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.

Week 5

We began our study of the Logistic Family. We postulated the equation as a model of population growth with two assumptions and ended up with

Q_\mu(x)=\mu x(1-x)

where x\in[0,1] can be interpreted as the proportion of a maximum population with a growth rate \mu\in[0,4].  We began analysing when zero was attracting/repelling and when \displaystyle \frac{\mu-1}{\mu} was attracting/repelling. We were rudely interrupted by the fire drill!

 

http://kkcb.com/one-of-the-best-scenes-of-the-office-is-dwights-fire-drill/

Week 6

In Week 6 we will finish of our study of the Logistic Mapping and perhaps begin our study of the Tent Mapping.

Exercises

I have emailed ye a copy of the exercises and ye should be able to look at these questions 38, 39, 42, 43 for the Week 6 tutorial (assuming that ye are ready for Wednesday’s Test).

Test and Other CA

The test will take place on February 12 in Week 6. 

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 after page 31. in these typeset notes.

The following theorems from the notes are examinable: the very bottom of page 12 and start of page 13. Also the Fixed-Point Factor-Theorem (which was called such on the board. It is not in the notes but is found here. 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!

The Concept MCQ will take place in Week 8.

The homework will be given to you towards the end of the semester and I will give ye three weeks to do it. It will probably be on complex numbers and won’t be as long as last year’s homework.

You will be given marks for the best two out of Test, Concept MCQ and Homework.

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question about finding a formula for the iterates of Q_1(x).

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