1. PROPERTIES OF LINEAR SYSTEMS AND THE LINEARITY PRINCIPLE
Section 3.1
PROPERTIES OF LINEAR SYSTEMS AND THE LINEARITY PRINCIPLE

2. Intro to linear systems
Lots of useful systems of DEs are in the form
Examples include the damped (or undamped) harmonic oscillator (see p. 234) and the competing stores model (see p. 235).
Use LinearPhasePortraits to experiment with different values of a, b, c, and d.

3. Equilibrium solutions
Find the equilibrium solution(s) to
Do the values of a, b, c, and d have an effect on the equilibrium solution(s)?

4. Competing stores model
Read p
Quantities:
x(t) = daily profit of Paul’s store at time t.
y(t) = daily profit of Bob’s store at time t.
a = effect of Paul’s profits on the change in Paul’s profits. Explain: a > 0 means ___; a < 0 means ___.
b = effect of Bob’s profits on the change in Paul’s profits. Explain: b > 0 means ___; b < 0 means ___.
Explain c and d.
Do p