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E-raamat: Advanced Problem Solving Using Maple: Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis

, (U.S. Naval Post Graduate School)
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Advanced Problem Solving Using Maple: 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 texts 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 COMAPs Math Contest in Modeling (MCM).
Preface ix
1 Introduction to Problem Solving and Maple
1(32)
1.1 Problem Solving
1(2)
1.2 Introduction to Maple
3(2)
1.3 The Structure of Maple
5(2)
1.4 General Introduction to Maple
7(23)
1.5 Maple Training
30(1)
1.6 Maple Applications Center
30(3)
2 Discrete Dynamical Models
33(62)
2.1 Introduction
33(1)
2.2 Modeling with Dynamical Systems
34(3)
2.3 Linear Systems
37(15)
2.4 Equilibrium Values and Long-Term Behavior
52(3)
2.5 A Graphical Approach to Equilibrium Values
55(11)
2.6 Modeling Nonlinear Discrete Dynamical Systems
66(6)
2.7 Systems of Discrete Dynamical Systems
72(8)
2.8 Case Studies: Predator-Prey Model, SIR Model, and Military Models
80(15)
3 Problem Solving with Single-Variable Optimization
95(26)
3.1 Single-Variable Unconstrained Optimization
95(10)
3.2 Numerical Search Techniques with Maple
105(16)
4 Problem Solving with Multivariable Constrained and Unconstrained Optimization
121(84)
4.1 Unconstrained Optimization: Theory
121(12)
4.2 Unconstrained Optimization: Examples
133(12)
4.3 Unconstrained Optimization: Numerical Methods
145(17)
4.4 Constrained Optimization: The Method of Lagrange Multipliers
162(17)
4.5 Constrained Optimization: Kuhn-Tucker Conditions
179(26)
5 Problem Solving with Linear Systems of Equations Using Linear Algebra Techniques
205(30)
5.1 Introduction
205(2)
5.2 Introduction to Systems of Equations
207(5)
5.3 Models with Unique Solutions Using Systems of Linear Equations
212(15)
5.4 Stoichiometric Chemical Balancing and Infinitely Many Solutions
227(8)
6 Review of Regression Models and Advanced Regression Models
235(48)
6.1 Re-Introduction to Regression
236(2)
6.2 Modeling, Correlation, and Regression
238(1)
6.3 Linear, Nonlinear, and Multiple Regression
239(11)
6.4 Advanced Regression Techniques with Examples
250(30)
6.5 Conclusions and Summary
280(3)
7 Problem Solving with Game Theory
283(56)
7.1 Introduction
283(4)
7.2 Background of Game Theory
287(13)
7.3 Examples of Zero-Sum Games
300(23)
7.4 Examples of Partial Conflict Games
323(13)
7.5 Conclusion
336(3)
8 Introduction to Problem Solving with Multi-Attribute Decision Making
339(50)
8.1 Introduction
340(1)
8.2 Data Envelopment Analysis
341(10)
8.3 Simple Additive Weighting
351(9)
8.4 Analytical Hierarchy Process
360(13)
8.5 Technique of Order Preference by Similarity to the Ideal Solution
373(8)
8.6 Methods of Choosing Weights
381(8)
Index 389
Dr. William P. Fox is a professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his BS degree from the United States Military Academy at West Point, New York, his MS in operations research at the Naval Postgraduate School, and his Ph.D. at Clemson University. He has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including sixteen books, one hundred and fifty journal articles, and about one hundred and fifty conference presentations, and workshops. He is president-emeritus of the NPS faculty council. He was Past- President of the Military Application Society of INFORMS and is the current Vice Chair for Programs for BIG SIGMAA.





Bill Bauldry, Prof of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State in 1985. He joined the math dept at Appalachian State in 1986 where he served two terms as dept chair and received the Arts & Sciences Jimmy Smith Outstanding Service Award in 2007. Bill has authored texts on calculus, linear algebra, and his most recent, an Intro to Real Analysis including Lebesgue Measure. 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 has been a judge in COMAPs Math Contest in Modeling (MCM) since 2002, and currently serves as the Assoc Director of the MCM.
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