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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

We started working with the cross product and began to look at the applications of vectors to work. and moments.

## Week 4

We will finish looking at the applications of vectors to work and moments and perhaps begin Chapter 2: Matrices.

## Test 1

The 15% Test 1 will take place at 16:00 on 15 October, Week 6, in B263. There is a sample test in the notes. Chapter 1: Vectors is going to be examined.

## Study

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

## 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.

## Tutorials

Are now running as per your timetable.

## Week 2

We looked at how to both visualise vectors and describe them algebraically. We learned how to find the magnitude  and direction of a vector, and add them and scalar multiply them. We spoke about displacement vectors and introduced the vector product known as the dot product.

## Week 3

We will start working with the vector product and begin to look at the applications of vectors to work and moments.

## Test 1

The test will probably be the Monday of Week 5: if progress with the vectors material is slow, we may push this out to Week 6. Official notice will be given in Week 3 (or Week 4 if necessary). There is a sample test in the notes.

## Study

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

## 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.

## Manuals

The manuals are available in the Copy Centre and must be purchased as soon as possible. More information has been sent out via email.

## Tutorials

Tutorial for BioEng2A: Thursdays at 12:00 in B180 A272 STARTS THURSDAY 20/09

Tutorial for BioEng2B: Mondays at 17:00 in B189 STARTS MONDAY 24/09

Tutorial for SET2: Mondays at 9:00 in E15 STARTS MONDAY 24/09

If you are a little worried about your maths this semester, perhaps after the Quick Test or in general, I would just like to remind you about the Academic Learning Centre. Next week, some students will receive slips detailing areas of maths that they should brush up on. The timetable is as below:

Maths/Statistics Support in the ALC (Academic Learning Centre)

 Monday 1.00pm-2.00pm D259 4.00pm-5.00pm D259 Tuesday 1.00pm-2.00pm D259 4.00pm-6.00pm D259 Thursday 10.00am-12.00pm D259 Friday 11.00am- 1.00pm D259

## Week 1

We only had one lecture but began our study of Chapter 2, Vector Algebra by studying the difference between a scalar (single number) and a vector (list of numbers).

## Week 2

We will look at how to both visualise vectors and describe them algebraically. We will learn how to find the magnitude  and direction of a vector, add them and scalar multiply them. We will speak about displacement vectors and introduce the vector product known as the dot product.

## Test 1

The test will probably be the Monday of Week 5: if progress with the vectors material is slow, we may push this out to Week 6. Official notice will be given in Week 3 (or Week 4 if necessary). There is a sample test in the notes.

## 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.

## 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.