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**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 3

In Week 3 we finished Curve Fitting and started the second chapter on Differential Equations — with a particular emphasis on Beam Equations.

## Week 4

In Week 4 we will start looking in particular at simply supported beams.

**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.**

## Manuals

If you haven’t got your manual yet please get it ASAP.

## Tutorials

Are now running as per your timetable.

## Week 2

We introduced Lagrange Interpolation and Least Squares curve fitting.

## Week 3

We will speak briefly about the Pearson correlation coefficient, and will begin talking about fitting curves/models that aren’t of the form

## Manuals

The manuals are available in the Copy Centre. Please purchase ASAP. More information has been sent via email.

## Tutorials

Tutorials, which are absolutely vital, start next week.

## Week 1

In week one we had one and a half classes. One class was given over to a general overview of MATH7019 and we spent about half an hour introducing the topic of Curve Fitting.

## Week 2

We will introduce Lagrange Interpolation and start talking about Least Squares curve fitting.

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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 and are in direct proportion when there is some (real number) constant such that .

*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 and , 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 and 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 and such that for each value of there is a single value of , then we say that * is a function of *: is the cause and is the effect.

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

## 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 Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.

## 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 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.

## Student Resources

## 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 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 are to be taken as these constants. It is only and 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.

Some comments on common mistakes.

## 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.

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