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Prologue | |

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Preface | |

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Introductory Models | |

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Fibonacci Numbers | |

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Construction Summary: Fibonacci Numbers | |

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Exercises | |

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Growth Models | |

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Construction Summary: Exponential Growth | |

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Exercises | |

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Extended Growth Models | |

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Construction Summary: Logistic Growth | |

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Exercises | |

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Comparing Different Growth Models | |

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Construction Summary: Comparing Growth Models | |

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Exercises | |

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Dynamical Models and Difference Equations | |

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Simple Epidemics | |

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Construction Summary: Simple Epidemics | |

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Exercises | |

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Harvesting Models | |

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Constant Harvesting Policy | |

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Introducing Mathematical Notation | |

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Proportional Harvesting Policy | |

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Construction Summary: Harvesting Models | |

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Exercises | |

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Population Dynamics | |

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Further Mathematics: Experimenting with Population Dynamics | |

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Construction Summary: Population Dynamics | |

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Exercises | |

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A Predator-Prey Model | |

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Further Mathematics: Difference Equations versus Differential Equations | |

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Construction Summary: A Predator-Prey Model | |

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Exercises | |

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Iterated Maps and Functions | |

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Further Mathematics: Fixed Points and Calculus | |

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Construction Summary: Function Iteration for Square Function | |

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Construction Summary: Function Iteration for Nonlinear Function | |

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Exercises | |

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More about Iterated Functions | |

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Further Mathematics: An Unanswered Question | |

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Construction Summary: More about Iterated Functions | |

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Exercises | |

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The Feigenbaum Diagram | |

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Construction Summary: The Feigenbaum Diagram | |

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Exercises | |

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Sierpinski's Triangle | |

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Construction Summary: Sierpinski's Triangle | |

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Exercises | |

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Physics Applications | |

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Simple Projectile Motion | |

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Further Mathematics: A Calculus-Based Solution | |

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Construction Summary: Simple Projectile Motion | |

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Exercises | |

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Projectile Motion with Air Resistance | |

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Construction Summary: Projectile Motion with Air Resistance | |

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Exercises | |

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Planetary Orbits: Half-Step Method | |

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Construction Summary: Planetary Orbits (Half-Step Method) | |

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Exercises | |

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The Shape of the Moon's Orbit | |

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Construction Summary: Shape of the Moon's Orbit | |

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Exercises | |

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Heat Propagation | |

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One-Dimensional Model | |

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Construction Summary: Heat Flow in a Rod | |

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Two-Dimensional Model | |

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Construction Summary: Heat Flow in a Plate | |

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Exercises | |

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Number Theory | |

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Numbers in Different Bases | |

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Construction Summary: Simple Expansion | |

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Construction Summary: Integer Expansion with Target Base > 10 | |

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Construction Summary: Integer Expansion with Source Base Different from 10 | |

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Exercises | |

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Decimal Expansions | |

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Construction Summary: Decimal Expansions | |

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Exercises | |

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Greatest Common Divisor | |

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Further Mathematics: Euclid's Algorithm | |

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Construction Summary: Greatest Common Divisor | |

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Exercises | |

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Sieve of Eratosthenes | |

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Basic Model | |

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Compact Version | |

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Construction Summary: Sieve of Eratosthenes | |

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Exercises | |

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Functions and Graphing | |

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Graphing I: Basic Techniques | |

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Two Basic Examples | |

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Construction Summary: Graphing Functions of One Variable | |

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Interactive Graphing | |

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Construction Summary: Graphing Functions with a Trace Point | |

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Graphs of Several Functions | |

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Construction Summary: Graphing Two Functions of One Variable | |

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Exercises | |

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Graphing II: Polar and Parametric Equations | |

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Basic Construction | |

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Incorporating Animation Effects | |

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Construction Summary: Graphing Polar Equations | |

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Exercises | |

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Bezier Curves | |

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Basic Construction | |

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Construction Summary: Bezier Curves | |

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An Alternate Approach | |

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Construction Summary: Bezier Curves via Matrices | |

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Exercises | |

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Bisection Algorithm | |

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Construction Summary: Bisection Algorithm | |

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Exercises | |

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The Newton and Secant Methods | |

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Newton's Method | |

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Construction Summary: Newton's Method | |

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The Secant Method | |

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Construction Summary: Secant Method | |

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Exercises | |

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Fitting a Curve to Data | |

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Polynomial Interpolation | |

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Construction Summary: Fitting a Curve to Data | |

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A Matrix Approach to Interpolation | |

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Construction Summary: Polynomial Interpolation via Matrices | |

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A Glance at the Least-Squares Approximation | |

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Construction Summary: Least-Squares Regression | |

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Exercises | |

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The Binomial Coefficients | |

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Construction Summary: The Binomial Coefficients | |

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Exercises | |

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Creative Mathematics in Everyday Settings | |

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A Bicycle Investigation | |

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Construction Summary: Bicycle Investigation | |

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Ski Racing | |

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Construction Summary: Ski Racing | |

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The Golden Ratio | |

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Construction Summary: Golden Ratio (Direct), Compute Ratio Directly | |

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Construction Summary: Golden Ratio (Iteration), Compute Ratio by Iteration | |

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Paper Formats | |

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Construction Summary: Paper Formats | |

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Game of Life | |

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Construction Summary: Game of Life | |

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Exercises | |

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Problems to Solve by Yourself | |

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Exercises | |

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Combinatorics and Probability | |

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Birthday Problem | |

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Construction Summary: Birthday Problem | |

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Exercises | |

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Birth Control: The Geometric Distribution | |

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Construction Summary: Birth Control (Geometric Distribution) | |

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Exercises | |

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Genetics: The Hardy-Weinberg Principle | |

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Further Mathematics: The Algebra of Hardy-Weinberg | |

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Construction Summary: Genetics (Hardy-Weinberg Principle) | |

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Exercises | |

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Simulation | |

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Simulating Bernoulli Trials and the Binomial Distribution | |

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Construction Summary: Binomial Simulation | |

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Rolling a Pair of Dice | |

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Construction Summary: Dice Simulation | |

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The Birthday Problem Revisited | |

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Construction Summary: Birthday Problem Simulation | |

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Exercises | |

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Finding Optimal Solutions | |

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Optimal Bridge Location | |

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Construction Summary: Optimal Bridge Location, Part 1 | |

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Construction Summary: Optimal Bridge Location, Part 2 | |

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Exercises | |

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Apportionment Algorithms | |

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Hamilton's Method | |

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Construction Summary: Apportionment Algorithms (Hamilton) | |

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Jefferson's Method | |

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Construction Summary: Apportionment Algorithms (Jefferson) | |

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Exercises | |

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Medicine Dosage | |

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Construction Summary: Medicine Dosage, Basic Model | |

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Construction Summary: Medicine Dosage, Data for Graph | |

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Exercises | |

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Inventory Control | |

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Further Mathematics: Deriving Optimal Values Analytically | |

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Construction Summary: Inventory Control | |

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Exercises | |

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Game Theory | |

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Construction Summary: Game Theory | |

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Exercises | |

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Appendix | |

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Spreadsheet Basics and Book Conventions | |

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Functions and Additional Spreadsheet Features | |

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Spreadsheet Functions | |

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Data Table | |

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Inserting and Deleting Rows and Columns | |

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Conditional Formatting | |

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Spreadsheet Graphing Fundamentals | |

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Additional Spreadsheet Graphing Techniques | |

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Labels | |

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Additional Formatting | |

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Three-Dimensional Graphs | |

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Interactive Spreadsheet Tools | |

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The Scroll Bar | |

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Buttons and Macros | |

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Goal Seek | |

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Solver | |

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Reformatting Models for User Interaction | |

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General Layout | |

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Formatting and Protection | |

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Comments | |

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Adding Interactive Tools to Microsoft Excel Models | |

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Logistic Growth | |

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Harvesting | |

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References | |

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Index | |