Building And Solving Mathematical Programming Models In Engineering And Science

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Building and Solving Mathematical Programming Models in Engineering and Science

Author : Enrique Castillo
Publisher : Wiley-Interscience
ISBN 13 : 9780471150435
Total Pages : 568 pages
Book Rating : 4.1/5 (54 download)

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Book Synopsis Building and Solving Mathematical Programming Models in Engineering and Science by : Enrique Castillo

Download or read book Building and Solving Mathematical Programming Models in Engineering and Science written by Enrique Castillo and published by Wiley-Interscience. This book was released on 2001-11-01 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamental concepts of mathematical modeling Modeling is one of the most effective, commonly used tools in engineering and the applied sciences. In this book, the authors deal with mathematical programming models both linear and nonlinear and across a wide range of practical applications. Whereas other books concentrate on standard methods of analysis, the authors focus on the power of modeling methods for solving practical problems-clearly showing the connection between physical and mathematical realities-while also describing and exploring the main concepts and tools at work. This highly computational coverage includes: * Discussion and implementation of the GAMS programming system * Unique coverage of compatibility * Illustrative examples that showcase the connection between model and reality * Practical problems covering a wide range of scientific disciplines, as well as hundreds of examples and end-of-chapter exercises * Real-world applications to probability and statistics, electrical engineering, transportation systems, and more Building and Solving Mathematical Programming Models in Engineering and Science is practically suited for use as a professional reference for mathematicians, engineers, and applied or industrial scientists, while also tutorial and illustrative enough for advanced students in mathematics or engineering.

Building and Solving Mathematical Programming Models in Engineering and Science

Author : Enrique Castillo
Publisher : John Wiley & Sons
ISBN 13 : 0471461652
Total Pages : 568 pages
Book Rating : 4.4/5 (714 download)

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Book Synopsis Building and Solving Mathematical Programming Models in Engineering and Science by : Enrique Castillo

Download or read book Building and Solving Mathematical Programming Models in Engineering and Science written by Enrique Castillo and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamental concepts of mathematical modeling Modeling is one of the most effective, commonly used tools in engineering and the applied sciences. In this book, the authors deal with mathematical programming models both linear and nonlinear and across a wide range of practical applications. Whereas other books concentrate on standard methods of analysis, the authors focus on the power of modeling methods for solving practical problems-clearly showing the connection between physical and mathematical realities-while also describing and exploring the main concepts and tools at work. This highly computational coverage includes: * Discussion and implementation of the GAMS programming system * Unique coverage of compatibility * Illustrative examples that showcase the connection between model and reality * Practical problems covering a wide range of scientific disciplines, as well as hundreds of examples and end-of-chapter exercises * Real-world applications to probability and statistics, electrical engineering, transportation systems, and more Building and Solving Mathematical Programming Models in Engineering and Science is practically suited for use as a professional reference for mathematicians, engineers, and applied or industrial scientists, while also tutorial and illustrative enough for advanced students in mathematics or engineering.

Model Building in Mathematical Programming

Author : H. Paul Williams
Publisher : John Wiley & Sons
ISBN 13 : 1118506189
Total Pages : 432 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Model Building in Mathematical Programming by : H. Paul Williams

Download or read book Model Building in Mathematical Programming written by H. Paul Williams and published by John Wiley & Sons. This book was released on 2013-01-18 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 5th edition of Model Building in Mathematical Programmingdiscusses the general principles of model building in mathematicalprogramming and demonstrates how they can be applied by usingseveral simplified but practical problems from widely differentcontexts. Suggested formulations and solutions are given togetherwith some computational experience to give the reader a feel forthe computational difficulty of solving that particular type ofmodel. Furthermore, this book illustrates the scope and limitationsof mathematical programming, and shows how it can be applied toreal situations. By emphasizing the importance of the building andinterpreting of models rather than the solution process, the authorattempts to fill a gap left by the many works which concentrate onthe algorithmic side of the subject. In this article, H.P. Williams explains his originalmotivation and objectives in writing the book, how it has beenmodified and updated over the years, what is new in this editionand why it has maintained its relevance and popularity over theyears: ahref="http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html"http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html/a

Building and Solving Mathematical Programming Models

Author : José Manuel García Sánchez
Publisher : Springer Nature
ISBN 13 : 3030976262
Total Pages : 408 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Building and Solving Mathematical Programming Models by : José Manuel García Sánchez

Download or read book Building and Solving Mathematical Programming Models written by José Manuel García Sánchez and published by Springer Nature. This book was released on 2022-05-13 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation. The problems are divided into 5 difficulty levels. Problems in the first few levels are focused on learning the model construction methodology, while those in the last level include complex optimization environments. For each problem solution, the specific steps are illustrated, promoting reader comprehension. In addition, all the models are implemented in an optimization library, LINGO, their solutions have been analyzed and their correct construction has been verified. The book also includes a simple guide to implementing models in LINGO in a straightforward manner and in any input data format (text files, spreadsheets or databases). As an ideal companion to the author’s previously published work Modelling in Mathematical Programming, the book is intended as a basic tool for students of operations research, and for researchers in any advanced area involving mathematical programming.

Model Building in Mathematical Programming

Author : H. Paul Williams
Publisher : John Wiley & Sons
ISBN 13 : 9781118443330
Total Pages : 0 pages
Book Rating : 4.4/5 (433 download)

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Book Synopsis Model Building in Mathematical Programming by : H. Paul Williams

Download or read book Model Building in Mathematical Programming written by H. Paul Williams and published by John Wiley & Sons. This book was released on 2013-03-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Methods and Models in Mathematical Programming

Author : S. A. MirHassani
Publisher : Springer Nature
ISBN 13 : 3030270459
Total Pages : 389 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Methods and Models in Mathematical Programming by : S. A. MirHassani

Download or read book Methods and Models in Mathematical Programming written by S. A. MirHassani and published by Springer Nature. This book was released on 2019-12-09 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be able to generalize and reuse concepts in other problems by relying on mathematical logic.Undergraduate and postgraduate students of different academic disciplines would find this book a suitable option preparing them for jobs and research fields requiring modeling techniques. Furthermore, this book can be used as a reference book for experts and practitioners requiring advanced skills of model building in their jobs.

Applied Integer Programming

Author : Der-San Chen
Publisher : John Wiley & Sons
ISBN 13 : 1118210026
Total Pages : 489 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Applied Integer Programming by : Der-San Chen

Download or read book Applied Integer Programming written by Der-San Chen and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems. Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book. Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems.

Decomposition Techniques in Mathematical Programming

Author : Antonio J. Conejo
Publisher : Springer Science & Business Media
ISBN 13 : 3540276866
Total Pages : 542 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Decomposition Techniques in Mathematical Programming by : Antonio J. Conejo

Download or read book Decomposition Techniques in Mathematical Programming written by Antonio J. Conejo and published by Springer Science & Business Media. This book was released on 2006-04-28 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.

Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology

Author : Neculai Andrei
Publisher : Springer
ISBN 13 : 3319583565
Total Pages : 506 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology by : Neculai Andrei

Download or read book Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology written by Neculai Andrei and published by Springer. This book was released on 2017-12-04 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.

Nonlinear Optimization Applications Using the GAMS Technology

Author : Neculai Andrei
Publisher : Springer Science & Business Media
ISBN 13 : 1461467977
Total Pages : 356 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Nonlinear Optimization Applications Using the GAMS Technology by : Neculai Andrei

Download or read book Nonlinear Optimization Applications Using the GAMS Technology written by Neculai Andrei and published by Springer Science & Business Media. This book was released on 2013-06-22 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a collection of nonlinear optimization applications from the real world, expressed in the General Algebraic Modeling System (GAMS). The concepts are presented so that the reader can quickly modify and update them to represent real-world situations.

Coastal Engineering 2006 - Proceedings Of The 30th International Conference (In 5 Volumes)

Author : Jane Mckee Smith
Publisher : World Scientific
ISBN 13 : 9814475521
Total Pages : 1128 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Coastal Engineering 2006 - Proceedings Of The 30th International Conference (In 5 Volumes) by : Jane Mckee Smith

Download or read book Coastal Engineering 2006 - Proceedings Of The 30th International Conference (In 5 Volumes) written by Jane Mckee Smith and published by World Scientific. This book was released on 2007-04-03 with total page 1128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Proceedings contains 445 papers presented at the 30th International Conference on Coastal Engineering, which was held in San Diego, California, USA, 3-8 September 2006. The Proceedings is divided into five parts: Waves; Swash, Nearshore Currents, and Long Waves; Coastal Management, Risk, and Ecosystem Restoration; Sediment Transport and Morphology; and Coastal Structures. The individual papers cover a broad range of topics including theory, numerical and physical modeling, field measurements, case studies, design, and management. These papers provide engineers, scientists, and planners state-of-the-art information on coastal engineering and coastal processes.

Electric Energy Systems

Author : Antonio Gomez-Exposito
Publisher : CRC Press
ISBN 13 : 1351754491
Total Pages : 716 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis Electric Energy Systems by : Antonio Gomez-Exposito

Download or read book Electric Energy Systems written by Antonio Gomez-Exposito and published by CRC Press. This book was released on 2018-06-14 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electric Energy Systems, Second Edition provides an analysis of electric generation and transmission systems that addresses diverse regulatory issues. It includes fundamental background topics, such as load flow, short circuit analysis, and economic dispatch, as well as advanced topics, such as harmonic load flow, state estimation, voltage and frequency control, electromagnetic transients, etc. The new edition features updated material throughout the text and new sections throughout the chapters. It covers current issues in the industry, including renewable generation with associated control and scheduling problems, HVDC transmission, and use of synchrophasors (PMUs). The text explores more sophisticated protections and the new roles of demand, side management, etc. Written by internationally recognized specialists, the text contains a wide range of worked out examples along with numerous exercises and solutions to enhance understanding of the material. Features Integrates technical and economic analyses of electric energy systems. Covers HVDC transmission. Addresses renewable generation and the associated control and scheduling problems. Analyzes electricity markets, electromagnetic transients, and harmonic load flow. Features new sections and updated material throughout the text. Includes examples and solved problems.

Solving Large-Scale Production Scheduling and Planning in the Process Industries

Author : Georgios M. Kopanos
Publisher : Springer
ISBN 13 : 3030011836
Total Pages : 291 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Solving Large-Scale Production Scheduling and Planning in the Process Industries by : Georgios M. Kopanos

Download or read book Solving Large-Scale Production Scheduling and Planning in the Process Industries written by Georgios M. Kopanos and published by Springer. This book was released on 2018-10-01 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a number of efficient techniques for solving large-scale production scheduling and planning problems in process industries. The main content is supplemented by a wealth of illustrations, while case studies on large-scale industrial applications, ranging from continuous to semicontinuous and batch processes, round out the coverage. The book examines a variety of complex, real-world problems, and demonstrates solutions that are applicable to scenarios and countries around the world. Specifically, these case studies include: • the production planning of the bottling stage of a major brewery at the Cervecería Cuauhtémoc Moctezuma (Heineken Int) in Mexico;• the production scheduling for multi-stage semicontinuous processes at an ice-cream production facility of Unilever in the Netherlands;• the resource-constrained production planning for the yogurt production line at the KRI KRI dairy production facility in Greece; and• the production scheduling for large-scale, multi-stage batch processes at a pharmaceutical batch plant in Germany. In addition, the book includes industrial-inspired case studies of: • the simultaneous planning of production and logistics operations considering multi-site facilities for semicontinuous processes; and• the integrated planning of production and utility systems in process industries under uncertainty. Solving Large-scale Production Scheduling and Planning in the Process Industries offers a valuable reference guide for researchers and decision-makers alike, as it shows readers how to evaluate and improve existing installations, and how to design new ones. It is also well suited as a textbook for advanced courses on production scheduling and planning in industry, as it addresses the optimization of production and logistics operations in real-world process industries.

Algebraic Modeling Systems

Author : Josef Kallrath
Publisher : Springer Science & Business Media
ISBN 13 : 3642235921
Total Pages : 255 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Algebraic Modeling Systems by : Josef Kallrath

Download or read book Algebraic Modeling Systems written by Josef Kallrath and published by Springer Science & Business Media. This book was released on 2012-02-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book Algebraic Modeling Systems – Modeling and Solving Real World Optimization Problems – deals with the aspects of modeling and solving real-world optimization problems in a unique combination. It treats systematically the major algebraic modeling languages (AMLs) and modeling systems (AMLs) used to solve mathematical optimization problems. AMLs helped significantly to increase the usage of mathematical optimization in industry. Therefore it is logical consequence that the GOR (Gesellschaft für Operations Research) Working Group Mathematical Optimization in Real Life had a second meeting devoted to AMLs, which, after 7 years, followed the original 71st Meeting of the GOR (Gesellschaft für Operations Research) Working Group Mathematical Optimization in Real Life which was held under the title Modeling Languages in Mathematical Optimization during April 23–25, 2003 in the German Physics Society Conference Building in Bad Honnef, Germany. While the first meeting resulted in the book Modeling Languages in Mathematical Optimization, this book is an offspring of the 86th Meeting of the GOR working group which was again held in Bad Honnef under the title Modeling Languages in Mathematical Optimization.

Complementarity Modeling in Energy Markets

Author : Steven A. Gabriel
Publisher : Springer Science & Business Media
ISBN 13 : 1441961232
Total Pages : 637 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Complementarity Modeling in Energy Markets by : Steven A. Gabriel

Download or read book Complementarity Modeling in Energy Markets written by Steven A. Gabriel and published by Springer Science & Business Media. This book was released on 2012-07-20 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This addition to the ISOR series introduces complementarity models in a straightforward and approachable manner and uses them to carry out an in-depth analysis of energy markets, including formulation issues and solution techniques. In a nutshell, complementarity models generalize: a. optimization problems via their Karush-Kuhn-Tucker conditions b. on-cooperative games in which each player may be solving a separate but related optimization problem with potentially overall system constraints (e.g., market-clearing conditions) c. conomic and engineering problems that aren’t specifically derived from optimization problems (e.g., spatial price equilibria) d. roblems in which both primal and dual variables (prices) appear in the original formulation (e.g., The National Energy Modeling System (NEMS) or its precursor, PIES). As such, complementarity models are a very general and flexible modeling format. A natural question is why concentrate on energy markets for this complementarity approach? s it turns out, energy or other markets that have game theoretic aspects are best modeled by complementarity problems. The reason is that the traditional perfect competition approach no longer applies due to deregulation and restructuring of these markets and thus the corresponding optimization problems may no longer hold. Also, in some instances it is important in the original model formulation to involve both primal variables (e.g., production) as well as dual variables (e.g., market prices) for public and private sector energy planning. Traditional optimization problems can not directly handle this mixing of primal and dual variables but complementarity models can and this makes them all that more effective for decision-makers.

Mathematical and Computational Modeling

Author : Roderick Melnik
Publisher : John Wiley & Sons
ISBN 13 : 1118853857
Total Pages : 336 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Mathematical and Computational Modeling by : Roderick Melnik

Download or read book Mathematical and Computational Modeling written by Roderick Melnik and published by John Wiley & Sons. This book was released on 2015-05-21 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-the-art achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, industrial, and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.

Advances in Mathematical and Statistical Modeling

Author : Barry C. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 0817646264
Total Pages : 368 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Advances in Mathematical and Statistical Modeling by : Barry C. Arnold

Download or read book Advances in Mathematical and Statistical Modeling written by Barry C. Arnold and published by Springer Science & Business Media. This book was released on 2009-04-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enrique Castillo is a leading figure in several mathematical and engineering fields. Organized to honor Castillo’s significant contributions, this volume is an outgrowth of the "International Conference on Mathematical and Statistical Modeling," and covers recent advances in the field. Applications to safety, reliability and life-testing, financial modeling, quality control, general inference, as well as neural networks and computational techniques are presented.