WILL WARD

This exercise is from Nonlinear Dynamics and Chaos, 2nd Edition by Steven H. Strogatz Part 1: One-Dimensional Flows 2 Flows on the Line Exercise 2.2.3 Analyze the following equation graphically. Sketch the vector field on the real line, find all the fixed points, classify their stability, and sketch the graph of for different initial conditions. Then try to obtain the analytical solution for . From the above graph of , it's straightforward to sketch the vector field shown below it. The fixed points are = -1, 0, and 1. is positive to the left of = -1, so the flow is to the right. To the right of = -1, is negative, so the flow is to the left. From these two facts, it's clear that = -…

More and more, when you check out someone's GitHub profile, you see that they've been able to customize it. The first few times I noticed it, I didn't think to do the same thing to my profile. However, if everyone's going to start doing it, it would feel weird not to do something to make the profile a little more eye-catching. You can find out more about doing this at GitHub Docs. GitHub Docs - Managing your profile README

Warning: Spoilers Follow From Stat 110, Chapter 1 Ex 1.31 Elk dwell in acertain forest. There are N elk, of which a simple random sample of size n are captured and tagged ("simple random sample" means that all sets of n elk are equally likely). The captured elk are returned to the population, and then a new sample is drawn, this time with size m. This is an important method that is widely used in ecology, known as capture-recapture. What is the probability that exactly k of the m elk in the new sample were previously tagged? (Assume that an elk that was captured before doesn't become more or less likely to be captured again.) Answer The number of ways you can have m elk is . The number of…