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Edition: 3RD 03

Copyright: 2003

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

Copyright: 2003

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

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.

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 Si milarity. Automobile Gasoline Mileage. Body Weight and Height, Strength and Agil ity.

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 Polynomia l Models. Smoothing: Low-Order Polynomial Models. Cubic Spline Models.

5. SIMULATION MODELING.

Simulation Deterministic Behavior: Area under a Curver. Generating Random Number s. Simulating Probabilistic Behavior. Inventory Model: Gasoline and Consumer Dem and. Queuing Models.

6. DISCRETE PROBABILITY MODELING.

Probabilistic Modeling With Discrete Systems. Modeling Component and System Reli ability. Linear Regression.

7. DISCRETE OPTIMIZATION MODELING LINEAR PROGRAMMING AND NUMERICAL SEARCH METHOD S.

An Overview of Discrete Optimization Modeling. Linear Programming I: Geometric S olutions. Linear Programming II: Algebraic Solutions. Linear Programming III: Th e 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 Shortag e and Taxation.

10. MODELING WITH SYSTEMS OF DIFFERENTIAL EQUATION.

Population Growth. Prescribing Drug Dosage. Braking Distance Revisited. Graphica l Solutions of Autonomous Differential Equations. Numerical Approximation Method s.

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. Euler 's Method for Systems of Differential Equations.

12. CONTINUOUS OPTIMIZATION MODELING.

An Inventory Problem: Minimizing the cost of Delivery and Storage. A Manufacturi ng Problem: Maximizing Profit in Producing Competing Products. Constrained Conti nuous Optimization. Managing Renewable Resources: The Fishing Industry.

Appendix A: Problems from the Mathematics Contest in Modeling .1985-1996 (also a vailable on accompanying CD).

Appendix B: An Algorithm for an Elevator Simulation Model.

Appendix C: The Revised Simplex Method.

Frank R. Giordano, Maurice D. Weir and William P. Fox

Edition: 3RD 03Copyright: 2003

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

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.

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 Si milarity. Automobile Gasoline Mileage. Body Weight and Height, Strength and Agil ity.

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 Polynomia l Models. Smoothing: Low-Order Polynomial Models. Cubic Spline Models.

5. SIMULATION MODELING.

Simulation Deterministic Behavior: Area under a Curver. Generating Random Number s. Simulating Probabilistic Behavior. Inventory Model: Gasoline and Consumer Dem and. Queuing Models.

6. DISCRETE PROBABILITY MODELING.

Probabilistic Modeling With Discrete Systems. Modeling Component and System Reli ability. Linear Regression.

7. DISCRETE OPTIMIZATION MODELING LINEAR PROGRAMMING AND NUMERICAL SEARCH METHOD S.

An Overview of Discrete Optimization Modeling. Linear Programming I: Geometric S olutions. Linear Programming II: Algebraic Solutions. Linear Programming III: Th e 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 Shortag e and Taxation.

10. MODELING WITH SYSTEMS OF DIFFERENTIAL EQUATION.

Population Growth. Prescribing Drug Dosage. Braking Distance Revisited. Graphica l Solutions of Autonomous Differential Equations. Numerical Approximation Method s.

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. Euler 's Method for Systems of Differential Equations.

12. CONTINUOUS OPTIMIZATION MODELING.

An Inventory Problem: Minimizing the cost of Delivery and Storage. A Manufacturi ng Problem: Maximizing Profit in Producing Competing Products. Constrained Conti nuous Optimization. Managing Renewable Resources: The Fishing Industry.

Appendix A: Problems from the Mathematics Contest in Modeling .1985-1996 (also a vailable on accompanying CD).

Appendix B: An Algorithm for an Elevator Simulation Model.

Appendix C: The Revised Simplex Method.