First Course in Mathematical Modeling

ISBN-10: 0534384285
ISBN-13: 9780534384289
Edition: 3rd 2003 (Revised)
List price: $360.95
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Description: 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  More...

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Book details

List price: $360.95
Edition: 3rd
Copyright year: 2003
Publisher: Brooks/Cole
Publication date: 7/29/2002
Binding: Hardcover
Pages: 550
Size: 7.25" wide x 9.25" long x 1.00" tall
Weight: 2.552
Language: English

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.

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.

Modeling with Discrete Dynamical Systems
Modeling Change with Difference Equations
Approximating Change with Difference Equations
Solutions to Dynamical Systems
Systems of Difference Equations
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
Model Fitting
Fitting Models to Data Graphically
Analytic Methods of Model Fitting
Applying the Least-Squares Criterion
Choosing a Best Model
Experimental Modeling
Harvesting in the Chesapeake Bay and Other One-Term Models
High-Order Polynomial Models
Smoothing: Low-Order Polynomial Models
Cubic Spline Models
Simulation Modeling
Simulation Deterministic Behavior: Area under a Curver
Generating Random Numbers
Simulating Probabilistic Behavior
Inventory Model: Gasoline and Consumer Demand
Queuing Models
Discrete Probability Modeling
Probabilistic Modeling With Discrete Systems
Modeling Component and System Reliability
Linear Regression
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
Dimensional Analysis and Similitude
Dimensions as Products
The Process of Dimensional Analysis
A Damped Pendulum
Examples Illustrating Dimensional Analysis
Similitude
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
Modeling with Systems of Differential Equation
Population Growth
Prescribing Drug Dosage
Braking Distance Revisited
Graphical Solutions of Autonomous Differential Equations
Numerical Approximation Methods
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
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
Problems from the Mathematics Contest in Modeling. 1985-1996 (also available on accompanying CD)
An Algorithm for an Elevator Simulation Model
The Revised Simplex Method

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