Introduction | |
1. INTRODUCTORY MODELS | |
Fibonacci Numbers | |
Growth Models | |
Extended Growth Models | |
Comparing Different Growth Models | |
2. DYNAMICAL MODELS AND DIFFERENCE EQUATIONS | |
Simple Epidemics | |
Harvesting | |
Population Dynamics | |
A Predator Prey Model | |
Iterated Maps and Functions | |
Sierpinski Triangle | |
3. PHYSICS APPLICATIONS | |
Simple Projectile Motion | |
Projectile Motion with Air Resistance | |
Planetary Orbit: Half Step Method | |
Epicycloid: Loop Free or Convex Moon Orbit | |
Heat Propagation | |
4. NUMBER THEORY | |
Decimal Expansions | |
Greatest Common Divisor | |
Prime Numbers: Sieve of Eratosthenes | |
5. FUNCTIONS, GRAPHING, AND CALCULUS | |
Graphing I: Functions of One Variable | |
Graphing II: Polar and Parametric Equations | |
Bezier Curves | |
Derivatives | |
Bisection Method | |
Newton's Method | |
Fitting Curves to Data (Polynomial Interpolation) | |
6. CREATIVE MATHEMATICS IN EVERYDAY SETTINGS | |
A Bicycle Investigation | |
Ski Racing | |
Birthday Problem | |
Golden Ratio | |
Paper Formats | |
Bridge Location | |
Game of Life | |
7. SOCIETAL APPLICATIONS | |
Legislative Apportionment | |
Drug Administration Strategy | |
Restock of Inventory | |
Birth Control | |
Genetics (Hardy-Weinberg Law) | |
Simulation | |
Appendix |
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