Based on many years of applied research, modeling and educating future decision makers, the authors have selected the critical set of mathematical modeling skills for decision analysis to include in this book. The book focuses on the model formulation and modeling building skills, as well as the technology to support decision analysis. The authors cover many of the main techniques that have been incorporated into their three-course sequence in mathematical modeling for decision making in the Department of Defense Analysis at the Naval Postgraduate School. The primary objective of this book is illustrative in nature. It begins with an introduction to mathematical modeling and a process for formally thinking about difficult problems, illustrating many scenarios and illustrative examples. The book incorporates the necessary mathematical foundations for solving these problems with military applications and related military processes to reinforce the applied nature of the mathematical modeling process.

This volume is proceedings of the international conference of the Parallel Computational Fluid Dynamics 2002. In the volume, up-to-date information about numerical simulations of flows using parallel computers is given by leading researchers in this field. Special topics are "Grid Computing" and "Earth Simulator." Grid computing is now the most exciting topic in computer science. An invited paper on grid computing is presented in the volume. The Earth-Simulator is now the fastest computer in the world. Papers on flow-simulations using the Earth-Simulator are also included, as well as a thirty-two page special tutorial article on numerical optimization.

Parallel CFD 2000, the Twelfth in an International series of meetings featuring computational fluid dynamics research on parallel computers, was held May 22-25, 2000 in Trondheim, Norway.
Following the trend of the past conferences, areas such as numerical schemes and algorithms, tools and environments, load balancing, as well as interdisciplinary topics and various kinds of industrial applications were all well represented in the work presented. In addition, for the first time in the Parallel CFD conference series, the organizing committee chose to draw special attention to certain subject areas by organizing a number of special sessions.
We feel the emphasis of the papers presented at the conference reflect the direction of the research within parallel CFD at the beginning of the new millennium. It seems to be a clear tendency towards increased industrial exploitation of parallel CFD. Several presentations also demonstrated how new insight is being achieved from complex simulations, and how powerful parallel computers now make it possible to use CFD within a broader interdisciplinary setting.
Obviously, successful application of parallel CFD still rests on the underlying fundamental principles. Therefore, numerical algorithms, development tools, and parallelization techniques are still as important as when parallel CFD was in is infancy. Furthermore, the novel concepts of affordable parallel computing as well as metacomputing show that exciting developments are still taking place.
As is often pointed out however, the real power of parallel CFD comes from the combination of all the disciplines involved: Physics, mathematics, and computer science. This is probably one of the principal reasons for the continued popularity of the Parallel CFD Conferences series, as well as the inspiration behind much of the excellent work carried out on the subject. We hope that the papers in this book, both on an individual basis and as a whole, will contribute to that inspiration. Further details of Parallel CFD'99, as well as other conferences in this series, are available at http: //www.parcfd.org

ParCFD 2001, the thirteenth international conference on Parallel Computational Fluid Dynamics took place in Egmond aan Zee, the Netherlands, from May 21-23, 2001. The specialized, high-level ParCFD conferences are organized yearly on traveling locations all over the world. A strong back-up is given by the central organization located in the USA http: //www.parcfd.org.

These proceedings of ParCFD 2001 represent 70% of the oral lectures presented at the meeting. All published papers were subjected to a refereeing process, which resulted in a uniformly high quality.

The papers cover not only the traditional areas of the ParCFD conferences, e.g. numerical schemes and algorithms, tools and environments, interdisciplinary topics, industrial applications, but, following local interests, also environmental and medical issues. These proceedings present an up-to-date overview of the state of the art in parallel computational fluid dynamics.

Bias analysis quantifies the influence of systematic error on an epidemiology study's estimate of association. The fundamental methods of bias analysis in epi- miology have been well described for decades, yet are seldom applied in published presentations of epidemiologic research. More recent advances in bias analysis, such as probabilistic bias analysis, appear even more rarely. We suspect that there are both supply-side and demand-side explanations for the scarcity of bias analysis. On the demand side, journal reviewers and editors seldom request that authors address systematic error aside from listing them as limitations of their particular study. This listing is often accompanied by explanations for why the limitations should not pose much concern. On the supply side, methods for bias analysis receive little attention in most epidemiology curriculums, are often scattered throughout textbooks or absent from them altogether, and cannot be implemented easily using standard statistical computing software. Our objective in this text is to reduce these supply-side barriers, with the hope that demand for quantitative bias analysis will follow.

This textbook and guide focuses on methodologies for bias analysis in epidemiology and public health, not only providing updates to the first edition but also further developing methods and adding new advanced methods. As computational power available to analysts has improved and epidemiologic problems have become more advanced, missing data, Bayes, and empirical methods have become more commonly used. This new edition features updated examples throughout and adds coverage addressing: Measurement error pertaining to continuous and polytomous variables Methods surrounding person-time (rate) data Bias analysis using missing data, empirical (likelihood), and Bayes methods A unique feature of this revision is its section on best practices for implementing, presenting, and interpreting bias analyses. Pedagogically, the text guides students and professionals through the planning stages of bias analysis, including the design of validation studies and the collection of validity data from other sources. Three chapters present methods for corrections to address selection bias, uncontrolled confounding, and measurement errors, and subsequent sections extend these methods to probabilistic bias analysis, missing data methods, likelihood-based approaches, Bayesian methods, and best practices.

Advanced Problem Solving Using Maple (TM): Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. Scenarios are developed within the scope of the problem-solving process. The text focuses on discrete dynamical systems, optimization techniques, single-variable unconstrained optimization and applied problems, and numerical search methods. Additional coverage includes multivariable unconstrained and constrained techniques. Linear algebra techniques to model and solve problems such as the Leontief model, and advanced regression techniques including nonlinear, logistics, and Poisson are covered. Game theory, the Nash equilibrium, and Nash arbitration are also included. Features: The text's case studies and student projects involve students with real-world problem solving Focuses on numerical solution techniques in dynamical systems, optimization, and numerical analysis The numerical procedures discussed in the text are algorithmic and iterative Maple is utilized throughout the text as a tool for computation and analysis All algorithms are provided with step-by-step formats About the Authors: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his PhD at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles. William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP's Math Contest in Modeling (MCM).

Mathematical modeling is a powerful craft that requires practice. The more practice the better one will become in executing the art. The authors wrote this book to develop the craft of mathematical modeling and to foster a desire for lifelong learning, habits of mind and develop competent and confident problem solvers and decision makers for the 21st century. This book offers a problem-solving approach. The authors introduce a problem to help motivate the learning of a particular mathematical modeling topic. The problem provides the issue or what is needed to solve using an appropriate modeling technique. Then principles are applied to the problem and present the steps in obtaining an appropriate model to solve the problem. Modeling Change and Uncertainty: Covers both linear and nonlinear models of discrete dynamical systems. Introduces statistics and probability modeling. Introduces critical statistical concepts to handle univariate and multivariate data. Establishes a foundation in probability modeling. Uses ordinary differential equations (ODEs) to develop a more robust solution to problems. Uses linear programming and machine learning to support decision making. Introduces the reality of uncertainty and randomness that is all around us. Discusses the use of linear programing to solve common problems in modern industry. Discusses he power and limitations of simulations. Introduces the methods and formulas used in businesses and financial organizations. Introduces valuable techniques using Excel, MAPLE, and R. Mathematical modeling offers a framework for decision makers in all fields. This framework consists of four key components: the formulation process, the solution process, interpretation of the solution in the context of the actual problem, and sensitivity analysis. Modeling Change and Uncertainty will be of interest to mathematics departments offering advanced mathematical modeling courses focused on decision making or discrete mathematical modeling and by undergraduate, graduate students and practitioners looking for an opportunity to develop, practice, and apply the craft of mathematical modeling. Table of Contents 1. Perfect Partners: Combining Models of Change and Uncertainty with Technology 2. Modeling Change: Discrete Dynamical Systems (DDS) and Modeling Systems of DDS 3. Statistical and Probabilistic Models 4. Modeling with Probability 5. Differential Equations 6. Forecasting with Linear Programming and Machine Learning 7. Stochastic Models and Markov Chains 8. Linear Programming 9. Simulation of Queueing Models 10. Modeling of Financial Analysis 11. Reliability Models 12. Machine Learning and Unconstrained Optimal Process Dr. William P. Fox is currently a visiting professor of Computational Operations Research at the College of William and Mary. He is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School and teaches a three-course sequence in mathematical modeling for decision making. He received his Ph.D. in Industrial Engineering from Clemson University. He has taught at the United States Military Academy for twelve years until retiring and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including twenty plus books and one hundred and fifty journal articles. Colonel (R) Robert E. Burks, Jr., Ph.D. is an Associate Professor in the Defense Analysis Department of the Naval Postgraduate School (NPS) and the Director of the NPS' Wargaming Center. He holds a Ph.D. in Operations Research from the Air Force Institute of Technology. He is a retired logistics Army Colonel with more than thirty years of military experience in leadership, advanced analytics, decision modeling, and logistics operations who served as an Army Operations Research analyst at the Naval Postgraduate School, TRADOC Analysis Center, United States Military Academy, and the United States Army Recruiting Command. Other book by William P. Fox and Robert E. Burks: Advanced Mathematical Modeling with Technology, 2021, CRC Press. Other books by William P. Fox from CRC Press: Mathematical Modeling in the Age of the Pandemic, 2021, CRC Press. Advanced Problem Solving Using Maple: Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis (w/William Bauldry), 2020, CRC Press. Mathematical Modeling with Excel (w/Brian Albright), 2020, CRC Press. Nonlinear Optimization: Models and Applications, 2020, CRC Press. Advanced Problem Solving with Maple: A First Course (w/William Bauldry), 2019. CRC Press. Mathematical Modeling for Business Analytics, 2018, CRC Press.

One cannot watch or read about the news these days without hearing about the models for COVID-19 or the testing that must occur to approve vaccines or treatments for the disease. The purpose of Mathematical Modeling in the Age of a Pandemic is to shed some light on the meaning and interpretations of many of the types of models that are or might be used in the presentation of analysis. Understanding the concepts presented is essential in the entire modeling process of a pandemic. From the virus itself and its infectious rates and deaths rates to explain the process for testing a vaccine or eventually a cure, the author builds, presents, and shows model testing. This book is an attempt, based on available data, to add some validity to the models developed and used, showing how close to reality the models are to predicting "results" from previous pandemics such as the Spanish flu in 1918 and more recently the Hong Kong flu. Then the author applies those same models to Italy, New York City, and the United States as a whole. Modeling is a process. It is essential to understand that there are many assumptions that go into the modeling of each type of model. The assumptions influence the interpretation of the results. Regardless of the modeling approach the results generally indicate approximately the same results. This book reveals how these interesting results are obtained.

Mathematical modeling is both a skill and an art and must be practiced in order to maintain and enhance the ability to use those skills. Though the topics covered in this book are the typical topics of most mathematical modeling courses, this book is best used for individuals or groups who have already taken an introductory mathematical modeling course. Advanced Mathematical Modeling with Technology will be of interest to instructors and students offering courses focused on discrete modeling or modeling for decision making. Each chapter begins with a problem to motivate the reader. The problem tells "what" the issue is or problem that needs to be solved. In each chapter, the authors apply the principles of mathematical modeling to that problem and present the steps in obtaining a model. The key focus is the mathematical model and the technology is presented as a method to solve that model or perform sensitivity analysis. We have selected , where applicable to the content because of their wide accessibility. The authors utilize technology to build, compute, or implement the model and then analyze the it. Features: MAPLE (c), Excel (c), and R (c) to support the mathematical modeling process. Excel templates, macros, and programs are available upon request from authors. Maple templates and example solution are also available. Includes coverage of mathematical programming. The power and limitations of simulations is covered. Introduces multi-attribute decision making (MADM) and game theory for solving problems. The book provides an overview to the decision maker of the wide range of applications of quantitative approaches to aid in the decision making process, and present a framework for decision making. Table of Contents 1. Perfect Partners: Mathematical Modeling and Technology 2. Review of Modeling with Discrete Dynamical Systems and Modeling Systems of DDS 3. Modeling with Differential Equations 4. Modeling System of Ordinary Differential Equation 5. Regression and Advanced Regression Methods and Models 6. Linear, Integer and Mixed Integer Programming 7. Nonlinear Optimization Methods 8. Multivariable Optimization 9. Simulation Models 10. Modeling Decision Making with Multi-Attribute Decision Modeling with Technology 11. Modeling with Game Theory 12. Appendix Using R Index Biographies Dr. William P. Fox is currently a visiting professor of Computational Operations Research at the College of William and Mary. He is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School and teaches a three-course sequence in mathematical modeling for decision making. He received his Ph.D. in Industrial Engineering from Clemson University. He has taught at the United States Military Academy for twelve years until retiring and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including twenty plus books and one hundred and fifty journal articles. Colonel (R) Robert E. Burks, Jr., Ph.D. is an Associate Professor in the Defense Analysis Department of the Naval Postgraduate School (NPS) and the Director of the NPS' Wargaming Center. He holds a Ph.D. in Operations Research form the Air Force Institute of Technology. He is a retired logistics Army Colonel with more than thirty years of military experience in leadership, advanced analytics, decision modeling, and logistics operations who served as an Army Operations Research analyst at the Naval Postgraduate School, TRADOC Analysis Center, United States Military Academy, and the United States Army Recruiting Command.

One cannot watch or read about the news these days without hearing about the models for COVID-19 or the testing that must occur to approve vaccines or treatments for the disease. The purpose of Mathematical Modeling in the Age of a Pandemic is to shed some light on the meaning and interpretations of many of the types of models that are or might be used in the presentation of analysis. Understanding the concepts presented is essential in the entire modeling process of a pandemic. From the virus itself and its infectious rates and deaths rates to explain the process for testing a vaccine or eventually a cure, the author builds, presents, and shows model testing. This book is an attempt, based on available data, to add some validity to the models developed and used, showing how close to reality the models are to predicting "results" from previous pandemics such as the Spanish flu in 1918 and more recently the Hong Kong flu. Then the author applies those same models to Italy, New York City, and the United States as a whole. Modeling is a process. It is essential to understand that there are many assumptions that go into the modeling of each type of model. The assumptions influence the interpretation of the results. Regardless of the modeling approach the results generally indicate approximately the same results. This book reveals how these interesting results are obtained.

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB(R), and Maple(TM) to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB (R), and Maple (TM) to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

Problem Solving is essential to solve real-world problems. Advanced Problem Solving with Maple: A First Course applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. It is intended for a course introducing students to mathematical topics they will revisit within their further studies. The authors present mathematical modeling and problem-solving topics using Maple as the computer algebra system for mathematical explorations, as well as obtaining plots that help readers perform analyses. The book presents cogent applications that demonstrate an effective use of Maple, provide discussions of the results obtained using Maple, and stimulate thought and analysis of additional applications. Highlights: The book's real-world case studies prepare the student for modeling applications Bridges the study of topics and applications to various fields of mathematics, science, and engineering Features a flexible format and tiered approach offers courses for students at various levels The book can be used for students with only algebra or calculus behind them About the authors: Dr. William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his Ph.D. at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles. William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP's Math Contest in Modeling (MCM). *Please note that the Maple package, "PSM", is now on the public area of the Maple Cloud. To access it: * From the web: 1. Go to the website https://maple.cloud 2. Click on "packages" in the left navigation pane 3. Click on "PSM" in the list of packages. 4. Click the "Download" button to capture the package. * From Maple: 1. Click on the Maple Cloud icon (far right in the Maple window toolbar). Or click on the Maple Cloud button on Maple's Start page to go to the website. 2. Click on the "packages" in the navigation pane 3. Click on "PSM" in the list of packages. The package then downloads into Maple directly.

Sorghum is one of the world's major cereals, cultivated in the semi-arid tropics for a growing range of uses. Like other crops it faces the need to meet rising demand whilst reducing its environmental impact and adapting to the challenges of climate change. This volume summarises the wealth of research addressing these challenges. Part 1 reviews the chemistry of sorghum and its physiology, before discussing its use as a food grain, in feed and as a forage and energy crop. The second part of the book discusses ways of improving cultivation in regions such as South America, Asia and Africa. With its distinguished editor and international team of expert authors, this will be a standard work for cereal scientists, sorghum breeders and growers as well as government and non-government agencies supporting sorghum cultivation. It is accompanied by a companion volume which reviews genetics, breeding and production techniques.

This text presents a wide variety of common types of models found in other mathematical modeling texts, as well as some new types. However, the models are presented in a very unique format. A typical section begins with a general description of the scenario being modeled. The model is then built using the appropriate mathematical tools. Then it is implemented and analyzed in Excel via step-by-step instructions. In the exercises, we ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios.

This book contains the papers presented at the Parallel Computational Fluid Dynamics 1998 Conference.

The book is focused on new developments and applications of parallel technology. Key topics are introduced through contributed papers and invited lectures. These include typical algorithmic developments, such as: distributed computing, domain decomposition and parallel algorithm. Some of the papers address the evaluations of software and machine performance and software tool environments. The application of parallel computers to complex fluid dynamics problems are also conveyed through sessions such as DNS/LES, combustion and reacting flows, industrial applications, water resources and environmental flows.

The editors believe this book will provide many researchers, much beyond those contributing to this volume, with fresh information and reference.

This text presents a wide variety of common types of models found in other mathematical modeling texts, as well as some new types. However, the models are presented in a very unique format. A typical section begins with a general description of the scenario being modeled. The model is then built using the appropriate mathematical tools. Then it is implemented and analyzed in Excel via step-by-step instructions. In the exercises, we ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios.

Advanced Problem Solving Using Maple (TM): Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. Scenarios are developed within the scope of the problem-solving process. The text focuses on discrete dynamical systems, optimization techniques, single-variable unconstrained optimization and applied problems, and numerical search methods. Additional coverage includes multivariable unconstrained and constrained techniques. Linear algebra techniques to model and solve problems such as the Leontief model, and advanced regression techniques including nonlinear, logistics, and Poisson are covered. Game theory, the Nash equilibrium, and Nash arbitration are also included. Features: The text's case studies and student projects involve students with real-world problem solving Focuses on numerical solution techniques in dynamical systems, optimization, and numerical analysis The numerical procedures discussed in the text are algorithmic and iterative Maple is utilized throughout the text as a tool for computation and analysis All algorithms are provided with step-by-step formats About the Authors: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his PhD at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles. William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP's Math Contest in Modeling (MCM).

Problem Solving is essential to solve real-world problems. Advanced Problem Solving with Maple: A First Course applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. It is intended for a course introducing students to mathematical topics they will revisit within their further studies. The authors present mathematical modeling and problem-solving topics using Maple as the computer algebra system for mathematical explorations, as well as obtaining plots that help readers perform analyses. The book presents cogent applications that demonstrate an effective use of Maple, provide discussions of the results obtained using Maple, and stimulate thought and analysis of additional applications. Highlights: The book's real-world case studies prepare the student for modeling applications Bridges the study of topics and applications to various fields of mathematics, science, and engineering Features a flexible format and tiered approach offers courses for students at various levels The book can be used for students with only algebra or calculus behind them About the authors: Dr. William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his Ph.D. at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles. William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP's Math Contest in Modeling (MCM). *Please note that the Maple package, "PSM", is now on the public area of the Maple Cloud. To access it: * From the web: 1. Go to the website https://maple.cloud 2. Click on "packages" in the left navigation pane 3. Click on "PSM" in the list of packages. 4. Click the "Download" button to capture the package. * From Maple: 1. Click on the Maple Cloud icon (far right in the Maple window toolbar). Or click on the Maple Cloud button on Maple's Start page to go to the website. 2. Click on the "packages" in the navigation pane 3. Click on "PSM" in the list of packages. The package then downloads into Maple directly.

Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.

This collection reviews advances in research on improving barley cultivation across the value chain. Part 1 reviews advances in understanding barley physiology in such areas as plant growth, grain development and plant response to abiotic stress. Chapters also review current developments in exploiting genetic diversity and mapping the barley genome. Building on this foundation, the second part of the book summarises advances in breeding with chapters on breeding trial design as well as advances in molecular breeding techniques such as genome wide association studies (GWAS) and targeted induced lesions in genomes (TILLING). Part 3 looks further along the value chain at ways of optimising cultivation practices. There are chapters on post-harvest storage as well as fungal diseases, weeds and integrated methods for their management. The final part of the book assesses current developments in optimising barley for particular end uses such as malting, brewing and animal feed as well as current research on the nutraceutical properties of barley.

examines engineering examples and applications, while also including social sciences and more examples. presents a course can be tailored for students at all levels and background. explains projects and labs to instructors and students to make the course more interesting for both. Features labs that can be used for group work, in class, or for self-directed study.

Based on many years of applied research, modeling and educating future decision makers, the authors have selected the critical set of mathematical modeling skills for decision analysis to include in this book. The book focuses on the model formulation and modeling building skills, as well as the technology to support decision analysis. The authors cover many of the main techniques that have been incorporated into their three-course sequence in mathematical modeling for decision making in the Department of Defense Analysis at the Naval Postgraduate School. The primary objective of this book is illustrative in nature. It begins with an introduction to mathematical modeling and a process for formally thinking about difficult problems, illustrating many scenarios and illustrative examples. The book incorporates the necessary mathematical foundations for solving these problems with military applications and related military processes to reinforce the applied nature of the mathematical modeling process.