ECON815 (Queen's)

Submitted by pabsta on Thu, 01/28/2010 - 23:19

Solutions to homework 2

Right here (some minor corrections since the tutorial + correction in question 1 f) ).

I received your copies and I am done marking. Some general comments below.

I must say that I'm impressed by the consistency of the answers across copies... Perhaps there was a solution in some book out there ?

a) A lot of simple algebra mistakes where done when trying to find eigenvectors/values. More importantly, when building the matrix V, one must put the eigenvector in the same column as the associated eigenvalue. E.g. : if $D:=\begin{pmatrix} \lambda_1 & 0 \\ 0 & \lambda_2 \end{pmatrix}$ , then it must be that $V:=\begin{pmatrix} v_1 & v_2 \end{pmatrix}$ . A good practice would be to check your solutions.
b) A lot of people drew the linear approximations as if they stretched forever. Remember that these are approximations which are good only around the candidate equilibrium. As the distance increases, the real path diverges from this line, especially if you end-up crossing a stability loci/axis.

a) If you did not found the solution to one, revise the material.
b) Most of you took the long way to solve this (linear, non-homogenous case) while the equation was separable.
c) The professor's solution is somewhat complicated (but works !). Again, separability works, but roots of the equation (y = 0) and (y=1) works as well (roots => stability => dot y = 0). Nobody mentionned that.
d) Notice that if $\ddot y = \dot y$ , simple differentiation allows us to find $\frac{d^ny}{dt^n} = \ddot y = \dot y$ . One should recognise from this the signature of an exponential function. A bad joke on the matter (the last one).

Some slides for this friday. A correction in the definition of the Taylor expansion has been made.

A sketch of the solutions of the problems in the slides above.

Here are the slides from the 22. I corrected a small error regarding the definition of eigenvectors and in slide 51.

My office hours are thursdays, from 12pm to 14hpm, the weeks I do not give tutorials. I live (...) in DUN 337.