A First Course in Mathematical Modeling, 5th Edition

Frank R. Giordano, William P. Fox, Steven B. Horton

Copyright 2014
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A First Course in Mathematical Modeling 5th Edition by Frank R. Giordano/William P. Fox/Steven B. Horton

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Overview
Meet the Authors
What's New
Features
Table of Contents
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Overview

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, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling.

Meet the Authors

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Frank R. Giordano

Frank R. Giordano began his teaching career at the United States Military Academy, West Point, New York, where he served for 21 years, including seven years as professor and head of the Department of Mathematical Sciences. He currently is a Professor of Defense Analysis and Operations Research at the Naval Postgraduate School, Monterey, CA. He has served as project director for several major National Science Foundation grants devoted to modeling, including one to initiate a high school modeling contest (the HiMCM). For the past 15 years, he has served as the director of the Mathematical Contest in Modeling. Frank R. Giordano began his teaching career at the United States Military Academy, West Point, New York, where he served for 21 years, including seven years as professor and head of the Department of Mathematical Sciences. He currently is a Professor of Defense Analysis and Operations Research at the Naval Postgraduate School, Monterey, CA. He has served as project director for several major National Science Foundation grants devoted to modeling, including one to initiate a high school modeling contest (the HiMCM). For the past 15 years, he has served as the director of the Mathematical Contest in Modeling.

William P. Fox

William P. Fox is a professor in the Department of Defense Analysis at the Naval Postgraduate School in Monterey, CA. Previously; he was an instructor, assistant professor, associate professor, and professor of operations research while serving in the Department of Mathematical Sciences at the United States Military Academy (USMA) for more than 12 years. He also served as the Chair of Mathematics at Francis Marion University for eight years before coming to the Naval Postgraduate School. Dr. Fox has taught a variety of mathematics courses in his career, and his areas of interest include mathematical modeling, optimization, statistics, and simulations. He holds his undergraduate degree from USMA, a master's degree from the Naval Postgraduate School, and a Ph.D. from Clemson University.

Steven B. Horton

Steven B. Horton is professor of operations research and acting deputy head in the Department of Mathematical Sciences at the United States Military Academy (USMA), West Point. He has taught a variety of mathematics courses at West Point since joining the faculty in 1991. Dr. Horton holds his undergraduate degree from USMA, master's degrees from Georgia Tech and the National Defense University, and a Ph.D. from Georgia Tech.

What's New

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A new chapter on Modeling with Decision Theory including Probability and Expected Value, Decision Trees, and Conditional Probabilities.
A new chapter on Game Theory including sections on Illustrative Modeling Examples and Total Conflict as a Linear Program Model: Pure and Mixed Strategies.
New and revised problems, examples, and projects.
Chapters on Dimensional Analysis and Similitude and Graphs of Functions as Models have been removed from the text, and are available on the companion website for instructors who still want to include this material in their course.

Features

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Offering new chapters on Modeling with Decision Theory and Game Theory.
The fifth edition is packed with scenarios and illustrative examples, enabling students to see theories and models in action.
Exercises and projects give students hands-on experience putting what they have learned into relevant practice.
UMAP Models are included on the website for easy reference and review.
Problems from the COMAP Mathematical Contest in Modeling also are included on the website, giving students experience clarifying, analyzing, and proposing solutions to the same open-ended problems on the rigorous MCM.
Tying in a variety of current tools, technology labs and technology worked examples are available on the web for many technologies, including Excel, Maple, and Mathematica.

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1. Modeling Change.
2. The Modeling Process, Proportionality, and Geometric Similarity.
3. Model Fitting.
4. Experimental Modeling.
5. Simulation Modeling.
6. Discrete Probabilistic Modeling.
7. Optimization of Discrete Models.
8. Modeling with Graph Theory.
9. Modeling with Decision Theory.
10. Game Theory.
11. Modeling with a Differential Equation.
12. Modeling with Systems of Differential Equations.
13. Optimization of Continuous Modeling.
14. Dimensional Analysis and Similitude.
15. Graphs of Functions as Models.
Appendix A: Problems from the Mathematics Contest in Modeling, 1985-2007.
Appendix B: An Elevator Simulation Model.
Appendix C: The Revised Simplex Method.
Appendix D. Brief Review of Integration Techniques.