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The manuals are available in the Copy Centre (at a cost of €15) and should be purchased as soon as possible.

## Timetable Issues

For this week only, the SEE2 tutorial at 3 pm on Thursday will not go ahead. Instead the SEE2 tutorial will be held in **A272 at 12 pm on Wednesday.**

Please keep an eye on your email on Monday. If the AV situation is not sorted in A272 by then I will be trying to arrange alternative rooms (which has its own risks).

## Week 1

We began our study of Chapter 1, Vector Algebra by studying the difference between a scalar (single number) and a vector (list of numbers). We looked at how to both visualise vectors and describe them algebraically. We learned how to find the magnitude and direction of a vector, add them and scalar multiply them. We spoke about displacement vectors.

## Week 2

In Week 2 we will talk about vector products: the dot product and the vector product.

## Test 1

The test will probably be the Tuesday evening, 11 October, of Week 5. Official notice will be given in Week 3. There is a sample test in the notes.

## Study

Please feel free to ask me questions about the exercises via email.

## Student Resources

Please see Student Resources for information on the Academic Learning Centre, etc.

## Mathematics Exam Advice

- The first piece of advice is to read questions carefully. Don’t glance at a question and go off writing: take a moment to understand what you have been asked to do.
- Don’t use tippex; instead draw a simple line(s) through work that you think is incorrect.
- For equations, check your solution by substituting your solution into the original equation. If your answer is wrong and you know it is wrong: write that on your script.

If you do have time at the end of the exam, go through each of your answers and ask yourself:

- have I answered the question that
__was asked__? - does my answer make sense?
- check your answer (e.g. differentiate/antidifferentiate an antiderivative/derivative, substitute your solution into equations, check your answer against a rough estimate, or what a picture is telling you, etc)

## Student Feedback

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

## Test 2 – Results

Have been emailed to you along with final CA results.

## Week 12

We looked at centroids of laminas and centres of gravity of solids of revolution.

We had one and a half classes of tutorial time.

## Week 13

There is an exam paper at the back of your notes — I will go through this on the board in the lecture times (in the usual venues):

- Monday 16:00
- Tuesday 09:00
- Thursday 09:00

We will also have tutorial time in the tutorial slots. You can come to as many tutorials as you like.

- Monday at 09:00 in B180
- Monday at 17:00 in B189
- Wednesday at 10:00 in F1. 3

The exam is on Friday 13 December. Past exam papers (MATH6040 runs in Semester 1 and Semester 2) may be found here.

## Student Feedback

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

## Test 2 – Results

Possibly early next week. I am a little behind in my corrections after being sick last week though. Definitely Thursday.

## Week 11

We had our test on Monday, then will looked at completing the square, and work on Tuesday and Thursday.

Here is some video of revision antidifferentiation.

## Week 12

We will look at centroids of laminas and centres of gravity of solids of revolution. Any spare lecture time will be given over to tutorial time.

## Week 13

There is an exam paper at the back of your notes — I will go through this on the board in the lecture times (in the usual venues):

- Monday 16:00
- Tuesday 09:00
- Thursday 09:00

We will also have tutorial time in the tutorial slots. You can come to as many tutorials as you like.

- Monday at 09:00 in B180
- Monday at 17:00 in B189
- Wednesday at 10:00 in F1. 3

The exam is on Friday 13 December.

## Test 2

On Chapter 3, on at **5 pm (not 4 pm) Monday 25 November, Week 11 in Melbourne Hall. You will have one full hour.**

The BioEng2B tutorial will take place from 4 pm sharp to 4.45 pm in B263 on that day.

Chapter 3: Differentiation is going to be examined. A Summary of Differentiation (p.147-8): you will want to know this stuff very well. You will be given a copy of these tables.

There is a sample test on p. 149 of the notes.

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.

Between tutorials and private study you really should aim to have completed as least the following:

- P. 113, Q. 1-6 (not 5c or 6iii)
- P. 119, Q. 1-4
- P. 127, Q. 1-4
- P. 138, Q. 1-3
- P. 146, Q. 1-4
- The Sample Test

There are more questions in most of these exercises.

If you are having any problem, take a photo of your work and email me your question.

## Week 10

We started Chapter 4 on (Further) Integration with a revision of antidifferentiation, and had a look at Integration by Parts. We used implicit differentiation to differentiate inverse sine.

## Week 11

We have our test on Monday, then we will look at completing the square, and work on Tuesday and Thursday.

## Week 12

We will look at centroids of laminas and centres of gravity of solids of revolution. Any spare lecture time will be given over to tutorial time.

## Week 13

There is an exam paper at the back of your notes — I will go through this on the board in the lecture times (in the usual venues):

- Monday 16:00
- Tuesday 09:00
- Thursday 09:00

We will also have tutorial time in the tutorial slots. You can come to as many tutorials as you like.

- Monday at 09:00 in B180
- Monday at 17:00 in B189
- Wednesday at 10:00 in F1. 3

The exam is on Friday 13 December.

## Test 2

On Chapter 3, on at **5 pm (not 4 pm) Monday 25 November, Week 11 in Melbourne Hall. **

The BioEng2B tutorial will take place from 4 pm sharp to 4.45 pm in B263 on that day.

Chapter 3: Differentiation is going to be examined. A Summary of Differentiation (p.147-8): you will want to know this stuff very well. You will be given a copy of these tables.

There is a sample test on p. 149 of the notes.

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.

Between tutorials and private study you really should aim to have completed as least the following:

- P. 113, Q. 1-6 (not 5c or 6iii)
- P. 119, Q. 1-4
- P. 127, Q. 1-4
- P. 138, Q. 1-3
- P. 146, Q. 1-4
- The Sample Test

There are more questions in most of these exercises.

If you are having any problem, take a photo of your work and email me your question.

## Week 9

We looked at partial differentiation and its applications to differentials and error analysis.

I had hoped to do a Concept MCQ for Chapter 3 but we kind of ran out of time… I would ask ye to complete this (on your own) before Monday.

## Week 10

We will start Chapter 4 on (Further) Integration. A good revision of integration/antidifferentiation may be found here, but this material will be gone through in Monday’s lecture..

## Test 2

On Chapter 3, on at **5 pm (not 4 pm) Monday 25 November, Week 11 in Melbourne Hall. **

The BioEng2B tutorial will take place from 4 pm sharp to 4.45 pm in B263 on that day.

Chapter 3: Differentiation is going to be examined. A Summary of Differentiation (p.147-8): you will want to know this stuff very well. You will be given a copy of these tables.

There is a sample test on p. 149 of the notes.

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 finished looking at Related Rates and then we looked at and finished Implicit Differentiation.

I have video of the above material here.

We then start looking at Functions of Several Variables.

## Week 9

We will look at partial differentiation and its applications to differentials and error analysis.

We might start Chapter 4 on (Further) Integration. A good revision of integration/antidifferentiation may be found here.

## Test 1

Results and Marking Scheme have been emailed to you.

## Test 2

On Chapter 3, is planned for **5 pm (not 4 pm) Monday 25 November. **Please contact me if this poses a problem for you.

## Outlook

For *most *students, Chapters 1 and 2 are easier and you will want to do well on them. Things are going to get a little harder for the rest of the semester and you will need to attend class regularly and prepare well for Test 2.

You have already been recommended to use your Reading Week:

“*If you plan on doing some work on MATH6040 over the Reading Week, may I recommend looking at Chapter 2 exercises:*

*P. 95, Q. 1 (find*

__b only__), Q. 2-4*P. 85, Q. 1*

*P. 80, Q. 1-4*

*P. 84, Q. 1-2*

*P. 64, Q. 1-4 (remember BEMDAS — AD^T = A(D^T) not = (AD)^T)*

*If you are happy with these look at the differentiation revision: p.103, Q.1-2*

*You can email me at any time if you have any questions.*

”

## Week 7

We started Chapter 3 with a review of differentiation followed by a look at Parametric Differentiation.

Here are two videos if you missed this material:

We mentioned briefly the Reuleaux Triangle and it’s use in the “Harry Watt Square Drill Bit”. See here for an animation of how this works.

## Week 8

We will finish looking at Related Rates and then look at Implicit Differentiation. If you are interested in a very “mathsy” approach to curves you can look at this.

## Test 1

As I said in Tuesday’s lecture, I was a little concerned to see so many people still writing when time was up.

I said that the test is normally 55 rather than 50 minutes long (due to restrictions placed on me by the Exams Office (that I subsequently saw were unnecessary)), but that I had thought I had adjusted the test appropriately.

There are two main reasons why people might have been still writing with time up:

- people, primarily due to missing too many classes, were not prepared properly, and/or
- the test was too long

I can apologise unreservedly if it was the case that the test was too long.

How I can I fix this?

First of all, for the second test I will give ye the full hour rather than 55 minutes.

The second thing I will do is look back on last year’s results for Test 1 and look at the average of those:

- with zero attendance warnings
- with one attendance warnings
- with two attendance warnings
- with three attendance warnings

If these differ significantly from this year’s averages, I will adjust upwards the marks appropriately.

If I don’t see a significant difference I am going to put the fact that people were still writing with no time left as primarily down to them not having prepared properly for the test.

## Week 6

We had the test on Monday and this meant we could not start a review of differentiation. On Tuesday we looked at Cramer’s Rule, and then on Thursday we did one more question followed by a Concept MCQ on Matrices.

I actually have videos from last year if you missed some classes from Week 6:

## Week 7

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

If you want to look ahead here are two videos:

## Test 1

Test 1, worth 15%, takes place from 16:00 to 16:50 sharp, Monday 14 October in the Melbourne Hall (rows I-K). I will have emailed your 15:00-16:00 lecturers so that they will leave you plenty of time to get to the Melbourne.

There is a sample on P.46 of the notes to give you an idea of the length and layout only.

Almost everything in Chapter 1 is examinable. Additional practise questions may be found by looking at past exam papers (usually vectors are Q. 1, sometimes Q. 2).

You will want to be familiar with all the concepts in the Vector Summary, P. 42-45.

You can check your work against the Sample Test Marking Scheme.

Any questions at all, you can email me, perhaps with a screenshot of your attempt. There are also a number of you in the Telegram group which has thus far been silent.

**HINT** (*very* rare): Look at “*Vector of a Given Magnitude in a Given Direction*” on p.15-16. Thus, also, Example 3 **Winter 2017 **on p.37-38, Example 4 **Summer 2016 **on p.38, and **Autumn 2018 **on p.39-40.

## Week 5

We look at Matrix Inverses — “dividing” for Matrices. This allowed us to solve matrix equations. We looked at linear systems, and determinants.

## Week 6

We will finish looking at Chapter 2 and then we will start Chapter 3 with a review of differentiation followed, perhaps, by a look at Parametric Differentiation.

**Your timetable is wrong in the naming of this module. MATH6040 is Technological Maths 201 and not Technological Maths 2. You did Technological Maths 2: MATH6015, last year.**

## Test 1

Test 1, worth 15%, takes place from 16:00 to 16:50 sharp, Monday 14 October in the Melbourne Hall (rows I-K). I have emailed your 15:00-16:00 lecturers so that they will leave you plenty of time to get to the Melbourne.

There is a sample on P.46 of the notes to give you an idea of the length and layout only.

Almost everything in Chapter 1 is examinable. Additional practise questions may be found by looking at past exam papers (usually vectors are Q. 1, sometimes Q. 2).

You will want to be familiar with all the concepts in the Vector Summary, P. 42-45.

## Week 4

We finished looking at the applications of vectors to work and moments and began Chapter 2: Matrices. We did some examples of matrix arithmetic. Here find a note that answers the question: why do we multiply matrices like we do?

We also did a Concept MCQ to summarise Chapter 1.

## Week 5

We will look at Matrix Inverses — “dividing” for Matrices. This will allow us to solve matrix equations. We will look at linear systems, and possibly determinants.

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