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## Student Feedback

You are invited to give your feedback on this module here.

## Test 2

Results not too far away… watch this space.

## Week 12

We looked at centroids and centres of gravity.

## Student Feedback

You are invited to give your feedback on this module here.

## Test 2

I hope to have these corrected at some stage next week. I will also send out the solutions at some point.

## Week 11

We looked at completing the square and work.

## Week 12

We will look at centroids and centres of gravity.

## Test 2

Thursday 23 November at 09:00 in the usual lecture venue. You will be given a copy of these tables. Based on Chapter 3, samples at the back of Chapter 3 and also here (Q. 4 has a typo — it should be $e^{-x}\sin(y)$). I strongly advise you that attending tutorials alone will not be sufficient preparation for this test and you will have to devote extra time outside classes to study aka do exercises.

## Week 10

We started Chapter 4 by looking at integration by parts. We started looking at completing the square.

## Week 11

We will look at completing the square and work.

## Test 2

Tuesday 21 November Thursday 23 November at 09:00 in the usual lecture venue. You will be given a copy of these tables. Based on Chapter 3, sample at back of Chapter 3. I strongly advise you that attending tutorials alone will not be sufficient preparation for this test and you will have to devote extra time outside classes to study aka do exercises.

## Week 9

We finished looking at Partial Differentiation and then saw how it can be used in error analysis.

## Week 10

We will start Chapter 4 by looking at integration by parts. We might look at completing the square and work.

## Test 2

Tuesday 21 November at 09:00 in the usual lecture venue. Based on Chapter 3, sample at back of Chapter 3. I strongly advise you that attending tutorials alone will not be sufficient preparation for this test and you will have to devote extra time outside classes to study aka do exercises.

## Week 8

We missed a lecture with the bank holiday: we looked at Implicit Differentiation and  started Partial Differentiation.

## Week 9

We will finish looking at Partial Differentiation and see how it can be used in error analysis.

In school, we learn how a line has an equation… and a circle has an equation… what does this mean?

points $(x_0,y_0)$ on curve $\longleftrightarrow$ solutions $(x_0,y_0)$ of equation

however this note explains all of this from first principles, with a particular emphasis on the set-theoretic fundamentals.

## Set Theory

set is a collection of objects. The objects of a set are referred to as the elements or members and if we can list the elements we include them in curly-brackets. For example, call by $S$ the set of whole numbers (strictly) between two and nine. This set is denoted by

$S=\{3,4,5,6,7,8\}$.

We indicate that an object $x$ is an element of a set $X$ by writing $x\in X$, said, $x$ in $X$ or $x$ is an element of $X$. We use the symbol $\not\in$ to indicate non-membership. For example, $2\not\in S$.

Elements are not duplicated and the order doesn’t matter. For example:

$\{x,x,y\}=\{x,y\}=\{y,x\}$.

## Catch Up Material

If you have not already, you should watch:

## Week 7

We looked at Parametric Differentiation and Related Rates

## Week 8

We will look at Implicit Differentiation and Partial Differentiation.

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.

## Test 1

I will have your test with me in tutorials both this week and next.

## Week 6

We had one remaining Cramer’s Rule example (video here). We started Chapter 3 with a quick review of differentiation (video here) followed by an introduction to operators (video here), and then looked at Parametric Differentiation.

## Week 7

We will finish looking at parametric differentiation and then look at related rates.

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.

## Test 1 Results & Comments

Have been emailed to you along with the marking scheme.

I want to make the following remarks. Below we have a plot of Final Grade vs Test 1 Mark for last year’s class.

Everyone under the horizontal line failed MATH6040. Note the students in the bottom right. They got ~70% and ~80% in the Vectors test and still failed. There were various students with ~55-100% in Vectors who barely passed. On average, the final grade was about 0.6 times the Test 1 Result + 8. This means that on average students with below 53%  on Test 1 failed MATH6040. That is people to the left of the vertical line.

Therefore, note vectors is the easiest chapter in MATH6040 so don’t get too carried away with your mark. Conversely, if you have done poorly you need to take immediate action: by attending all your tutorials and possibly the Academic Learning Centre. The three students in the top left would have taken this advice. The seven students in the bottom left would not have.

The second thing to note about the results is the impact of attendance on grades. On average:

• those with satisfactory attendance got 74% — a distinction
• those with one attendance warnings got 63% — a merit 1
• those with two attendance warnings got 37% — a FAIL

The third thing to note is that perceived ability is not as important as attendance. Of those who attended the quick test, the correlation coefficient between Quick Test mark and Test 1 mark was only 0.27 while the correlation coefficient between Attendance Warnings and Test 1 mark was -0.59.

Roughly, this suggests that attendance is twice as important as ability.

## Week 5

We looked at Determinants and their use in Cramer’s Rule.

## Week 6

We will start Chapter 3 with a quick review of differentiation followed by looking at Parametric Differentiation.

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.

## Test 1

The 15% Test 1 will take place at 16:00 on 9 October, Week 5, in B263. There is a sample test in the notes.

## Week 4

We did some examples of matrix arithmetic and looked at Matrix Inverses — “dividing” for Matrices. This allowed us to solve matrix equations. Here find a note that answers the question: why do we multiply matrices like we do?

## Week 5

We will look at linear systems, and determinants.

 J.P. McCarthy on About Leaving Cert Applied… Student on About Leaving Cert Applied… J.P. McCarthy on MATH6038: Spring 2018, Week… Student on MATH6038: Spring 2018, Week… The Line of Best Fit… on Quadratics: A First Look