

1  (51) 


1  (1) 

Testing for Proportionality 


2  (2) 

Modeling Change with Difference Equations 


4  (5) 


5  (1) 


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) 


21  (4) 


25  (1) 


26  (2) 


28  (2) 

An Investment Annuity Revisited 


30  (5) 

Systems of Difference Equations 


35  (17) 


35  (3) 


38  (3) 

Competitive Hunter ModelSpotted Owls and Hawks 


41  (3) 

Using Tendencies of the Political Parties 


44  (8) 

The Modeling Process, Proportionality, and Geometric Similarity 


52  (45) 


52  (2) 


54  (11) 

Vehicular Stopping Distance 


59  (6) 

Modeling Using Proportionality 


65  (10) 


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) 


97  (29) 


97  (4) 

Fitting Models to Data Graphically 


101  (6) 

Analytic Methods of Model Fitting 


107  (7) 

Applying the LeastSquares Criterion 


114  (5) 


119  (7) 

Vehicular Stopping Distance 


122  (4) 


126  (49) 


126  (1) 

Harvesting in the Chesapeake Bay and Other OneTerm Models 


127  (11) 


130  (1) 


131  (7) 

HighOrder Polynomial Models 


138  (8) 

Elapsed Time of a Tape Recorder 


140  (6) 

Smoothing: LowOrder 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) 


159  (16) 

Vehicle Stopping Distance Revisited 


167  (8) 


175  (42) 


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) 


205  (12) 


205  (8) 


213  (4) 

Discrete Probabilistic Modeling 


217  (19) 


217  (1) 

Probabilistic Modeling with Discrete Systems 


217  (6) 

Rental Car Company Revisited 


217  (2) 


219  (4) 

Modeling Component and System Reliability 


223  (4) 


224  (1) 


224  (1) 

Series and Parallel Combinations 


224  (3) 


227  (9) 


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) 


240  (1) 

Approximation by a Piecewise Linear Function 


241  (9) 

Linear Programming I: Geometric Solutions 


250  (9) 


251  (1) 


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) 


271  (2) 

Linear Programming IV: Sensitivity Analysis 


273  (6) 


279  (13) 

Using the Dichotomous Search Method 


282  (3) 

Using the Golden Section Search Method 


285  (2) 

ModelFitting Criterion Revisited 


287  (1) 

Optimizing Industrial Flow 


288  (4) 

Dimensional Analysis and Similitude 


292  (44) 


292  (3) 


295  (9) 


298  (3) 


301  (3) 

The Process of Dimensional Analysis 


304  (9) 

Terminal Velocity of a Raindrop 


309  (2) 

Automobile Gas Mileage Revisited 


311  (2) 


313  (6) 

Examples Illustrating Dimensional Analysis 


319  (11) 


319  (5) 

How Long Should You Roast a Turkey? 


324  (6) 


330  (6) 

Drag Force on a Submarine 


331  (5) 

Graphs of Functions as Models 


336  (32) 


336  (14) 


345  (1) 


346  (1) 


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) 


368  (3) 


371  (11) 


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) 


399  (1) 

Logistic Growth Revisited 


400  (4) 

Numerical Approximation Methods 


404  (8) 


406  (1) 

A Savings Certificate Revisited 


407  (5) 

Modeling with Systems of Differential Equations 


412  (46) 


412  (1) 

Graphical Solutions of Autonomous Systems of FirstOrder Differential Equations 


413  (6) 

A Linear Autonomous System 


414  (1) 

A Nonlinear Autonomous System 


415  (4) 

A Competitive Hunter Model 


419  (8) 


427  (10) 


437  (13) 


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) 


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) 


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, 19852002 

490  (33) 
Appendix B An Elevator Simulation Algorithm 

523  (9) 
Appendix C The Revised Simplex Method 

532  (3) 
Index 

535  