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“Straight-Line-Graph-Through-The-Origin”

The words of Mr Michael Twomey, physics teacher, in Coláiste an Spioraid Naoimh, I can still hear them.

There were two main reasons to produce this straight-line-graph-through-the-origin:

• to measure some quantity (e.g. acceleration due to gravity, speed of sound, etc.)
• to demonstrate some law of nature (e.g. Newton’s Second Law, Ohm’s Law, etc.)

We were correct to draw this straight-line-graph-through-the origin for measurement, but not always, perhaps, in my opinion, for the demonstration of laws of nature.

The purpose of this piece is to explore this in detail.

## Direct Proportion

Two variables $P$ and $Q$ are in direct proportion when there is some (real number) constant $k$ such that $P=k\cdot Q$.

Correlation does not imply causation is a mantra of modern data science. It is probably worthwhile at this point to define the terms correlation, imply, and (harder) causation.

### Correlation

For the purposes of this piece, it is sufficient to say that if we measure and record values of variables $x$ and $y$, and they appear to have a straight-line relationship, then the correlation is a measure of how close the data is to being on a straight line. For example, consider the following data:

The variables $y$ and $x$ have a strong correlation.

### Causation

Causality is a deep philosophical notion, but, for the purposes of this piece, if there is a relationship between variables $y$ and $x$ such that for each value of $x$ there is a single value of $y$, then we say that $y$ is a function of $x$: $x$ is the cause and $y$ is the effect.

In this case, we write $y=f(x)$, said $y$ is a function of $x$. This is a causal relationship between $x$ and $y$. (As an example which shows why this definition is only useful for the purposes of this piece, is the relationship between sales $t$ days after January 1, and the sales, $S$, on that day: for each value of $t$ there is a single value of $S$: indeed $S$ is a function of $t$, but $t$ does not cause $S$).

## Student Feedback

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

## Assessment 2

Results have been emailed to you. You have a chance to see your work this Friday in tutorial. Some comments here.

## Week 12

I postponed Monday’s lecture. We nearly finished off Chapter 4 by looking at Error Analysis. I had to email ye on the last two rounding error examples.

## Week 13

We will go through last year’s exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one. Usual class times and locations.

We will also have tutorials on Friday 8 December in the usual times and venues.

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

## Student Feedback

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

## Assessment 2

Results have been emailed to you. You have a chance to see your work this Friday in tutorial. Some comments here.

## Week 11

We looked at more general Taylor Series: not just near $a=0$ and also for functions of several variables.

## Week 12

We will finish off Chapter 4 by looking at Error Analysis.

## Week 13

We will go through last year’s exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one. Usual class times and locations.

We will also have tutorials on Friday 8 December in the usual times and venues.

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

## Assessment 2

Has now been submitted. I am going to do my utmost to get these corrected ASAP.

## Week 10

We looked at Hypothesis Testing and began Chapter 4 with a Revision of Differentiation. We looked then at Maclaurin Series.

## Week 11

We will look at more general Taylor Series: not just near $a=0$ and also for functions of several variables.

## Assessment 2

Deadline 16:00, Monday 20 November, Week 11. Note that when you open MATH7019A2 – Student Data, you should see a list of numbers that you are supposed to use in the questions. All of the $w_i,\,L_i,\,a,\,b$ are to be taken as these constants. It is only $E$ and $I$ that are to be kept as ‘free variables’.

## Week 9

We finished looking at the normal distribution and then looked at Sampling Theory.

## Week 10

We will look at Hypothesis Testing and begin Chapter 4 with a Revision of Differentiation.

## Assessment 1

Apologies that it took until this week to get the results back to you. I will bring the assignments with me tomorrow (Friday 3 November, Week 8) for you to have a look at.

By and large I was happy with the work. I might, however, send out a warning. I think it has been the case that students do far better in Assessment 1 than they do in the Final Exam.

## Assessment 2

Deadline 16:00, Monday 20 November, Week 11

## Week 8

We missed the Monday Lecture with the bank holiday. On Wednesday we looked at the Poisson distribution and started talking about the Normal distribution.

## Week 9

We will finish looking at the Normal distribution and then look at Sampling Theory.

## Catch-Up Material

Please watch this cantilever example and this summary of beams if you have not done so already.

## Week 7

We finished looking at Chapter 2 by looking at the Three Term Taylor Method for approximating solutions of ordinary differential equations.

On Wednesday we started Chapter 3 (Probability and Statistics) by looking at some general concepts in probability and then we looked at random variables with a binomial distribution.

We lose a tutorial on Friday with the day off.

## Week 8

We miss another lecture on Monday with the bank holiday. Wednesday, we will look at the Poisson distribution and perhaps the Normal distribution.

## Assessment 1

I would have hoped to have finished the corrections by now however this has been delayed by a number of factors. My hope would be to have the results for you next week. Apologies for this delay.

## Assessment 2

Deadline 16:00, Monday 20 November, Week 11

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage — especially those of us who struggled in the test.

## Student Resources

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.

## Week 6

The storm cost us one lecture. Please watch this cantilever example and this summary of beams to catch up. Wednesday, we looked at Euler’s Method in the morning and had an extra tutorial in the evening.

## Week 7

In Week 7 we will look at the Three Term Taylor Method and begin Chapter 3 on Probability and Statistics.

## Assessment 2

Assessment 2 will be handed out on Friday but doesn’t have to be completed until the Monday of Week 11, giving you more than five full weeks to complete it.

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage — especially those of us who struggled in the test.

## Student Resources

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.

## Week 5

In Week 5 we finished looking at simply supported beams. We then looked at fixed end beams and cantilevered beams.

## Week 6

In Week 6 we will summarise what we learnt about beam and look at numerical approximations to solutions of differential equations that we cannot solve exactly.

## Assessment 1

Assessment 1 has been emailed to all of you. The hand in date is, tomorrow,  17:30 Thursday 12 October 2017. I will be in A283 from 10:00-12:00 and 13:00-17:30. Work handed in late shall be assigned a mark of zero.

## Assessment 2

Assessment 2 will be handed out on Friday but doesn’t have to be completed until the Monday of Week 11, giving you more than five full weeks to complete it.

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage — especially those of us who struggled in the test.