I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

## Tutorial Venue

I have applied to get this changed to WGB G03… I didn’t get everything. The timetable is

• This week coming, 14 February LL2
• Next week, 21 February WGB G03
•  28 February LL2
• 7 March LL2
• 14 March WGB G03
• 21 March WGB G03
• 28 March WGB G03

## Test

The test will now take place on Monday week February 18. Everything up to but not including section 3.4 in the typeset notes is examinable. We have everything for the test covered. Please find a sample test and the test I gave last year in your typeset notes.

The following theorems from the notes are examinable: Theorem 1 & Theorem 2 (very bottom of page 12 and start of page 13 — called Theorem 1 & 2 on the board). Also the Fixed-Point Factor-Theorem (which was called such on the board. It is not in the notes but is found here https://jpmccarthymaths.com/2012/02/26/ms3011-homework/#comment-331). When I say examinable you should be able to

• state the theorem
• prove the theorem
• understand the theorem and the proof

Learning off the proof letter by letter won’t do you!

## Week 5

In week 5 we did a couple of questions that used the theory that we developed in the first few weeks.

Then we began our study of the Logistic Family. We postulated the equation as a model of population growth with two assumptions. We showed how the population could be written as a dynamical system and showed that when the growth-rate parameter $\mu=2$ then all initial states $x_0\in(0,1)$ converge to the attracting fixed point of $Q_2(x)=2x(1-x)$.

We will continue this study next week.

## Exercises

Exercises for Thursday 14 February are to look at the following:

Sample Test & Actual Test in written notes

Autumn 2012: Question 2(a), 3 (a)

Summer 2011: Question 2(a), (b), (d), 4

Summer 2009: Question 4 (a), (b)