You are currently browsing the category archive for the ‘MS 2001’ category.

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 have finished section 1.3.

## Tutorials

The tutorials start on Wednesday.

At the start of the tutorial I will answer any questions about the notes/theory/course.

After this however I am going to put ye into two competing groups.

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.

We have covered up to the point where we showed not all real numbers are fractions.

## Tutorial Slot

We are going with Wednesdays 10-11 in Windle room ANLT (beside the Old Bar). These start in Week 3 (10 October 2012).

## Tutorial Question Bank

Question 35 from the Additional but Harder Exercises for De nitions I (in notes).

Please find pdf files containing solutions to the summer exam here and here.

Due to not having Adobe Acrobat in the lab and not being very good at using the scanner these files are mixed up and by and large comprise the odd pages and the even pages.

## Test Results

First of all results are down the bottom. You are identified by the last five digits of your student number. The scores are itemized as you can see. At the bottom there are some average scores.

If you would like to see your paper or have it discussed please email me.

Students with no score were either absent in which case they score zero — or certified absent in which case their marks carry forward to the summer exam.

## Marking Scheme, Continuous Assessment Summary and Remarks

Mostly under construction…

The Marking Scheme.

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.

## These Weeks

In lectures, we finished off the notes.

## Review Week

I will hold a tutorial on Tuesday at the same time and place. I should have the results of Test 2 by then.

## Appraisal

Thank you very much for your work on the appraisal. Sorry about all the hairstyles.

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.

## Test 2

See here for full details.

## This Week

In lectures, we covered sections 4.3 to Summary 4.5.5 inclusive.

In the tutorial we answered Q. 9 (ii) from Exercise Sheet 1, Q. 10 (iii), 16 from Exercise Sheet 3 and Q.2 from Exercise Sheet 4.

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.

## Test 2

The second test will take place 7 December 2011 at 09:00 in WGB G 05 (not the same room as the lecture).

Everything from Section 2.4 Continuity on Closed Intervals to Section 4.5 Asymptotes and Asymptotics (inclusive of both) is examinable.

Please find a Sample. Note that this is a new sample. I don’t want any of ye thinking just that because Test 1 was very similar to last year’s Test 1 and Sample that Test 2 will be very similar to last year’s Test 2 and sample. The sample is to show you the structure of the test. The paragraphs above and below describe what can come up. Hence have a cautious look at last year’s Sample, Test A and Test B (the latter two with solutions).

Just a chance for me to give some feedback on some of your most common… feedback. Of course your opinions are correct – they are your opinions. Here are my opinions on some of your opinions.

Normally the failing of teaching evaluation, is that ye never see the fruits of your criticisms. However, as I am currently drafting the MS 2002 notes ye have had a chance to improve your lot in this module at least.

A lot of people felt that through a combination of not leaving ye enough time to fill in notes, talking to fast or just going to fast, that ye didn’t have enough time to digest explanations. At least for the rest of this module we can address that.

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 Rolle’s Theorem to the end of the chapter on differentiation.

In the tutorial we answered exercises Q. 2, 5, 6 & 7(b) from Exercise Sheet 3. I had been very confused by Q. 7(b). We showed that $f(x)=x+\sin x$ had a horizontal tangent at $x=\pi$ but I couldn’t see how it could have a unique max or min given that $f(0)=0$ and $f(2\pi)=2\pi$ — but as we shall see in the next ten days, while $f'(x)=0$ is necessary for a (differentiable) max or min, it is not sufficient. That is

(differentiable) maximum or minimum $\Rightarrow$ $f'(x)=0$

but

$f'(x)=0\not\Rightarrow$ (differentiable) maximum or minimum

necessarily. There is a third possibility, that of a saddle point that is neither a local maximum nor minimum. This is the case with $f(x)=x+\sin x$ as this plot shows (by the way that Wolfram Alpha is an unbelievable piece of kit — have a play around with it).

## Test 2

Just giving fair warning about test 2 — it will be held on December 7. More details next week.

## Problems

You need to do exercises – all of the following you should be able to attempt. Do as many as you can/ want in the following order of most beneficial:

### Wills’ Exercise Sheets

Q. 6, 11, 12, 13, 14, 16 & 17 from Exercise Sheet 3.

Q. 1 from Exercise Sheet 4.

More Exercise Sheets

Nothing from Problems.

### Past Exam Papers

Q. 4(a) from Summer 2010.

Q. 3 from Autumn 2010.

Q. 3(b) from Summer 2009.

Q. 3 from Autumn 2009.

Q. 3(b) & 4(b) from Summer 2008.

Q. 4 from Autumn 2008.

Q. 4 from Summer 2007.

Q. 4(a) from Autumn 2007.

Q. 4(a) & 5(b) from Summer 2006.

Q. 5(a) & 6(a) Autumn 2006.

Q. 5(a) from Summer 2005.

Nothing from Autumn 2005.

Q. 5(a) & 6(a) from Summer 2004.

Q. 3(a), 5(a) & 6(a) from Autumn 2004.

Q. 5(a) & 6(a) from Summer 2003.

Q. 5(a) & 6(a) from Autumn 2003.

Nothing from Summer 2002.

Q. 4(c), 5(a) & 6(a) from Summer 2001.

Q. 4(c), 5 & 6(a)   from Summer 2000.

### From the Class

1. Prove Rolle’s Theorem in the case where $f(a)\neq m$.
2. Prove that the function $F(x)$ defined in the proof of the Mean Value Theorem satisfies $F(a)=F(b)$.
3. Prove Proposition 3.2.3 (iii)
4. Prove that $2012^n>2011$ for $n\geq2$$n\in\mathbb{N}$.

## Supplementary Notes

A list of implicitly defined curves.

I HAVE TAKEN CARE OF THE DUPLICATE STUDENT NUMBER FOUR DIGIT ENDINGS — ALL OF THESE STUDENTS HAVE RECEIVED AN EMAIL SO YOU DON’T HAVE TO CHECK FOR A DUPLICATE. I HAVE EDITED THE MARK DISPLAY TO TAKE THIS INTO ACCOUNT (the duplicates are last five digits)

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

On Wednesday, we covered from (but not including) Corollary 3.1.6 to Rolle’s Theorem (although we only started the proof).

In the tutorial we answered exercises Q. 1, 3 & 8(a) from Exercise Sheet 3.

## Problems

You need to do exercises – all of the following you should be able to attempt. Do as many as you can/ want in the following order of most beneficial:

### Wills’ Exercise Sheets

Q. 3, 5, 7, 8 (b), 9 & 10 from Exercise Sheet 3.

More Exercise Sheets

Q. 3 from from Problems.

### Past Exam Papers

Q. 1(c) & 4(b) from Summer 2010.

Q. 1(c) & 4 from Autumn 2010.

Q. 1(c) & 4 from Summer 2009.

Q. 1(c) & 4 from Autumn 2009.

Q. 4(a) from Summer 2008.

Q. 1(c) & 4(a) from Autumn 2008.

Q. 1(c) & 3 from Summer 2007.

Q. 1(c) from Autumn 2007.

Q. 3(b), 4(b) & 5(a) from Summer 2006.

Q. 3(b) & 4(b) Autumn 2006.

Q. 4(a) from Summer 2005.

Q. 4 & 5(a) from Autumn 2005.

Q. 4 from Summer 2004.

Q. 4(b) from Autumn 2004.

Q. 4(b) from Summer 2003.

Q. 4 from Autumn 2003.

Q. 4 & 5(a) from Summer 2002.

Q. 1(b), 5(b) & 6(b) from Summer 2001.

Q. 1(b),  from Summer 2000.

Nothing here.

## Supplementary Notes

The proof of the chain rule and the “chain rule by rule” here.