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Welcome and Course Overview
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How to Take this Course
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Introduction to Functions
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Iteration
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Fixed Points and Stability
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Summary
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Homework (Optional)
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Homework Solutions (Optional)
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Test
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Introduction
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The Idea of the Derivative
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Differential Equations
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Qualitative Solutions
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Computational Solutions
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Summary
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Newton, Laplace, and Determinism
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Homework (Optional)
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Test
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Introducing the Logistic Equation
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Iterating the Logistic Equation
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The Butterfly Effect
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Modeling Styles
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Lyapunov Exponents (Optional)
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Logistic Equation Programs
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Summary
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Homework (Optional)
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Test
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The Logistic Differential Equation
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Logistic Equation with Harvest
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Bifurcation Diagrams
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Bifurcations
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Hysteresis (Optional)
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Summary
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Homework (Optional)
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Test
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Final State Diagrams
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The Bifurcation Diagram
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Bifurcation Diagram Explorations
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Logistic Equation Programs
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Summary
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Homework (Optional)
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Test
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Introduction
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Universality in Maps
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Universality in Physical Systems
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Renormalization
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Summary
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Bifurcation Diagram Programs
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Homework (Optional)
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Further Reading (Optional)
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Test
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Lotka Volterra Differential Equations
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The Phase Plane
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The Hénon Map
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The Lorenz Equations
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Summary
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Hénon Map Program
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Homework (Optional)
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Test
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Further Reading (Optional)
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The Hénon Attractor
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The Lorenz Attractor
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Stretching and Folding
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Links to Programs
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Summary
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Homework (Optional)
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Test
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Diffusion
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Reaction-Diffusion Equations
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Computer Experiments
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Real Experiments
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Summary
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Links to Programs
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Additional Resources (Optional)
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No Homework for Unit 9
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No Test for Unit 9
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Summary and Overview
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Interview: Stephen H. Kellert
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Interview: Stephen W. Morris
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Themes and Conclusions
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Farewell
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3.5 Modeling Styles » Additional Reading (Optional)
Much has been written about different styles of models. Here are some papers for those who want to dig deeper into this. The first two papers I recommend especially highly
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Levins, R. (2006). Strategies of abstraction. Biology and Philosophy, 21(5), 741-755. pdf
- Joshua M. Epsetin (2008). Why model? Journal of Artificial Societies and Social Simulation vol. 11, no. 4(12). html pdf.
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Levins, R. (1966). The strategy of model building in population biology. American scientist, 54(4), 421-431. pdf
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May, R. M. (2004). Uses and abuses of mathematics in biology. Science, 303(5659), 790-793. pdf