MS2001: Week 4

October 19, 2012 in MS 2001 | Leave a comment

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Test

The test will take place at 3 pm on Friday 2 November in Week 6.

I would’ve intended that everything up to and including section 2.3 would be examinable for the test. However it looks like we will not finish section 2.3 next week so Section 2.3: Continuity will not be on the test.

You can find the tests I set for the last two years after Exercise Sheet 1 — which is itself after page 49. Also there is a sample from last year here.

As we will not have covered continuity, we will not be able to do the questions two as they are phrased. However we have covered limits.

I will make some brief remarks on these tests now.

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MATH7021: Week 5

October 19, 2012 in MATH7021 | Leave a comment

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Test 1

The first test is on this Thursday 25 October at 8.20 p.m.

Please find a sample test.

Note that the format will be the same as this.

  1. Forward Difference Methods (14 marks)
  2. Gaussian Elimination Methods including Partial Pivoting 7 marks)
  3. The Jacobi and Gauss-Siedel Method (7 marks)
  4. Laplace Transforms of Differential Equations (7 marks)

MATH6015: Week 5

October 19, 2012 in MATH6015 | Leave a comment

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Test 1 Results

You are identified by the last four digits of your student number. Note that there are six of us in the forties. Although technically a pass, I would point out that the marking scheme was fairly generous: if you scored 44/100 things are not all well at all. You need to work harder.

We have to realise that maths is learnt linearly. This means that a lot of what we are doing in MATH6015 depends on what we did in MATH6014. In turn everything we do in MATH6040 will rely on MATH6015. Next year we study differential equations in MATH7020: what we are doing now is laying the foundations for this. If our foundations are shaky we’re in a tight spot.

Those of us who failed are in a serious spot at the moment. I will speak with you on Monday.

It is O.K. to find material difficult. It is OK to make silly mistakes. It is not OK to miss lectures, not use the tutorials and ignore the problem. Worst of all is not making the difficult mental effort to understand what we are doing. Here is Richard Feynmann, one of the greatest scientific minds of all time:

If Richard Feynmann can be confused so can all of us. The difference we can make is to persevere, try, try and try to understand what the hell we are doing. This is difficult but eventually you will get it.

Giving up is not an option.

To the people who excelled well done. You should be particularly proud if you battled this confusion and won.

I have two students who did not write their name down on the test. I have identified who the tests belong to but I can’t figure out which is which. These people can get their results on Monday.

Notes

So far we have covered up to and including the Constraint Optimisation Problems: MATH6015 Lecture Notes (with gaps). We have now finished the first part of the course and we now move onto integration.

Also I don’t know why I didn’t advise this earlier — you would be well worth investing in a ring binder (to be kept at home or whatever) for your notes. You can see already the amount of sheets. You should be organised with these and only bring the ones we are working on to class.

Next Week

On Monday we will have a tutorial where we will try and tie up as many differentiation loose ends as possible, particularly max/min & optimisation problems.

In the rest of the week we shall start our study of integration.

MATH6000: Week 5

October 18, 2012 in MATH6000 | Leave a comment

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Attendance

The attendance at lectures and tutorials has dropped alarmingly.

If you don’t attend lectures and tutorials now you will fail this module and you will be made attend the entire module again in Semester II. Please don’t let yourself be one of these people.

Assessment 1 Results

You are identified by the last four digits of your student number (I don’t have some of the Common Entry Sci student numbers please email me and I can give you your results if you’re not here). At the bottom of your group there are some average scores:

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Some Proofs by Pictures

October 17, 2012 in General | Leave a comment

We have \sin^{2n}(x)+\cos^{2n}(x) has period \pi/2 for n\in\mathbb{N}\backslash \{1\}:


 

Also \sin^{2n+1}(x)+\cos^{2n+1}(x) has period 2\pi for n\in\mathbb{N}:

 

We have \sin^{-2n}(x)+\cos^{-2n}(x) has period \pi/2 for n\in\mathbb{N}:

 

Also \sin^{-2n+1}(x)+\cos^{-2n+1}(x) has period 2\pi for n\in\mathbb{N}:

 

A Linear Algebra Problem

October 14, 2012 in General, MA 2055 | Leave a comment

Just a nice little problem I saw. The solution is not difficult but here I present a different one which I like.

Let \mathbb{P}_{1,001} be the vector space of polynomials of degree at most 1,000. Let T:\mathbb{P}_{1,001}\rightarrow \mathbb{P}_{1,001} be the linear map defined by:

\displaystyle T\{p(x)\}=2p'(x)-p(x).

Find the eigenvalues and eigenfunctions of the linear map T.

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MS2001: Week 3

October 12, 2012 in MS 2001 | Leave a comment

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Lectures

We are just about finished with Chapter 1.

Tutorials

I don’t think what I was going on about last week is going to work is it? We’ll play it by ear now.

I will happily answer questions from past papers also but I won’t but them in the question bank.

Tutorial 2 Question Bank

Questions 4, and 6 – 8 from Exercise Sheet 1 (after page 59 in the notes).

Questions 1 – 3 from MS2001: Exercises (before page 63 in the notes)

Questions 17 – 22 and 24 – 26 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

Tutorial 1 Question Bank

Questions 1, 2 and 5 from Exercise Sheet 1 (after page 59 in the notes).

Questions 1 to 16 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

MATH7021: Week 4

October 12, 2012 in MATH7021 | 2 comments

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Test 1

Consider this notice for the test on Thursday 25 October at 8.20 p.m (just under two weeks away) (I have spoken with Ted and I think there is going to be making a change to his assignment so for now we are full speed ahead for Week 6.  Note that there is still a small chance that this will be held in Week 7 Thursday 1 November at 8.20 p.m.).

Please find a sample test. I will give ye a copy of this Thursday night which will include the Finite Differences table and the Laplace Transform tables.

Note that the format will be the same as this.

  1. Forward Difference Methods (14 marks)
  2. Gaussian Elimination Methods including Partial Pivoting 7 marks)
  3. The Jacobi and Gauss-Siedel Method (7 marks)
  4. Laplace Transforms (7 marks)

Q. 4 will be covered Thursday night.

MATH6015: Week 4

October 12, 2012 in MATH6015 | Leave a comment

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Notes

So far we have covered up to and including the Duality of Algebra & Geometry: MATH6015 Lecture Notes (with gaps).

Also I don’t know why I didn’t advise this earlier — you would be well worth investing in a ring binder (to be kept at home or whatever) for your notes. You can see already the amount of sheets. You should be organised with these and only bring the ones we are working on to class.

Test!

The first test will take place at 9 am this Friday 19 October (Week 5). It is a test that could arguably take 42 minutes but I’ll give ye from 9.05 — 10 am. Please find a sample. You will be given a copy of these tables. Don’t worry I’ll scribble out the “UCC”!

Note that the format will be the same of this.

  1. Differentiation from First Principles
  2. Tangent Lines
  3. Differentiate by Rule
  4. Differentiate by Rule
  5. Differentiate by Rule
  6. Rates of Change
  7. Rate of Change/ Geometry of Graph

Next Week

On Monday we will have a tutorial where we will try and get everything sorted for the test. In the rest of the week we shall look at applying what we’ve learned about the AG-GA Dictionary to finding the local maxima and minima of functions. If you haven’t got a copy, you might want the answers to the Chain Rule exercises.

MATH6000: Week 4

October 12, 2012 in MATH6000 | Leave a comment

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Notes

As of 12 October: MATH6000 Lecture Notes (with gaps).

Also an E-Book: Engineering Mathematics by John Bird.

Also I don’t know why I didn’t advise this earlier — you would be well worth investing in a ring binder (to be kept at home or whatever) for your notes. You can see already the amount of sheets. You should be organised with these and only bring the ones we are working on to class.

Assessment 2

Your second assessment is on Wednesday 24 October in Week 6.

Trigonometry, Approximation and Statistics will be examined.

The sample is currently being drafted.

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