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## Week 1

In Week 1, by briefly looking at a number of examples (many of which we have seen before), we had a review of some central ideas from approximation theory such as approximation, measurement error, accuracy & precision, iteration, convergence, meshing, error, etc.

We started looking at where ordinary differential equations come into Engineering.

In VBA we had a quick review lab, focussing on plotting data, command buttons, message boxes, input boxes, If-statements and do-loops.

If you have not completed Lab 1 (p.120), I recommend that you do at least up to the first Do-Loop exercise to get you back in the VBA groove.

Read the rest of this entry »### Assessment Corrections

Have finally been completed. Please check your grade and if you have any queries please don’t hesitate to email me.

### Assessment 4

Written Assessment 2 will not be entirely unlike Written Assessment 1. The Week 12 Zoom will be Monday 26 April 15:00 instead of Tuesday 27 April.

25% Written Assessment 1, based on Weeks 6-10, so everything from p.74 to 106.

It will be a one hour assessment, but I am going to give ye 15 minutes grace, as well as 15 minutes to upload. The test will run therefore from **09.30 to 11.00, Tuesday 27 April. **It is open book — you can use your manual, any Canvas materials, as well as Excel/VBA.

40% of the marks will be for Section 1.9

30% of the marks will be for Section 2.1

40% of the marks will be for Section 2.2

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.) (Links to an external site.).

## Week 10

### Lectures

- Heat Equation I (Links to an external site.) (19 minutes)
- Heat Equation II (Links to an external site.) (36 minutes)

This (Links to an external site.) explains the connection between the Heat Equation and the Jacobi Method approximations to the Laplace Equation

There is a longer, more in-person (old, last year) version of the above material. How different they are I am not too sure.

- Derivation of Heat Equation (Links to an external site.) (26 minutes)
- Finite Differences for the Heat Equation (Links to an external site.) (29 minutes)
- Heat Equation Finite Differences Example I (Links to an external site.) (11 minutes)
- Heat Equation Finite Differences Example II (Links to an external site.) (16 minutes, continued from above, the dog interrupted)

### Theory Exercises and Q & A

Q&A on Tuesday 13 April as normal: p.104, Q.1-3

## Week 11

No more lectures, no more labs: you will focus on VBA Assessment 2. Q&A on Tuesday.

## Week 12

No more lectures, no more labs: you will focus on Written Assessment 2. Q&A on **Monday.**

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## Student Resources

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

### Assessment Corrections

I cannot promise at this point when these will be completed. It is my intention to have these corrected before the end of Week 9. Watch this space.

### Assessments 3 and 4

I will give proper notice for VBA Assessment 2 by the end of Week 9 and for Written Assessment 2 during Easter.

## Week 9

### Lectures

- Laplace’s Difference Equation I (21 minutes)
- Laplace’s Difference Equation II (22 minutes)
- Heat Flux Density (4 minutes)

There is a longer, more in-person (old, last year) version of the above material:

- Laplace’s Difference Equation (26 minutes)
- Mean Value Property (12 minutes)
- Laplace’s Difference Equation Examples (29 minutes)
- Laplace’s Equation Irregular Boundary (9 minutes)
- Calculating Heat Flux Density (7 minutes)

### Lab 7

See VBA Lab 7

### Theory Exercises and Q & A

Q&A on Tuesday as normal:

p.97, Q. 1,2 and p. 98 exercises

## Week 10

I have linked here to last year’s videos but will be recording fresh videos. How different they will be I am not too sure.

- Derivation of Heat Equation (26 minutes)
- Finite Differences for the Heat Equation (29 minutes)
- Heat Equation Finite Differences Example I (11 minutes)
- Heat Equation Finite Differences Example II (16 minutes, continued from above, the dog interrupted)

## Outlook

## Week 11 and 12

### Lectures

None. Perhaps additional tutorial time in Week 11 for Written Assessment in Week 12.

### Labs

We will do our last lab, Lab 8 in Week 10. VBA Assessment 2 in Week 11.

## Assessment

This is provisional and subject to change.

**Week 6**, 25% First VBA Assessment, Based (roughly) on Weeks 1-4**Week 7,**25 % In-Class Written Test, Based (roughly) on Weeks 1-5**Week 11**, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9**Week 12,**25% Written Assessment(s), Based on Weeks 6-10

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## Student Resources

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

### Assessment Corrections

I cannot promise at this point when these will be completed. I am having a hardware issue at the moment which means that I might have to get the ball rolling for ye by correcting the Written Assessment first. Watch this space.

## Week 8

### Lectures

Some theory background for Chapter 2:

Intro to PDEs and Laplace’s Equation (39 minutes)

The first part of this on finite differences is important for the rest of the semester. The second, a handwaving derivation of Laplace’s Equation. It should give you an idea of what a PDE is, should help consolidate some “thermo”-type stuff, but is theoretical background.

There is a longer, more in-person (old) version of the above material: *Intro to PDEs (less than 20 minutes), and Derivation of the Laplace Equation (40 minutes).*

### Theory Exercises and Q & A

You might want to focus on labs that you didn’t get to look at yet (as well of course as Lab 6)

## Week 9

I have linked here to last year’s videos but will be recording fresh videos. How different they will be I am not too sure.

- Laplace’s Difference Equation (26 minutes)
- Mean Value Property (12 minutes)
- Laplace’s Difference Equation Examples (29 minutes)
- Laplace’s Equation Irregular Boundary (9 minutes)
- Calculating Heat Flux Density (7 minutes)

## Outlook

## Week 10

### Lectures

Perhaps of the order of 1.5 hours of lectures on the Heat Equation. We will then be finished the lecture material.

### Labs

We will do our last lab in Week 10.

## Assessment

This is provisional and subject to change.

**Week 6**, 25% First VBA Assessment, Based (roughly) on Weeks 1-4**Week 7,**25 % In-Class Written Test, Based (roughly) on Weeks 1-5**Week 11**, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9**Week 12,**25% Written Assessment(s), Based on Weeks 6-11

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## Student Resources

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

### Written Assessment 1 – Week 7

Next week’s Zoom will be Monday 15:00 instead of Tuesday.

25% Written Assessment 1, based on Weeks 1-5, so everything up to p.73.

It will be a one hour assessment, but I am going to give ye 15 minutes grace, as well as 15 minutes to upload. The test will run therefore from **09.30 to 11.00, Tuesday 9 March. **It is open book — you can use your manual, any Canvas materials, as well as Excel/VBA.

The questions mentioned below are only a guide to the content not the actual questions.

40% of the marks will be numerical methods (Euler, TTT, Heun); finding approximations like p.34, Q.1-3, p.37, Q.1-3, p.48, Q.1-4 (non-Excel parts of Q.4), p.60, Q.4-7.

30% of the marks will be numerical analysis; understanding these methods and their errors like p.34, Q. 4, p.38, Q.4-6. p.49, Q.5-8,

15% will be neither; like p.17, Q. 1-2, p.40, Q.1-3, p.60, Q.1-3

15% will be Runge-Kutta, like p.72, Q.1-2.

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.).

## Week 7

### Lectures

Just a very short lecture (time is taken up by Written Test 1):

Goal Seek for Boundary Value Problems

## Week 8

I have linked here to last year’s videos but will be recording fresh videos. How different they will be I am not too sure.

*We will look at Intro to PDEs (less than 20 minutes), and then watch the Derivation of the Laplace Equation (40 minutes).*

## Assessment

This is provisional and subject to change.

**Week 6**, 25% First VBA Assessment, Based (roughly) on Weeks 1-4**Week 7,**25 % In-Class Written Test, Based (roughly) on Weeks 1-5**Week 11**, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9**Week 12,**25% Written Assessment(s), Based on Weeks 6-11

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## Student Resources

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

### VBA Assessment 1 – Due 7 March

Hopefully I have designed something in which you can take your time, get things right, get some good marks, and show off what you can do. You are advised to complete VBA Lab 3 first.

*I recommend watching the Week 6 lectures, but perhaps it might suit students to complete VBA Assessment 1 before looking at Week 6 Exercises. Do not let VBA Assessment slide very late as you will need time to prepare for Written Assessment 1. Really you should be looking to complete VBA Assessment 1 a few days before the due date. There is no lab in Week 6 in order to give you more time.*

### Written Assessment 1 – Week 7

25% Written Assessment 1, based on Weeks 1-5, so everything up to p.73.

It will be a one hour assessment, but I am going to give ye 15 minutes grace, as well as 15 minutes to upload. The test will run therefore from **09.30 to 11.00, Tuesday 9 March. **It is open book — you can use your manual, any Canvas materials, as well as Excel/VBA.

40% of the marks will be numerical methods (Euler, TTT, Heun); finding approximations like p.34, Q.1-3, p.37, Q.1-3, p.48, Q.1-4 (non-Excel parts of Q.4), p.60, Q.4-7.

30% of the marks will be numerical analysis; understanding these methods and their errors like p.34, Q. 4, p.38, Q.4-6. p.49, Q.5-8

15% will be neither; like p.17, Q. 1-2, p.40, Q.1-3, p.60, Q.1-3

15% will be Runge-Kutta, like p.72, Q.1-2.

**MORE INFO: Added 25 February**

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.).

## Week 6

### Lectures

There are 61 minutes of lectures. You should schedule about an hour and a half to watch them and take the notes in your manual. You might need this extra time above 61 minutes because you will want to pause me. You should also take note of any confusions you have to ask about in the regular Q & A.

- Boundary Value Problems (28 minutes)
- Shooting Method (33 minutes)

### Lab 4

If you have not yet had a chance to look at Lab 4, but have questions, you can submit to Lab 4 Second Chance.

### Theory Exercises and Q & A

p.82, Q. 1-3

Q & A to ask about Theory Exercises or anything else every Tuesday 12.30 (waiting room open 12.25).

## Week 7

There will not be much in Week 7, just a short lecture on Goal Seek for boundary value problems.

## Assessment

This is provisional and subject to change.

**Week 6**, 25% First VBA Assessment, Based (roughly) on Weeks 1-4**Week 7,**25 % In-Class Written Test, Based (roughly) on Weeks 1-5**Week 11**, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9**Week 12,**25% Written Assessment(s), Based on Weeks 6-11

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## Student Resources

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

### VBA Assessment 1 – Due Week 6 (7 March)

Hopefully I have designed something in which you can take your time, get things right, get some good marks, and show off what you can do. You are advised to complete VBA Lab 3 first.

*I recommend watching the Week 5 lectures, but perhaps it might suit students to complete VBA Assessment 1 before looking at Lab 4 and Week 5 Exercises. Do not let VBA Assessment slide very late as you will need time to prepare for Written Assessment 1. Really you should be looking to complete VBA Assessment 1 a few days before the due date. There will be no lab in Week 6 in order to give you more time.*

### Written Assessment 1 – Week 7

25% Written Assessment 1, based on Weeks 1-5, so everything up to p.73.

It will be a one hour assessment, but I am going to give ye 15 minutes grace, as well as 15 minutes to upload. The test will run therefore from **09.30 to 11.00, Tuesday 9 March. **It is open book — you can use your manual, any Canvas materials, as well as Excel/VBA.

40% of the marks will be numerical methods (Euler, TTT, Heun); finding approximations like p.34, Q.1-3, p.37, Q.1-3, p.48, Q.1-4 (non-Excel parts of Q.4), p.60, Q.4-7.

30% of the marks will be numerical analysis; understanding these methods and their errors like p.34, Q. 4, p.38, Q.4-6. p.49, Q.5-8

15% will be neither; like p.17, Q. 1-2, p.40, Q.1-3, p.60, Q.1-3

15% will be Runge-Kutta, like p.72, Q.1-2.

More information about practicalities in Week 6.

## Week 5

### Lectures

There are 82 minutes of lectures. You could schedule about 2 hours to watch them and take the notes in your manual. You might need this extra time above 82 minutes because you will want to pause me. You should also take note of any confusions you have to ask about in the regular Q & A.

- Second Order ODEs – Case Studies (37 minutes)
- Runge-Kutta Methods I (28 minutes)
- Runge-Kutta Methods II (17 minutes)

### Lab 4

Lab 4 may not be up until 18 February, and can be attempted after watching the lectures above (submission not live until 20 February).

### Theory Exercises and Q & A

p.60, Q.1-7

p.72, Q.1-3

Q & A to ask about Theory Exercises or anything else every Tuesday 12.30 (waiting room open 12.25).

## Week 6

We will look at boundary value problems (in particular the Shooting Method and Goal Seek).

There will be no lab in order to give you time to complete VBA Assessment 1.

## Assessment

This is provisional and subject to change.

**Week 6**, 25% First VBA Assessment, Based (roughly) on Weeks 1-4**Week 7,**25 % In-Class Written Test, Based (roughly) on Weeks 1-5**Week 11**, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9**Week 12,**25% Written Assessment(s), Based on Weeks 6-11

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## Student Resources

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

### VBA Assessment 1 – Week 6

Hopefully I have designed something in which you can take your time, get things right, get some good marks, and show off what you can do. Information on Written Assessment next week.

## Week 4

### Lectures

There are 84 minutes of lectures. You could schedule about 2 hours to watch them and take the notes in your manual. You might need this extra time above 84 minutes because you will want to pause me. You should also take note of any confusions you have to ask about in the regular Q & A.

- Heun’s Method Part I (29 minutes)
- Heun’s Method Part II (17 minutes)
- Higher Order ODEs I (38 minutes)

The Q&A is dedicated to answering questions but do not hesitate to contact me with questions at any time. My usual modus operandi is to answer emails every morning.

### Lab

Once you have watched the lectures you should attempt VBA Lab 3.

### Theory Exercises and Q & A

p.48, Q. 1-5

Additional Exercises:

p. 48, Q.5-8

Q & A to ask about Theory Exercises or anything else every Tuesday 12.30 (waiting room open 12.25).

## Week 5

We will continue looking at second order differential equations and how to attack them numerically.

We will begin a quick study of Runge-Kutta Methods.

In VBA we will look at Lab 4, on Second Order Initial Value Problems.

## Assessment

This is provisional and subject to change.

**Week 6**, 25% First VBA Assessment, Based (roughly) on Weeks 1-4**Week 7,**25 % In-Class Written Test, Based (roughly) on Weeks 1-5 (notice in Week 5)**Week 11**, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9**Week 12,**25% Written Assessment(s), Based on Weeks 6-11

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## 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 MATH7016. My recommendation is that you watch the lecture material, then complete the lab, and if there is any time left over do the suggested theory exercises.*

*It is up to you to decide when you complete learning tasks and timetable yourself. There are four hours of MATH7016 slots on your timetable but remember that half an hour is taken up with the weekly Q&A. Learners should decide for themselves whether the weekly Q&A is helping their learning.*

## Week 3

### Lectures

There are 79 minutes of lectures. You could schedule about 2 hoursto watch them and take the notes in your manual. You might need this extra time above 79 minutes because you will want to pause me. You should also take note of any confusions you have to ask about in the regular Q & A.

- Euler Method Theory Examples (28 minutes)
- Three Term Taylor Method (35 minutes)
- Taylor Series II (16 minutes)

The Q&A is dedicated to answering questions but do not hesitate to contact me with questions at any time. My usual modus operandi is to answer emails every morning.

### Lab

Once you have watched the lectures you should attempt VBA Lab 3.

### Theory Exercises and Q & A

p.37, Q.1-4

p.40, Q.1-3

Additional Exercises:

p. 38, Q.5-6

Q & A to ask about Theory Exercises or anything else every Tuesday 12.30 (waiting room open 12.25).

## Week 4

We can avoid implicit differentiation by looking at Huen’s Method, which is an adjustment of Euler’s Method in that it uses lines.

We will also introduce second order differential equations and how to attack them numerically.

In VBA we will look at Lab 3, on Heun’s Method.

## Assessment

This is provisional and subject to change. Notice for the first assessment will be in Week 4

**Week 6**, 25% First VBA Assessment, Based (roughly) on Weeks 1-4**Week 7,**25 % In-Class Written Test, Based (roughly) on Weeks 1-5**Week 11**, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9**Week 12,**25% Written Assessment(s), Based on Weeks 6-11

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## 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 MATH7016. My recommendation is that you watch the lecture material, then complete the lab, and if there is any time left over do the suggested theory exercises.*

*It is up to you to decide when you complete learning tasks and timetable yourself. There are four hours of MATH7016 slots on your timetable but remember that half an hour is taken up with the weekly Q&A. Learners should decide for themselves whether the weekly Q&A is helping their learning.*

## Week 2

### Lectures

There are about 82 minutes of lectures. You could schedule about 2 hours and 10 minutes to watch them and take the notes in your manual. You need this extra time above 82 minutes because you will want to pause me. You should also take note of any confusions you have to ask about in the regular Q & A (starting Tuesday 2 February)

- Euler Method Example I (12 minutes)
- Taylor Series I (37 minutes)
- Error Analysis for Euler’s Method (23 minutes)
- Euler’s Method Example II (9 minutes)

(Last year with the strike I recorded the same stuff in a classroom)

The Q&A is dedicated to answering questions but do not hesitate to contact me with questions at any time. My usual modus operandi is to answer emails every morning.

### Lab

Once you have watched the lectures you should attempt VBA Lab 2.

### Theory Exercises and Q & A

p.34, Q.1-4

Q & A to ask about Theory Exercises or anything else every Tuesday 12.30 (waiting room open 12.25).

## Week 3

We will do more on Taylor Series and the Euler Method. When we have that done we will look at Huen’s Method.

In VBA we will finish off our Euler Method Lab.

## Assessment

I really have not yet thought about assessment but this is what I am thinking at the moment. This is provisional and subject to change.

**Week 6**, 25% First VBA Assessment, Based (roughly) on Weeks 1-4**Week 7,**25 % In-Class Written Test, Based (roughly) on Weeks 1-5**Week 11**, 25% Second VBA Assessment, Based (roughly) on Weeks 6-9**Week 12,**25% Written Assessment(s), Based on Weeks 6-11

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## Student Resources

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

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