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### Differentiation Test

Test Tuesday 20 April 19:30 to 20:45. Five questions, one for each of the five sections in Chapter 3.

You can find old (e.g. Chapter 3) videos on my YT channel here. (Links to an external site.)

One more video that is actually Chapter 3 material (and the recording was a little messed up so no live writing… a new version will be in the Week 11 lectures.):

## Week 10

### Lectures

Revision of integration and integration by parts.

- Revision of Integration (Links to an external site.) (44 minutes)
- Integration by Parts (Links to an external site.) (36 minutes)

Here are last year’s lectures of the same material:

- Revision of Antidifferentiation: Direct and Manipulation (Links to an external site.) (27 minutes)
- Revision of Antidifferentiation: Substituion (Links to an external site.) (22 minutes)
- Integration by Parts (Links to an external site.) (30 minutes)

I recorded a lot of this material before in a live lecture: press here to watch live version (Links to an external site.) (84 minutes).

### Exercises

How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises.

Try:

- p. 165, Q.1-13
- p. 171, Q.1-5

Additional Exercises: p. 171, Q. 6-9

Submit work for Canvas feedback by Sunday 18 April for video feedback after Monday 19 April.

## Outlook

### Week 11

Perhaps of the order of 1.5 hours of lectures on completing the square (Links to an external site.), and work (Links to an external site.).

### Week 12

Perhaps of the order of 1.5 hours of lectures on centroids (Links to an external site.) of laminas and centres of gravity of solids of revolution (Links to an external site.).

### Weeks 13 and 14

I will continue to provide learning support.

## Assessment Schedule

**Week 11 ** – 25% Differentiation Test *(Zoom Tutorial in Week 10, after Easter)*

**Week 14 **– 25% Integration Test *(Zoom Tutorial in Week 13)*

## Study

Please feel free to ask me questions about the exercises via email. I answer emails every morning seven days a week.

## Student Resources

Please see Student Resources (Links to an external site.) for information on the Academic Learning Centre, etc.

*Easter might provide extra time to put into Chapter 3.*

## Matrices Test — Corrections

I have a bit of a backlog of corrections but hopefully I can get these to ye before Easter Sunday.

## Week 9

### Lectures

Final two sections of Chapter 3:

- Partial Differentiation I (31 minutes)
- Partial Differentiation II (38 minutes)
- Error Analysis using Differentials (30 minutes)
- Error Analysis Example (5 minutes)

Here are last year’s lectures of the same material:

- Functions of Several Variables (12 minutes)
- Partial Differentiation: Theory (25 minutes)
- Partial Differentiation: Examples (11 minutes)
- Higher Order Partial Derivatives (21 minutes)
- Partial Differentiation Tutorial (9 minutes)
- Differentials (10 minutes)
- Propagation of Errors (7 minutes)
- Propagation of Error Examples (25 minutes)

### Exercises

How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises.

Try:

- p. 143, Q. 1-5 [Note these exercises are
*interleaved –*there are questions here from earlier sections in Chapter 3] - p. 150, Q. 1-6 [Note these exercises are
*interleaved –*there are questions here from earlier sections in Chapter 3]

Additional Exercises: p. 143, Q. 6, p. 151, Q.7-8, 9-10

Submit work for Canvas feedback by Sunday 28 March for video feedback after Monday 29 March.

## Outlook

I will be providing learning support over Easter.

Looking further ahead, to after Easter, a good revision of integration/antidifferentiation may be found here. Here is some video of revision of antidifferentiation.

## Week 10

Perhaps of the order of 1.5 hours of lectures on starting Chapter 4 on (Further) Integration with a revision of antidifferentiation, and a look at Integration by Parts. We will use implicit differentiation to differentiate inverse sine.

## Week 11

Perhaps of the order of 1.5 hours of lectures on completing the square, and work.

## Week 12

Perhaps of the order of 1.5 hours of lectures on centroids of laminas and centres of gravity of solids of revolution.

## Assessment Schedule

**Week 11 ** – 25% Differentiation Test *(Zoom Tutorial in Week 10, after Easter)*

**Week 14 **– 25% Integration Test *(Zoom Tutorial in Week 13)*

## Study

Please feel free to ask me questions about the exercises via email. I answer emails every morning seven days a week.

## Student Resources

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

*Things are definitely getting more difficult now folks. I am happy with the work a lot of ye are putting in but from now on everyone will have to work hard if they want to succeed. The good news is that Easter might provide extra time to put into Chapter 3.*

## Week 8

### Lectures

Two sections of Chapter 3:

- Related Rates (28 minutes)
- Implicit Differentiation I (24 minutes)
- Implicit Differentiation II (22 minutes)

If you are interested in a very “mathsy” approach to curves you can look at this. I have live video of some of the above material here.

### Exercises

How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises.

When you are finished with the material for Test 2 (Weeks 4-6) you can try:

- p. 120, Q. 1-3
- p. 128, Q. 1-5 [Note these exercises are
*interleaved –*there are questions here from earlier sections in Chapter 2]

Additional Exercises: p. 121, Q. 4-7, p. 130, Q.5-7

Submit work for Canvas feedback by Sunday 21 March for video feedback after Monday 22 March.

## Week 9

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

Looking further ahead, a good revision of integration/antidifferentiation may be found here.

## Assessment Schedule

**Week 5 **– 25% Vectors Test

**Week 8 **– 25% Matrices Test *(Zoom Tutorial in Week 7)*

**Week 11 ** – 25% Differentiation Test *(Zoom Tutorial in Week 10)*

**Week 14 **– 25% Integration Test *(Zoom Tutorial in Week 13)*

## Study

Please feel free to ask me questions about the exercises via email. I answer emails every morning seven days a week.

## Student Resources

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

## Week 7

### Lectures

Some revision and some new material, need about two hours to carefully watch:

- Revision of Differentiation (21 minutes)
- Operators/Transforms (11 minutes)
- Parametric Differentiation I (34 minutes)
- Parametric Differentiation II (15 minutes)

### Exercises

When you are happy with Chapter 2 (Weeks 4-6) you can try:

- p. 103, Q. 1-3
- p. 115, Q. 1-3

Additional Exercises: p. 116, Q. 4-7

Submit work for Canvas feedback by Sunday 14 March for video feedback after Monday 15 March.

## Matrices Test — Week 8, 19:30 16 March

We will have a Zoom Tuesday 8 March at 20:00 for any questions that ye would like to ask about this assessment. This tutorial will be recorded in the cloud.

## Week 8

We will look 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.

I have live video of the above material here.

## Week 9

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

Looking further ahead, a good revision of integration/antidifferentiation may be found here.

## Assessment Schedule

**Week 5 **– 25% Vectors Test

**Week 8 **– 25% Matrices Test *(Zoom Tutorial in Week 7)*

**Week 11 ** – 25% Differentiation Test *(Zoom Tutorial in Week 10)*

**Week 14 **– 25% Integration Test *(Zoom Tutorial in Week 13)*

## Study

## Student Resources

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

## Week 6

### Lectures

Very little by way of lectures this week, so that you can put the bulk of your time towards catching up on Chapter 2

- Matrix Determinants (22 minutes)
- Cramer’s Rule (27 minutes)

### Exercises

Assuming you have a handle on the exercises from Week 4 and Week 5 you can try:

- p. 84, Q.1-3
- p.94, Q. 1-6

Additional Exercises: p. 96, Q. 1-10

Submit work for Canvas feedback by Sunday 7 March for video feedback after Monday 8 March. Ideally you don’t submit work that you are certain is correct, but instead submit work you need help and feedback with. Submit the images as a single pdf file. To do this, select all the images in a folder, right-click and press print. It will say something like *How do you want to print your pictures?* Press (Microsoft?) Print to PDF. If possible choose an orientation that has all the images in portrait.

## Matrices Test — Week 8, 19:30 16 March

The open-book assessment will be designed to be done in about 45 minutes, however you will be given one hour to complete the assignment along with an additional 15 minutes to upload your work. 45 minutes means about one and a half exam questions (see MATH6040 matrices questions (Links to an external site.) ( (usually matrices are Q. 2, sometimes Q. 1)) to get an idea of how long one exam question is). Please contact me if the timing is an issue.

The assessment is based on Chapter 2. There will be five questions broken into parts (a), (b), and (c). Some/most of the part (c)s should be easier than in the Vectors Test. Some of the part (a)s will be a little harder.

Additional practise questions (beyond the manual) may be found by looking at past MATH6040 exam papers (Links to an external site.).

Academic Dishonesty will not be accepted and suspected breaches, such as communication with others during the assessment, will be pursued in line with this policy (Links to an external site.).

We will have a Zoom Tuesday 8 March at 20:00 for any questions that ye would like to ask about this assessment. This tutorial will be recorded in the cloud.

## Week 7

We will do a quick revision of differentiation. If you want to look ahead here are two videos:

Then we will look at Parametric Differentiation.

## 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 want to try and do homework regularly.

## Assessment Schedule

**Week 5 **– 25% Vectors Test

**Week 8 **– 25% Matrices Test *(Zoom Tutorial in Week 7)*

**Week 11 ** – 25% Differentiation Test *(Zoom Tutorial in Week 10)*

**Week 14 **– 25% Integration Test *(Zoom Tutorial in Week 13)*

## Study

## Student Resources

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

## 25% Vectors Test, 19.30 Tuesday 23 February

This is just repeating some the information from Week 4:

*The open-book assessment will be designed to be done in about 45 minutes, but you have an hour and 15 minutes including time for uploading.*

*The assessment is based on Chapter 1. The questions into parts (a) (easy), (b) (medium), and (c) (hard).** You might be advised to do all the parts (a) and (b) first, try and get as close to 70% as possible with those, and then leave the parts (c) to the end. Otherwise you might waste time doing parts (c) when there are easier and more marks available in parts (b) and particularly (a).*

*Academic Dishonesty will not be accepted and suspected breaches, such as communication with others during the assessment, will be pursued in line with this policy.*

*We had a Zoom tutorial: it is in the cloud*.

## Week 5

### Lectures

As promised very few lectures so that if you have been a little behind on Chapter 2 already you can catch up after Test 1

- Linear Systems (26 minutes)

### Exercises

Assuming you are ready for the Vector Assessment, and have a handle on the Week 4 exercises try

p.79, Q.1-4

Additional Exercises: p. 79, Q.5-6

Submit work for Canvas feedback by Sunday 28 February for video feedback after Monday 1 March. Ideally you don’t submit work that you are certain is correct, but instead submit work you need help and feedback with. Submit the images as a single pdf file. To do this, select all the images in a folder, right-click and press print. It will say something like *How do you want to print your pictures?* Press (Microsoft?) Print to PDF. If possible choose an orientation that has all the images in portrait.

## Week 6

We will finish Chapter 2 by talking about determinants and Cramer’s Rule.

## Outlook

In Week 7 we will start differentiation. 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 want to try and do homework regularly.

## Assessment Schedule

**Week 5 **– 25% Vectors Test

**Week 8 **– 25% Matrices Test

**Week 11 ** – 25% Differentiation Test

**Week 14 **– 25% Integration Test

## Study

## Student Resources

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

*In theory you are supposed to spend seven hours per week on MATH6040: my recommendation is that you watch the lecture material, then spend whatever other time you have for MATH6040 on exercises. **It is up to you to decide when you complete learning tasks and timetable yourself. There are three hours of MATH6040 slots on your timetable that you can use if you want. Even with just three hours you should have at least one hour to try and submit exercises for video feedback.*

## 25% Vectors Test, 19.30 Tuesday 23 February

The open-book assessment will be designed to be done in about 45 minutes, however you will be given one hour to complete the assignment along with an additional 15 minutes to upload your work. 45 minutes means about one and a half exam questions (see MATH6040 vectors questions (usually vectors are Q. 1, sometimes Q. 2) to get an idea of how long one exam question is). Please contact me if the timing (19.30 Tuesday 23 February) is an issue.

The assessment is based on Chapter 1. As it is an open book assessment, I have decided to split the questions into parts (a), (b), and (c).

The parts (a) are easy, and worth 40% of the total mark. The parts (b) are of medium difficulty, and are worth 30% of the total mark. The parts (c) are more difficult and worth 30% of the marks. You might be advised to do all the parts (a) and (b) first, try and get as close to 70% as possible with those, and then leave the parts (c) to the end. Otherwise you might waste time doing parts (c) when there are easier and more marks available in parts (b) and particularly (a).

Additional practise questions (beyond the manual) may be found by looking at past MATH6040 exam papers.

Academic Dishonesty will not be accepted and suspected breaches, such as communication with others during the assessment, will be pursued in line with this policy. To make life easier for me in this regard your assessment will be student-number-personalised. In addition by submitting you will be pledging that you will undertake the assessment in good faith.

We will have a Zoom Tuesday 16 February at 20:00 for any questions that ye would like to ask about this assessment. This tutorial will be recorded in the cloud.

## Week 4

### Lectures

There are 116 minutes of lectures here. You should need about three hours to watch these (I recommend 50% extra time for pausing/rewinding)

- Matrix Arithmetic Theory (34 minutes)
- Matrix Arithmetic Examples (27 minutes)
- Matrix Inverses (37 minutes)
- Matrix Equations (18 minutes)

Some deeper discussion here: Why do we multiply matrices like we do? Why can’t I divide by zero?

### Exercises

Assuming you are ready for the Vector Assessment, try

- p.66, Q. 1-4
- p.70, Q.1-2
- p.73, Q.1-3
- Additional Exercises, p.66, Q.1, p.73, Q.4-5

Submit work for Canvas feedback by Sunday 21 February for video feedback after Monday 22 February. Ideally you don’t submit work that you are certain is correct, but instead submit work you need help and feedback with. Submit the images as a single pdf file. To do this, select all the images in a folder, right-click and press print. It will say something like *How do you want to print your pictures?* Press (Microsoft?) Print to PDF. If possible choose an orientation that has all the images in portrait.

## Week 5

You will have your test. In lectures, we will look at Linear Systems. We won’t do too much so you have time to revise either Chapter 1 or Week 4 exercises.

## Study

## Student Resources

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

*In theory you are supposed to spend seven hours per week on MATH6040: my recommendation is that you watch the lecture material, then spend whatever other time you have for MATH6040 on exercises. **It is up to you to decide when you complete learning tasks and timetable yourself. There are three hours of MATH6040 slots on your timetable that you can use if you want. Even with just three hours you should have at least one hour to try and submit exercises for video feedback.*

## 25% Vectors Test, 19.30 Tuesday 23 February

The open-book assessment will be designed to be done in about 45 minutes, however you will be given one hour to complete the assignment along with an additional 15 minutes to upload your work. 45 minutes means about one and a half exam questions (see MATH6040 vectors questions ( (usually vectors are Q. 1, sometimes Q. 2)) to get an idea of how long one exam question is). Please contact me if the timing is an issue.

The assessment is based on Chapter 1. As it is an open book assessment, it is my intention to make the test a little on the hard side (in terms of the questions I can ask from Chapter 1). I hope to have about 40% of the marks going for straightforward/easier stuff, 30% of the marks for slightly harder stuff, and about 30% of the marks will be harder again. That is an intention not a promise.

Additional practise questions (beyond the manual) may be found by looking at past MATH6040 exam papers.

Academic Dishonesty will not be accepted and suspected breaches, such as communication with others during the assessment, will be pursued in line with this policy. To make life easier for me in this regard your assessment will be student-number-personalised. In addition you will be pledging that you

We will have a Zoom Tuesday 16 February at 20:00 for any questions that ye would like to ask about this assessment. This tutorial will be recorded in the cloud.

## Week 3

### Lectures

There are few lectures this week meaning that you should have time to do and submit exercises. You should need only about an hour and a half to watch these (I recommend 50% extra time for pausing/rewinding)

Work done by a Force (26 minutes)

Moment of a Force (29 minutes)

Vectors Short Summary (5 minutes)

### Exercises

Assuming you have the Week 1 and Week 2 exercises done (maybe do these first), try

- p.44, Q. 1-6
- Additional Exercises, p.46, Q.7-13

Submit work for Canvas feedback by Sunday 14 February for video feedback after Monday 15 February. Ideally you don’t submit work that you are certain is correct, but instead submit work you need help and feedback with. Submit the images as a single pdf file. To do this, select all the images in a folder, right-click and press print. It will say something like *How do you want to print your pictures?* Press (Microsoft?) Print to PDF. If possible choose an orientation that has all the images in portrait.

## Week 4

We will start looking at Chapter 2: Matrices. We will some examples of matrix arithmetic and look at Matrix Inverses — “dividing” for Matrices. This will allow us to solve matrix equations.

## Study

## Student Resources

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

*In theory you are supposed to spend seven hours per week on MATH6040: my recommendation is that you watch the lecture material, then spend whatever other time you have for MATH6040 on exercises. **It is up to you to decide when you complete learning tasks and timetable yourself. There are three hours of MATH7021 slots on your timetable that you can use if you want. Even with just three hours you should have at least one hour to try and submit exercises for video feedback.*

## Week 2

### Lectures

You should need about two hours to watch these (I recommend 50% extra time for pausing/rewinding)

Vectors Example (20 minutes)

Vector/Cross Product I (36 minutes)

Vector/Cross Product II (29 minutes)

Latest annotated notes here.

### Exercises

- p.27, Q. 1-13 (you might have some of these done in Week 1)
- p.38, Q.1-5
- Additional Exercises, p.38, Q. 6-1

You may need the formula that the area of a triangle is equal to .

Submit work for Canvas feedback by Sunday 7 February for video feedback after Monday 8 February. Ideally you don’t submit work that you are certain is correct, but instead submit work you need help and feedback with. Submit the images as a single pdf file. To do this, select all the images in a folder, right-click and press print. It will say something like *How do you want to print your pictures?* Press (Microsoft?) Print to PDF. If possible choose an orientation that has all the images in portrait.

## Week 3

We will look at the applications of vectors to work and moments

## 25% Test 1 in Week 5

I will *probably* design student-number-personalised assessments. Watch this space: official notice in Week 3.

## Study

## Student Resources

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

*In theory (see Learner Workload) you are supposed to spend seven hours per week on MATH6040. I know this might not be possible for everyone. My recommendation is that you watch the lecture material (n/a in Week 1 if you attended the live lecture), then spend time doing exercises — how long will depend on the…*

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