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The unique feature of this compact student's introduction to Mathematica (R) and the Wolfram Language (TM) is that the order of the material closely follows a standard mathematics curriculum. As a result, it provides a brief introduction to those aspects of the Mathematica (R) software program most useful to students. Used as a supplementary text, it will help bridge the gap between Mathematica (R) and the mathematics in the course, and will serve as an excellent tutorial for former students. There have been significant changes to Mathematica (R) since the second edition, and all chapters have now been updated to account for new features in the software, including natural language queries and the vast stores of real-world data that are now integrated through the cloud. This third edition also includes many new exercises and a chapter on 3D printing that showcases the new computational geometry capabilities that will equip readers to print in 3D.
A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe "the entropic arrow of time.
Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems
Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. "Deterministic Operations Research" focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development.
Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports scheduling an the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimization problems, covering topics such as convexity. Farkas' Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm. The final chapters present network optimization and integer programming problems, highlighting various specialized topics including label-correcting algorithms for the shortest path problem, preprocessing and probing in integer programming, lifting of valid inequalities, and branch and cut algorithms.
Concepts and approaches are introduced by outlining examples that demonstrate and motivate theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to understand and encourages readers to understand how to think about the problem, not just what to think. Relevant historical summaries can be found throughout the book, and each chapter is designed as the continuation of the "story" of how to both model and solve optimization problems by using the specific problems-linear and integer programs-as guides. The book's various examples are accompanied by the appropriate models and calculations, and a related Web site features these models along with Maple(TM) and MATLAB(R) content for the discussed calculations.
Thoroughly class-tested to ensure a straightforward, hands-on approach, "Deterministic Operations Research" is an excellent book for operations research of linear optimization courses at the upper-undergraduate and graduate levels. It also serves as an insightful reference for individuals working in the fields of mathematics, engineering, computer science, and operations research who use and design algorithms to solve problem in their everyday work.
An essential introduction to the analysis and verification of control system software The verification of control system software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive. The failure of controller software can cost people their lives. In this authoritative and accessible book, Pierre-Lo c Garoche provides control engineers and computer scientists with an indispensable introduction to the formal techniques for analyzing and verifying this important class of software. Too often, control engineers are unaware of the issues surrounding the verification of software, while computer scientists tend to be unfamiliar with the specificities of controller software. Garoche provides a unified approach that is geared to graduate students in both fields, covering formal verification methods as well as the design and verification of controllers. He presents a wealth of new verification techniques for performing exhaustive analysis of controller software. These include new means to compute nonlinear invariants, the use of convex optimization tools, and methods for dealing with numerical imprecisions such as floating point computations occurring in the analyzed software. As the autonomy of critical systems continues to increase "as evidenced by autonomous cars, drones, and satellites and landers "the numerical functions in these systems are growing ever more advanced. The techniques presented here are essential to support the formal analysis of the controller software being used in these new and emerging technologies.
ELEMENTARY LINEAR ALGEBRA, 8E, INTERNATIONAL METRIC EDITION's clear, careful, and concise presentation of material helps you fully understand how mathematics works. The author balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. To engage you in the material, a new design highlights the relevance of the mathematics and makes the book easier to read. Data and applications reflect current statistics and examples, demonstrating the link between theory and practice. The companion website LarsonLinearAlgebra.com offers free access to multiple study tools and resources. CalcChat.com offers free step-by-step solutions to the odd-numbered exercises in the text.
The 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates how they can be applied by using several simplified but practical problems from widely different contexts. Suggested formulations and solutions are given together with some computational experience to give the reader a feel for the computational difficulty of solving that particular type of model. Furthermore, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpreting of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. In this article, H.P. Williams explains his original motivation and objectives in writing the book, how it has been modified and updated over the years, what is new in this edition and why it has maintained its relevance and popularity over the years: http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html
Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models. Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition. The first introduction to the subject written especially for economists Includes programming examples Features numerous exercises throughout Ideal for students and researchers alike
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations.
This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the authorís coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians.
Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models. Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition. * The first introduction to the subject written especially for economists* Includes programming examples* Features numerous exercises throughout* Ideal for students and researchers alike
Linear programming (LP), as a specific case of mathematical programming, has been widely encountered in a broad class of scientific disciplines and engineering applications. In view of its fundamental role, the solution of LP has been investigated extensively for the past decades. Due to the parallel-distributed processing nature and circuit-implementation convenience, the neurodynamic solvers based on recurrent neural network (RNN) have been regarded as powerful alternatives to online computation. This book discusses how linear programming is used to plan and schedule the workforce in an emergency room; the neurodynamic solvers, robotic applications, and solution non-uniqueness of linear programming; the mathematical equivalence of simple recourse and chance constraints in linear stochastic programming; and provides a decomposable linear programming model for energy supply chains.
The authoritative guide to modeling and solving complex problems with linear programming--extensively revised, expanded, and updated
The only book to treat both linear programming techniques and network flows under one cover, "Linear Programming and Network Flows, Fourth Edition" has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics.
The book begins with basic results on linear algebra and convex analysis, and a geometrically motivated study of the structure of polyhedral sets is provided. Subsequent chapters include coverage of cycling in the simplex method, interior point methods, and sensitivity and parametric analysis. Newly added topics in the "Fourth Edition" include:
The cycling phenomenon in linear programming and the geometry of cycling
Duality relationships with cycling
Elaboration on stable factorizations and implementation strategies
Stabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods
Line search and dual ascent ideas for the out-of-kilter algorithm
Heap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems
The authors present concepts and techniques that are illustrated by numerical examples along with insights complete with detailed mathematical analysis and justification. An emphasis is placed on providing geometric viewpoints and economic interpretations as well as strengthening the understanding of the fundamental ideas. Each chapter is accompanied by "Notes" and "References" sections that provide historical developments in addition to current and future trends. Updated exercises allow readers to test their comprehension of the presented material, and extensive references provide resources for further study.
"Linear Programming and Network Flows, Fourth Edition" is an excellent book for linear programming and network flow courses at the upper-undergraduate and graduate levels. It is also a valuable resource for applied scientists who would like to refresh their understanding of linear programming and network flow techniques.
Generalized linear models (GLMs) extend linear regression to models with a non-Gaussian, or even discrete, response. GLM theory is predicated on the exponential family of distributions-a class so rich that it includes the commonly used logit, probit, and Poisson models. Although one can fit these models in Stata by using specialized commands (for example, logit for logit models), fitting them as GLMs with Stata's glm command offers some advantages. For example, model diagnostics may be calculated and interpreted similarly regardless of the assumed distribution. This text thoroughly covers GLMs, both theoretically and computationally, with an emphasis on Stata. The theory consists of showing how the various GLMs are special cases of the exponential family, showing general properties of this family of distributions, and showing the derivation of maximum likelihood (ML) estimators and standard errors. Hardin and Hilbe show how iteratively reweighted least squares, another method of parameter estimation, are a consequence of ML estimation using Fisher scoring.
This monograph is aimed at presenting smooth and unified generalized fractional programming (or a program with a finite number of constraints). Under the current interdisciplinary computer-oriented research environment, these programs are among the most rapidly expanding research areas in terms of its multi-facet applications and empowerment for real world problems that can be handled by transforming them into generalized fractional programming problems. Problems of this type have been applied for the modeling and analysis of a wide range of theoretical as well as concrete, real world, practical problems. More specifically, generalized fractional programming concepts and techniques have found relevance and worldwide applications in approximation theory, statistics, game theory, engineering design (earthquake-resistant design of structures, design of control systems, digital filters, electronic circuits, etc.), boundary value problems, defect minimization for operator equations, geometry, random graphs, graphs related to Newton flows, wavelet analysis, reliability testing, environmental protection planning, decision making under uncertainty, geometric programming, disjunctive programming, optimal control problems, robotics, and continuum mechanics, among others. It is highly probable that among all industries, especially for the automobile industry, robots are about to revolutionize the assembly plants forever. That would change the face of other industries toward rapid technical innovation as well. The main focus of this monograph is to empower graduate students, faculty and other research enthusiasts for more accelerated research advances with significant applications in the interdisciplinary sense without borders. The generalized fractional programming problems have a wide range of real-world problems, which can be transformed in some sort of a generalized fractional programming problem. Consider fractional programs that arise from management decision science; by analyzing system efficiency in an economical sense, it is equivalent to maximizing system efficiency leading to fractional programs with occurring objectives: Maximizing productivity; Maximizing return on investment; Maximizing return/ risk; Minimizing cost/time; Minimizing output/input. The authors envision that this monograph will uniquely present the interdisciplinary research for the global scientific community (including graduate students, faculty, and general readers). Furthermore, some of the new concepts can be applied to duality theorems based on the use of a new class of multi-time, multi-objective, variational problems as well.
This self-contained book provides the reader with a comprehensive presentation of recent investigations on operator theory over non-Archimedean Banach and Hilbert spaces. This includes, non-archimedean valued fields, bounded and unbounded linear operators, bilinear forms, functions of linear operators and one-paramter families of bounded linear operators on free branch spaces.
Clear and comprehensive, this volume introduces theoretical,
computational, and applied concepts and is useful both as text and
as a reference book. Considerations of theoretical and
computational methods include the general linear programming
problem, the simplex computational procedure, the revised simplex
method, more. Examples and exercises with selected answers appear
in every chapter. 1995 edition.
The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. The book is suitable for a one semester course in linear algebra that can be used in a variety of contexts. The presentation of the material combines definitions and proofs with an emphasis on computational applications, providing examples that illustrate the use of software packages such as Mathematica(R), Maple(R), and Sage. Features: - Introduces the fundamental concepts of linear algebra and applies the theorems in computation-oriented applications - Presents a brief introduction of some aspects of abstract algebra that relate directly to linear algebra, such as groups, rings, modules, fields and polynomials over fields.
Control Theory for Linear Systems deals with the mathematical theory of feedback control of linear systems. It treats a wide range of control synthesis problems for linear state space systems with inputs and outputs. The book provides a treatment of these problems using state space methods, often with a geometric flavour. Its subject matter ranges from controllability and observability, stabilization, disturbance decoupling, and tracking and regulation, to linear quadratic regulation, H2 and H-infinity control, and robust stabilization. Each chapter of the book contains a series of exercises, intended to increase the reader's understanding of the material. Often, these exercises generalize and extend the material treated in the regular text.
This book aims to illustrate with practical examples the applications of linear optimization techniques. It is written in simple and easy to understand language and has put together a useful and comprehensive set of worked examples based on real life problems.
A thorough and highly accessible resource for analysts in a broad range of social sciences.
Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award-winning educator Ronald E. Miller provides detailed coverage of both classical, calculus-based approaches and newer, computer-based iterative methods.
Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to discuss applications, including iterative methods for root-finding and for unconstrained maximization, approaches to the inequality constrained linear programming problem, and the complexities of inequality constrained maximization and minimization in nonlinear problems. Other important features include:
With special emphasis on questions most frequently asked by those encountering this material for the first time, Optimization: Foundations and Applications is an extremely useful resource for professionals in such areas as mathematics, engineering, economics and business, regional science, geography, sociology, political science, management and decision sciences, public policy analysis, and numerous other social sciences.
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