and computer engineers, scientists, computer programmers, pure mathematicians, and research workers.

Annual Review in Automatic Programming

1st Edition
May 18, 2014
M. I. Halpern
English
eBook
9 7 8 1 4 8 3 1 6 0 4 8 1

Annual Review in Automatic Programming, Volume 9 deals with automatic programming, with emphasis on the programming language ALGOL 68. The book demonstrates the progression in the formal definition of programming languages from ALGOL 60 through to the revised version of ALGOL 68. Other topics range from real-time operating systems and process control languages to data flow analysis, microprocessors, design automation, real-time system specifications, and Fortran real-time programming. After an introduction to the formal definition of ALGOL 68, this volume turns to an operating system which provides for a flexible interface to support a wide spectrum of real-time language facilities. The chapters that follow focus on data flow through the elements of a real time application, the possibilities as well as the problems of future microprocessor applications in real-time systems, and the design goals and main principles of a monitor called SIMON. A language based upon an automaton model is also described, with particular reference to synchronizations between actions and events. In addition, the book presents a pilot study of the possibility to develop an integrated interactive system for computer aided design of control computer systems and considers the industrial real-time BASIC designed for process control. A chapter discussing the unique distributed DDC system developed by Tokyo Gas Company and Hitachi for city gas production plants concludes the book. This book will be of use to students and professionals interested in programming languages.

Introduction to Dynamic Programming

1st Edition
June 6, 2016
Leon Cooper + 1 more
E. Y. Rodin
English
eBook
9 7 8 1 4 8 3 1 3 6 6 2 2

Introduction to Dynamic Programming introduces the reader to dynamic programming and presents the underlying mathematical ideas and results, as well as the application of these ideas to various problem areas. A large number of solved practical problems and computational examples are included to clarify the way dynamic programming is used to solve problems. A consistent notation is applied throughout the text for the expression of quantities such as state variables and decision variables. This monograph consists of 10 chapters and opens with an overview of dynamic programming as a particular approach to optimization, along with the basic components of any mathematical optimization model. The following chapters discuss the application of dynamic programming to variational problems; functional equations and the principle of optimality; reduction of state dimensionality and approximations; and stochastic processes and the calculus of variations. The final chapter looks at several actual applications of dynamic programming to practical problems, such as animal feedlot optimization and optimal scheduling of excess cash investment. This book should be suitable for self-study or for use as a text in a one-semester course on dynamic programming at the senior or first-year, graduate level for students of mathematics, statistics, operations research, economics, business, industrial engineering, or other engineering fields.

Introduction to Dynamic Programming

1st Edition
May 20, 2014
Leon Cooper + 1 more
E. Y. Rodin
English
eBook
9 7 8 1 4 8 3 1 6 1 5 8 7

Introduction to Dynamic Programming provides information pertinent to the fundamental aspects of dynamic programming. This book considers problems that can be quantitatively formulated and deals with mathematical models of situations or phenomena that exists in the real world. Organized into 10 chapters, this book begins with an overview of the fundamental components of any mathematical optimization model. This text then presents the details of the application of dynamic programming to variational problems. Other chapters consider the application of dynamic programming to inventory theory, Markov processes, chemical engineering, optimal control theory, calculus of variations, and economics. This book discusses as well the approach to problem solving that is typical of dynamic programming. The final chapter deals with a number of actual applications of dynamic programming to practical problems. This book is a valuable resource for .graduate level students of mathematics, economics, statistics, business, operations research, industrial engineering, or other engineering fields.

Issues of Organizational Design

1st Edition
May 9, 2014
Børge Obel
English
eBook
9 7 8 1 4 8 3 1 8 9 6 7 3

Issues of Organizational Design: A Mathematical Programming View of Organizations analyzes the view that organizations can be represented satisfactorily by a mathematical programming model and relates it to other theories of organizational behavior. The potential of this approach to organizational analysis is evaluated. Comprised of seven chapters, this book begins with an overview of the three major schools of organizational theory: the classical/structural school, the human relations school, and the contingency school. It then defines what an organization is and outlines the relationship between organizational elements. The example of the two-product firm is used to illustrate the basic model framework, and how coordination, diversification, and incentives can be treated in this framework.Subsequent chapters explore the relationship between the contingency approach and the mathematical programming approach to organizational design; the coordination problem and the process of decision making in a decentralized organization; the decomposition of the organization into a number of smaller units; and types of evaluation and incentive schemes for addressing cheating in a multi-level organization. The book also presents a series of empirical studies where a mathematical programming view of organizations has been assumed before concluding with a discussion on the process of designing organizations. This monograph will be useful for students of organizational design and for practitioners who use models in connection with decision making.

Parametric Statistical Inference

1st Edition
May 20, 2014
Shelemyahu Zacks
V. Lakshmikantham + 1 more
English
eBook
9 7 8 1 4 8 3 1 5 0 4 9 9

Parametric Statistical Inference: Basic Theory and Modern Approaches presents the developments and modern trends in statistical inference to students who do not have advanced mathematical and statistical preparation. The topics discussed in the book are basic and common to many fields of statistical inference and thus serve as a jumping board for in-depth study. The book is organized into eight chapters. Chapter 1 provides an overview of how the theory of statistical inference is presented in subsequent chapters. Chapter 2 briefly discusses statistical distributions and their properties. Chapter 3 is devoted to the problem of sufficient statistics and the information in samples, and Chapter 4 presents some basic results from the theory of testing statistical hypothesis. In Chapter 5, the classical theory of estimation is developed. Chapter 6 discusses the efficiency of estimators and some large sample properties, while Chapter 7 studies the topics on confidence intervals. Finally, Chapter 8 is about decision theoretic and Bayesian approach in testing and estimation. Senior undergraduate and graduate students in statistics and mathematics, and those who have taken an introductory course in probability will highly benefit from this book.

Systems Approaches in Computer Science and Mathematics

1st Edition
May 20, 2014
G.E. Lasker
English
eBook
9 7 8 1 4 8 3 1 4 9 8 1 3

Applied Systems and Cybernetics, Volume V: Systems Approaches in Computer Science and Mathematics covers the proceedings of the International Congress on Applied Systems Research and Cybernetics. This book discusses trends and advances in the application of systems science and cybernetics to various fields. This volume reviews the systems approaches in computer science and mathematics and concentrates on several major areas of systems research in computer science and theoretical and applied mathematics. This book will be of great interest to computer scientists interested in the development of the theories and applications of computer science.

Computational Methods in Nonlinear Structural and Solid Mechanics

1st Edition
May 20, 2014
Ahmed K. Noor + 1 more
English
eBook
9 7 8 1 4 8 3 1 4 5 6 4 8

Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.

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Books in Mathematics

Nonlinear Programming 4

The Theory of Eisenstein Systems

Elliptic Problem Solvers

Annual Review in Automatic Programming

Introduction to Dynamic Programming

Introduction to Dynamic Programming

Issues of Organizational Design

Parametric Statistical Inference

Systems Approaches in Computer Science and Mathematics

Computational Methods in Nonlinear Structural and Solid Mechanics

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