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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 | |