Show that the linearization of (5) at .3; 1/ is u0 D 3u 3v, v0 D u C v. Then show that the coefficient matrix of this linear system has complex conjugate eigenvalues 1, 2 D 2 i p2 with positive real part. Hence .3; 1/ is a spiral source for (5).

Lecture 21: Related Rates (Section 3.11) Related Rates allows us to ﬁnd the rate of change of one quantity in terms of the rate of change of a related quantity. Consider the following example:...