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

Edition: 3RD 03Copyright: 2003

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

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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.

**Benefits: **

- NEW! Includes a CD-ROM, packaged free with the text, that contains software, additional modeling scenarios, projects, and past problems from the Mathematical Contest in Modeling.
- Motivates students to study advanced courses such as linear algebra, differential equations, optimization and linear programming, numerical analysis, probability, and statistics by familiarizing them with the power and utility of these subjects.
- NEW! Provides new scenarios, examples, and exercises throughout the text.
- NEW! Contains numerical, graphical, and analytic solutions in the opening chapter, , MODELING WITH DISCRETE DYNAMICAL SYSTEMS.
- NEW! Demonstrates how modern applied mathematics is facilitated by technology, including discrete dynamical systems, discrete optimization, and simulation.
- NEW! The authors' lab sheets are available online under Instructor Resources at the Brooks/Cole Mathematics Resource Center Web site (www.brookscole.com/mathematics).
- Enhances a student's problem solving capabilities with a six-step problem-solving process: problem identification, model construction or selection, identification and collection of data, model validation, calculation of solutions to the model, and model implementation and maintenance.
- Emphasizes model construction to promote student creativity and to demonstrate the artistic nature of model building, including the ideas of experimentation and simulation.
- Blends mathematical modeling techniques with the more creative aspects of modeling for variety and confidence building, and gradually transitions to the more difficult creative aspects.
- Includes individual and group projects in creative and empirical model construction, model analysis, and model research.

**Giordano, Frank R. : (Retired )**

Weir, Maurice D. :

Fox, William P. : West Point

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. CRETE 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

Euler's 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

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Summary

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.

**Benefits: **

- NEW! Includes a CD-ROM, packaged free with the text, that contains software, additional modeling scenarios, projects, and past problems from the Mathematical Contest in Modeling.
- Motivates students to study advanced courses such as linear algebra, differential equations, optimization and linear programming, numerical analysis, probability, and statistics by familiarizing them with the power and utility of these subjects.
- NEW! Provides new scenarios, examples, and exercises throughout the text.
- NEW! Contains numerical, graphical, and analytic solutions in the opening chapter, , MODELING WITH DISCRETE DYNAMICAL SYSTEMS.
- NEW! Demonstrates how modern applied mathematics is facilitated by technology, including discrete dynamical systems, discrete optimization, and simulation.
- NEW! The authors' lab sheets are available online under Instructor Resources at the Brooks/Cole Mathematics Resource Center Web site (www.brookscole.com/mathematics).
- Enhances a student's problem solving capabilities with a six-step problem-solving process: problem identification, model construction or selection, identification and collection of data, model validation, calculation of solutions to the model, and model implementation and maintenance.
- Emphasizes model construction to promote student creativity and to demonstrate the artistic nature of model building, including the ideas of experimentation and simulation.
- Blends mathematical modeling techniques with the more creative aspects of modeling for variety and confidence building, and gradually transitions to the more difficult creative aspects.
- Includes individual and group projects in creative and empirical model construction, model analysis, and model research.

Author Bio

**Giordano, Frank R. : (Retired )**

Weir, Maurice D. :

Fox, William P. : West Point

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. CRETE 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

Euler's 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

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

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.

**Benefits: **

- NEW! Includes a CD-ROM, packaged free with the text, that contains software, additional modeling scenarios, projects, and past problems from the Mathematical Contest in Modeling.
- Motivates students to study advanced courses such as linear algebra, differential equations, optimization and linear programming, numerical analysis, probability, and statistics by familiarizing them with the power and utility of these subjects.
- NEW! Provides new scenarios, examples, and exercises throughout the text.
- NEW! Contains numerical, graphical, and analytic solutions in the opening chapter, , MODELING WITH DISCRETE DYNAMICAL SYSTEMS.
- NEW! Demonstrates how modern applied mathematics is facilitated by technology, including discrete dynamical systems, discrete optimization, and simulation.
- NEW! The authors' lab sheets are available online under Instructor Resources at the Brooks/Cole Mathematics Resource Center Web site (www.brookscole.com/mathematics).
- Enhances a student's problem solving capabilities with a six-step problem-solving process: problem identification, model construction or selection, identification and collection of data, model validation, calculation of solutions to the model, and model implementation and maintenance.
- Emphasizes model construction to promote student creativity and to demonstrate the artistic nature of model building, including the ideas of experimentation and simulation.
- Blends mathematical modeling techniques with the more creative aspects of modeling for variety and confidence building, and gradually transitions to the more difficult creative aspects.
- Includes individual and group projects in creative and empirical model construction, model analysis, and model research.

**Giordano, Frank R. : (Retired )**

Weir, Maurice D. :

Fox, William P. : West Point

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. CRETE 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

Euler's 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