Ordinary Differential Equations MATH 119A
HOMEWORK 1

Read chapter 1-2 of Text (Nonlinear Dynamics and Chaos by Steven H. Strogatz)

0. What is your major? what area your research interests?

1. problem 2.2.3
2. problem 2.2.4
3. problem 2.2.7
4. problem 2.2.9
5. problem 2.2.13
6. problem 2.3.4
7. problem 2.4.7

8. Explain why there cannot be oscillations in the system described by x'=f(x).

9. The logistic equation for population dynamics is given by N'=r(1-N/K)N. Find the steady states of the equation and their stability - graphically and analytically. Given r=1,K=2,N(0)=3, how long will it take the system to EXACTLY reach the stable steady state (Explain why).