Advanced Mathematical Modeling with Technology

Abstract

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©, Excel©, and R© 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.