A First Course in Mathematical Modeling

by Giordano, Frank R.; Weir, Maurice D.

• ISBN13: 9780534033675
• ISBN10: 0534033679
• Format: Hardcover
• Copyright: 1985-01-01
• Publisher: Brooks/Cole Pub Co

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.

Table of Contents

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

Table of Contents provided by Publisher. All Rights Reserved.