Synopses & Reviews
This text provides an introduction to the entire 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 a student's problem solving capabilities. 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.
Review
"The approach to modeling is very solid, and corresponds with what I have seen as useful in teaching modeling at all levels for 25 years."
Review
"The examples, projects and exercises are excellent. Very varied and interesting, with a good mix of topics. It is great to be able to pick and choose from among the topics and examples. At the same time there is nothing superfluous about the coverage."
About the Author
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.Maurice D. Weir is professor emeritus at the Naval Postgraduate School. He began his teaching career at Whitman College, and then in 1969 became a professor of mathematics at the Naval Postgraduate School, where he also served as associate provost for instruction. Dr. Weir's research and teaching interests include combat systems modeling and simulation, mathematics education, mathematical modeling, and differential equations. Professor Weir won the Outstanding Civilian Service Medal from the United States Military Academy in 1986 and the Schieffelin Award for Excellence in Teaching at the Naval Postgraduate School in 1983. Professor Weir retired from teaching in 1999 but is still actively engaged in writing mathematics textbooks. He received his M.S. and D.A. degrees from Carnegie-Mellon.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.
Table of Contents
1. MODELING WITH DISCRETE DYNAMICAL SYSTEMS. Modeling Change with Difference Equations. Approximating Change with Difference Equations. Solutions to Dynamical Systems. Systems of Difference Equations. 2. THE MODELING PROCESS, PROPORTIONALITY AND GEOMETRIC SIMILARITY. Mathematical Models. Modeling Using Proportionality. Modeling Using Geometric Similarity. Automobile Gasoline Mileage. Body Weight and Height, Strength and Agility. 3. MODEL FITTING. Fitting Models to Data Graphically. Analytic Methods of Model Fitting. Applying the Least-Squares Criterion. Choosing a Best Model. 4. EXPERIMENTAL MODELING. Harvesting in the Chesapeake Bay and Other One-Term Models. High-Order Polynomial Models. Smoothing: Low-Order Polynomial Models. Cubic Spline Models. 5. SIMULATION MODELING. Simulation Deterministic Behavior: Area under a Curver. Generating Random Numbers. Simulating Probabilistic Behavior. Inventory Model: Gasoline and Consumer Demand. Queuing Models. 6. DISCRETE PROBABILITY MODELING. Probabilistic Modeling With Discrete Systems. Modeling Component and System Reliability. Linear Regression. 7. DISCRETE OPTIMIZATION MODELING LINEAR PROGRAMMING AND NUMERICAL SEARCH METHODS. An Overview of Discrete Optimization Modeling. Linear Programming I: Geometric Solutions. Linear Programming II: Algebraic Solutions. Linear Programming III: The Simplex Method. Linear Programming IV: Sensitivity Analysis. Numerical Search Methods. 8. DIMENSIONAL ANALYSIS AND SIMILITUDE. Dimensions as Products. The Process of Dimensional Analysis. A Damped Pendulum. Examples Illustrating Dimensional Analysis. Similitude. 9. GRAPHS OF FUNCTIONS AS MODELS. An Arms Race. Modeling an Arms Race in Stages. Managing Nonrenewable Resources: The Energy Crisis. Effects of Taxation on the Energy Crisis. A Gasoline Shortage and Taxation. 10. MODELING WITH SYSTEMS OF DIFFERENTIAL EQUATION. Population Growth. Prescribing Drug Dosage. Braking Distance Revisited. Graphical Solutions of Autonomous Differential Equations. Numerical Approximation Methods. 11. MODELING WITH SYSTEMS OF DIFFERENTIAL EQUATIONS. Graphical Solutions of Autonomous Systems of First-Order Differential Equations. A Competitive Hunter Model. A Predator-Prey Model. Two Military Examples. Eulers Method for Systems of Differential Equations. 12. CONTINUOUS OPTIMIZATION MODELING. An Inventory Problem: Minimizing the cost of Delivery and Storage. A Manufacturing Problem: Maximizing Profit in Producing Competing Products. Constrained Continuous Optimization. Managing Renewable Resources: The Fishing Industry. Appendix A: Problems from the Mathematics Contest in Modeling .1985-1996 (also available on accompanying CD). Appendix B: An Algorithm for an Elevator Simulation Model. Appendix C: The Revised Simplex Method.