A First Course in Mathematical Modeling,9780534384289

A First Course in Mathematical Modeling

by ; ;
Edition: 3rd
ISBN13: 9780534384289
ISBN10: 0534384285
Format: Hardcover
Pub. Date: 2002-07-29
Publisher(s): Brooks Cole
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List Price: $409.47

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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.

Table of Contents

Modeling Change
1(51)
Introduction
1(1)
Testing for Proportionality
2(2)
Modeling Change with Difference Equations
4(5)
A Savings Certificate
5(1)
Mortgaging a Home
6(3)
Approximating Change with Difference Equations
9(9)
Growth of a Yeast Culture
9(1)
Growth of a Yeast Culture Revisited
10(2)
Spread of a Contagious Disease
12(1)
Decay of Digoxin in the Bloodstream
13(1)
Heating of a Cooled Object
14(4)
Solutions to Dynamical Systems
18(17)
A Savings Certificate Revisited
18(3)
Sewage Treatment
21(4)
Prescription for Digoxin
25(1)
An Investment Annuity
26(2)
A Checking Account
28(2)
An Investment Annuity Revisited
30(5)
Systems of Difference Equations
35(17)
A Car Rental Company
35(3)
The Battle of Trafalgar
38(3)
Competitive Hunter Model-Spotted Owls and Hawks
41(3)
Using Tendencies of the Political Parties
44(8)
The Modeling Process, Proportionality, and Geometric Similarity
52(45)
Introduction
52(2)
Mathematical Models
54(11)
Vehicular Stopping Distance
59(6)
Modeling Using Proportionality
65(10)
Kepler's Third Law
67(8)
Modeling Using Geometric Similarity
75(13)
Raindrops from a Motionless Cloud
77(2)
Modeling a Bass Fishing Derby
79(9)
Automobile Gasoline Mileage
88(3)
Body Weight and Height, Strength and Agility
91(6)
Model Fitting
97(29)
Introduction
97(4)
Fitting Models to Data Graphically
101(6)
Analytic Methods of Model Fitting
107(7)
Applying the Least-Squares Criterion
114(5)
Choosing a Best Model
119(7)
Vehicular Stopping Distance
122(4)
Experimental Modeling
126(49)
Introduction
126(1)
Harvesting in the Chesapeake Bay and Other One-Term Models
127(11)
Harvesting Bluefish
130(1)
Harvesting Blue Crabs
131(7)
High-Order Polynomial Models
138(8)
Elapsed Time of a Tape Recorder
140(6)
Smoothing: Low-Order Polynomial Models
146(13)
Elapsed Time of a Tape Recorder Revisited
147(4)
Elapsed Time of a Tape Recorder Revisited Again
151(2)
vehicle Stopping Distance
153(2)
Growth of a Yeast Culture
155(4)
Cubic Spline Models
159(16)
Vehicle Stopping Distance Revisited
167(8)
Simulation Modeling
175(42)
Introduction
175(2)
Simulating Deterministic Behavior: Area Under a Curve
177(5)
Generating Random Numbers
182(4)
Simulating Probabilistic Behavior
186(8)
Inventory Model: Gasoline and Consumer Demand
194(11)
Queuing Models
205(12)
A Harbor System
205(8)
Morning Rush Hour
213(4)
Discrete Probabilistic Modeling
217(19)
Introduction
217(1)
Probabilistic Modeling with Discrete Systems
217(6)
Rental Car Company Revisited
217(2)
Voting Tendencies
219(4)
Modeling Component and System Reliability
223(4)
Series Systems
224(1)
Parallel Systems
224(1)
Series and Parallel Combinations
224(3)
Linear Regression
227(9)
Ponderosa Pines
229(2)
The Bass Fishing Derby Revisited
231(5)
Discrete Optimization Modeling
236(56)
An Overview of Discrete Optimization Modeling
237(13)
Determining a Production Schedule
237(3)
Space Shuttle Cargo
240(1)
Approximation by a Piecewise Linear Function
241(9)
Linear Programming I: Geometric Solutions
250(9)
The Carpenter's Problem
251(1)
A Data-Fitting Problem
252(7)
Linear Programming II: Algebraic Solutions
259(4)
Solving the Carpenter's Problem Algebraically
261(2)
Linear Programming III: The Simplex Method
263(10)
The Carpenter's Problem Revisited
268(3)
Using the Tableau Format
271(2)
Linear Programming IV: Sensitivity Analysis
273(6)
Numerical Search Methods
279(13)
Using the Dichotomous Search Method
282(3)
Using the Golden Section Search Method
285(2)
Model-Fitting Criterion Revisited
287(1)
Optimizing Industrial Flow
288(4)
Dimensional Analysis and Similitude
292(44)
Introduction
292(3)
Dimensions as Products
295(9)
A Simple Pendulum
298(3)
Wind Force on a Van
301(3)
The Process of Dimensional Analysis
304(9)
Terminal Velocity of a Raindrop
309(2)
Automobile Gas Mileage Revisited
311(2)
A Damped Pendulum
313(6)
Examples Illustrating Dimensional Analysis
319(11)
Explosion Analysis
319(5)
How Long Should You Roast a Turkey?
324(6)
Similitude
330(6)
Drag Force on a Submarine
331(5)
Graphs of Functions as Models
336(32)
An Arms Race
336(14)
Civil Defense
345(1)
Mobile Launching Pads
346(1)
Multiple Warheads
347(1)
MIRVs Revisited: Counting Warheads
348(2)
Modeling an Arms Race in Stages
350(5)
Managing Nonrenewable Resources: The Energy Crisis
355(4)
Effects of Taxation on the Energy Crisis
359(5)
A Gasoline Shortage and Taxation
364(4)
Modeling with a Differential Equation
368(44)
Introduction
368(3)
Population Growth
371(11)
Prescribing Drug Dosage
382(9)
Braking Distance Revisited
391(4)
Graphical Solutions of Autonomous Differential Equations
395(9)
Drawing a Phase Line and Sketching Solution Curves
396(3)
Cooling Soup
399(1)
Logistic Growth Revisited
400(4)
Numerical Approximation Methods
404(8)
Using Euler's Method
406(1)
A Savings Certificate Revisited
407(5)
Modeling with Systems of Differential Equations
412(46)
Introduction
412(1)
Graphical Solutions of Autonomous Systems of First-Order Differential Equations
413(6)
A Linear Autonomous System
414(1)
A Nonlinear Autonomous System
415(4)
A Competitive Hunter Model
419(8)
A Predator-Prey Model
427(10)
Two Military Examples
437(13)
Lanchester Combat Models
437(7)
Economic Aspects of an Arms Race
444(6)
Euler's Method for Systems of Differential Equations
450(8)
Using Euler's Method for Systems
451(1)
A Trajectory and Solution Curves
452(6)
Continuous Optimization Modeling
458(32)
Introduction
458(1)
An Inventory Problem: Minimizing the Cost of Delivery and Storage
459(9)
A Manufacturing Problem: Maximizing Profit in Producing Competing Products
468(6)
Constrained Continuous Optimization
474(6)
An Oil Transfer Company
474(2)
A Space Shuttle Water Container
476(4)
Managing Renewable Resources: The Fishing Industry
480(10)
Appendix A Problems from the Mathematics Contest in Modeling, 1985-2002 490(33)
Appendix B An Elevator Simulation Algorithm 523(9)
Appendix C The Revised Simplex Method 532(3)
Index 535

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