MS3011: Week 5

February 3, 2012 in MS 3011 | Leave a comment

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 jippo@campus.ie and I will add you to the mailing list.

This Week

In lectures, we have finished off section 3.

Next Week

I have managed to secure a new venue for the Thursday tutorials. This tutorial will now take place in WGB G 09 rather than the Windle Building.

Problems

Summer 2010 Q.1

Summer 2009 Q. 2 (b)

Autumn 2009 Q. 2(b)

Summer 2009 Q. 2(a), 6(a)

Autumn 2009 Q. 2(a), 4

Supplementary Notes

Summer 2011 Q. 2(a)

The logistic family of mappings is given by

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

where 0\leq\mu\leq 4 and 0\leq x\leq 1.

(a) Motivate the use of the logistic equation as a model for population growth explaining the reasoning behind each of the three terms, \mu, x and (1-x)

Solution : We want an equation to model a population P_n under the following two assumptions:

  1. For ‘small’ populations the growth is approximately geometric P_{n+1}\approx \mu \,P_n for some positive constant \mu.
  2. There is a maximum population M such that if the population reaches M then all the resources are exhausted and extinction ensues;  i.e. P_{n+1}=0 if P_n=M.

MS2002: Week 5

February 3, 2012 in MS 2002 | Leave a comment

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 jippo@campus.ie and I will add you to the mailing list.

This Week

In lectures, we started chapter 3 and are in section 3.2. We also looked at some simpler proofs of Theorems 1.3.2 and 3.1.4. These are reproduced below.

In tutorials we did p.36 Q 6, p.42 Q.2, 4 and  p.44 Q.1 (a)(e), 2(a).

Sample Test

Hopefully by Tuesday morning.

Additional Notes

Here we give an alternative proof of Theorem 3.1.4. It is very likely that you will be asked to prove some of Theorem 3.1.4 in the exam and you are free to choose which proof you prefer. You may even prove parts (ii) and (iii) of Theorem 3.1.4 using the proof in the notes and then use this proof for part (iv). In class I also gave an easier proof of Theorem 1.3.2 although this won’t be examinable.

Theorem 3.1.4

For all positive a and b, and any rational number r, we have

  1. \ln 1=0,
  2. \ln(ab)=\ln a+\ln b,
  3. \displaystyle\ln\left(\frac{a}{b}\right)=\ln a-\ln b,
  4. \ln a^r=r\ln a.

MS3011: Test

January 30, 2012 in MS 3011 | Leave a comment

Just giving ye fair notice that the test will take place at 10 am on Monday February 20 in WGB G 18.

Everything covered up to February 8 inclusive is examinable and you may expect a sample by about February 6.

MS2002: Test

January 30, 2012 in MS 2002 | Leave a comment

Just giving ye fair notice that the test will take place at 9 am on Wednesday February 22 in WGB G 05 — NOT not the ordinary lecture location.

Everything covered up to February 9 inclusive is examinable and you may expect a sample by about February 9.

MS3011: Week 4

January 27, 2012 in MS 3011 | Leave a comment

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

This Week

In lectures, we have finished up to (but not including) section 3.5.

Problems

Summer 2010 Q.2 (d)

The exercise on p.26

Summer 2011 Q. 2(a)

MS2002: Week 4

January 26, 2012 in MS 2002 | 2 comments

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

This Week

In lectures, we finished off chapter 2.

In tutorials we did p.17 Q.1 (d)(f), p.32 Q.1,9, p.36 Q. 7, 8, 12 and p.39 Q. 2, 3.

Teaching Practise

Be aware that these two weeks are a terrible risk to you falling behind in integration so make serious efforts to either keep up with the work or catch up ASAP: week 4’s lectures.

Note that I will not be scanning up any more of these notes.

MS3011: Week 3

January 19, 2012 in MS 3011 | Leave a comment

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

This Week

In lectures, we finished section 2.2 and we have started section 3.2.

In tutorials ye worked on the problems below:

Problems

Summer 2009 Q.6 (b)

Autumn 2009 Q. 1(b)

MS2002: Week 3

January 19, 2012 in MS 2002 | Leave a comment

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

This Week

In lectures, we finished off section 2.1 and did all of section 2.2.

In tutorials we did p.15 Q.1, p.17 Q.1(a)(b)(c) and p.23 Q.3, 6.

Teaching Practise

Be aware that these two weeks are a terrible risk to you falling behind in integration so make serious efforts to either keep up with the work or catch up ASAP: week 3’s lectures.

MS2002: Week 2

January 12, 2012 in MS 2002 | Leave a comment

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

This Week

In lectures, we covered from section 1.2 to Proposition 2.1.7.

Tutorials start next week Wednesday at 11 in Civil Eng 110. Email me if you have a timetable clash. Please indicate code of the module which is clashing.

Teaching Practise

For those going on teaching practise over the next two weeks note that I will scan the next week’s and the week after’s lecture notes and post them here. Be aware that these two weeks are a terrible risk to you falling behind in integration so make serious efforts to either keep up with the work or catch up ASAP.

MS3001: Week 2

January 11, 2012 in MS 3011 | Leave a comment

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

This Week

In lectures, we covered from section 1.4 to 2.1 and some of section 2.2

Tutorials start next week Thursday at 3 in Windle PDT. Email me if you have a timetable clash. Please indicate code of the module which is clashing. 

Problems

You need to do exercises – all of the following you should be able to attempt.

Exercise on page. 10.

From the Class

Nothing

Additional Notes

This is the question which I failed miserably to do in the Wednesday lecture.

August 2010 Question 2(c)(ii)

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