Feedback for Homework Due 03 18 2015
Problem 14(b), section 4.2: If T(y) is linear then for EVERY functions y1,y2 and EVERY constants c1,c2: T(c1*y1+c2*y2)=c1*T(y1)+c2*T(y2).
Negating, we get that T(y) is NOT linear if there exists functions y1,y2 and constants c1,c2 such that: T(c1*y1+c2*y2) is NOT equal to c1*T(y1)+c2*T(y2).
Your goal is to provide such an example of y1,y2,c1,c2 that T(c1*y1+c2*y2) is NOT equal to c1*T(y1)+c2*T(y2). E.g. y1=t, y2=t, c1=1, c2=1.
Problem 9, section 4.3: (0,0) is the critical point and it is unstable. There are many types of unstable points. In this case, it is a saddle point.