Fibonacci numbers, the Golden Ratio, and the laws of nature? -- Scaling laws of life, the Internet, and social networks -- Modeling change one step at a time -- Differential equation models : carbon dating, age of the universe, HIV modeling -- Modeling in the physical sciences, Kepler, Newton, and calculus -- Nonlinear population models : an introduction to qualitative analysis using phase planes -- Discrete time logistic map, periodic and chaotic solutions -- Snowball earth and global warming -- Interations : predator-prey, spraying of pests, carnivores in Australia -- Marriage and divorce -- Chaos in deterministic continuous systems, Poincaré and Lorenz -- El Niño and the southern oscillation -- Age of the earth : Lord Kelvin's model -- Collapsing bridges : Broughton and Tacoma narrows -- Appendix A : Differential equations and their solutions -- Appendix B : MATLAB codes.