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.
Probability and statistics courses are more popular than ever. Regardless of your major or your profession, you will most likely use concepts from probability and statistics often in your career. The primary goal behind this book is offering the flexibility for instructors to build most undergraduate courses upon it. This book is designed for either a one-semester course in either introductory probability and statistics (not calculus-based) and/or a one-semester course in a calculus-based probability and statistics course. The book focuses on engineering examples and applications, while also including social sciences and more examples. Depending on the chapter flows, a course can be tailored for students at all levels and background. Over many years of teaching this course, the authors created problems based on real data, student projects, and labs. Students have suggested these enhance their experience and learning. The authors hope to share projects and labs with other instructors and students to make the course more interesting for both. R is an excellent platform to use. This book uses R with real data sets. The labs can be used for group work, in class, or for self-directed study. These project labs have been class-tested for many years with good results and encourage students to apply the key concepts and use of technology to analyze and present results.
Advanced Problem Solving Using MapleTM: 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).
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®, and MapleTM 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.
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.
The advanced text covers dynamical systems, single variable and multi-variable optimization, linear algebra, advanced model fitting techniques, game theory, and multi-attribute decision processes"--
What sets Numerical Methods and Analysis with Mathematical Modelling apart are the modelling aspects utilizing numerical analysis (methods) to obtain solutions. The authors cover first the basic numerical analysis methods with simple examples to illustrate the techniques and discuss possible errors. The modelling prospective reveals the practical relevance of the numerical methods in context to real-world problems. At the core of this text are the real-world modelling projects. Chapters are introduced and techniques are discussed with common examples. A modelling scenario is introduced that will be solved with these techniques later in the chapter. Often, the modelling problems require more than one previously covered technique presented in the book. Fundamental exercises to practice the techniques are included. Multiple modelling scenarios per numerical methods illustrate the applications of the techniques introduced. Each chapter has several modelling examples that are solved by the methods described within the chapter. The use of technology is instrumental in numerical analysis and numerical methods. In this text, Maple, Excel, R, and Python are illustrated. The goal is not to teach technology but to illustrate its power and limitations to perform algorithms and reach conclusions. This book fulfills a need in the education of all students who plan to use technology to solve problems whether using physical models or true creative mathematical modeling, like discrete dynamical systems.
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.
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.
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