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MS 3011: Sample Test

February 6, 2012 in MS 3011 | 4 comments

Please find a sample test here.

Note that question 1 is going to be one of Summer 2011 Question 2(a), Summer 2009 Question 6(b)(i) or 6(b)(ii). Question 2 will be taken from the other exam questions that we have done in class or have set as exercises (The only thing that’ll change is the constants will be different for Tests A and B). Question 3 will be a graph question.

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.

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.

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)

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)

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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MS 3011: Week 1

January 4, 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.

Lecture notes must be purchased at the SU printing shop in the student centre. They are priced at €8.

 

Note that the notes are NOT available in An Scoláire on College Road. Perhaps some of ye have gone there and he has said that he will print them for tomorrow.


Please do not buy them there as they have already been printed by a cheaper supplier.

The notes are available in the SU SHOP IN THE STUDENT CENTRE.

 

All that remains to be decided is the format/date, etc. of the homework. Hopefully I will have definitive information in the next week or two.

Project Maths: A More Geometric Approach to De Moivre’s Theorem and Complex Roots

November 19, 2011 in General, Grinds, Leaving Cert, MA 1008, MS 3011 | 3 comments

Introduction

This is just a short note to provide an alternative way of proving and using De Moivre’s Theorem. It is inspired by the fact that the geometric multiplication of complex numbers appeared on the Leaving Cert Project Maths paper (even though it isn’t on the syllabus — lol). It assumes familiarity with the basic properties of the complex numbers.

Complex Numbers

Arguably, the complex numbers arose as a way to find the roots of all polynomial functions. A polynomial function is a function that is a sum of powers of x. For example, q(x)=x^2-x-6 is a polynomial. The highest non-zero power of a polynomial is called it’s degree. Ordinarily at LC level we consider polynomials where the multiples of x — the coefficients — are real numbers, but a lot of the theory holds when the coefficients are complex numbers (note that the Conjugate Root Theorem only holds when the coefficients are real). Here we won’t say anything about the coefficients and just call them numbers.

Definition

Let a_n,\,a_{n-1},\,\dots,\,a_1,\,a_0 be numbers such that a_n\neq 0. Then

p(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0,

is a polynomial of degree n.

In many instances, the first thing we want to know about a polynomial is what are its roots. The roots of a polynomial are the inputs x such that the output p(x)=0.

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