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VBA Assessment 2

See Canvas for the assessment information.

MCQ League

By Easter I will get the backlog of corrections done and then there will be one more MCQ to decide the winners of the €20, €10, and €5.

Week 10

In lectures we covered the final section, on the Heat Equation.

Then we did some exercises:

• p.115, Q. 1
• p.109, Q
• p.108, Q.1

In the VBA Lab we had a revision class.

Week 11

In the lecture slots, I will continue to do theory/calculation exercises from the notes.

In the VBA lab, we will have our second assessment.

Week 12

In the lecture slots, I will continue theory/calculation exercises from the notes.

In the VBA lab, we will do Lab 8.

Week 13

In the 10:00 Tuesday class I will do theory/calculation exercises from the notes. The final 40% written assessment is on Tuesday. More information will appear on Canvas next week.

Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises

Covid Disruption

We have had a very disturbed time with me catching the covid. DME2C are particularly badly hit. To help ease the situation, we will have a revision lab in Week 10 (VBA Assessment 2 is based on Labs 6 and 7).

Lab 8, which is examinable in the Written Assessment in Week 13, will now be held after Easter.

VBA Assessment 2

See Canvas for the assessment information.

MCQ League

This is currently in a mess. I would invite DME2C students do MCQ VI (below) and submit their answers here.

Week 8

We finished looking at boundary value problems (in particular Goal Seek) and began looking at partial differential equations by looking at Laplace’s Equation.

In VBA, DME2A and DME2B had Lab 6. We skipped Lab 5. DME2C were due to do Lab 6 on the Monday of Week 9 but my covid disrupted this. DME2C should have worked on Lab 6 before Friday 1 April:

Watch this (Links to an external site.) to start you off. Next attempt Lab 6 yourself. Just use Euler’s Method rather than any RK. If stuck, please watch this (Links to an external site.). Any questions please email.

Week 9

I was out with covid. Ye received the following instructions:

DME2 Lectures Tuesday and Wednesday

DME2 Lab 7

Watch this (Links to an external site.) to start off. Next attempt the lab yourself. If stuck, please watch this (Links to an external site.). Any questions please email.

Week 10

In lectures we will cover the final section, on the Heat Equation.

In the VBA Lab we will have a revision class. What you do in this class will depend on how much you have done independently in Week 9.

Week 11

In the lecture slots, I will do theory/calculation exercises from the notes.

In the VBA lab, we will have our second assessment.

Week 12

In the lecture slots, I will do theory/calculation exercises from the notes.

In the VBA lab, we will do Lab 8.

Week 13

In the 10:00 Tuesday class I will do theory/calculation exercises from the notes.

Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises

Week 7

We looked at boundary value problems (in particular the Shooting Method).

In VBA we had our first VBA Assessment

Week 8

We will finish looking at boundary value problems (in particular Goal Seek) and look at partial differential equations by looking at Laplace’s Equation.

In VBA we will have Lab 6. We will skip Lab 5.

DME2C Lab 18 March

With the bank holiday, there will be no DME2C Lab in Week 8, but two in Week 9, with the additional lab held:

• 09:00, Monday, 21 March, C125.

Assessment

See Canvas for the assessment schedule. There will be more information on assessments the Friday of the week two before the assessment week (i.e. info on Friday of Week 4 about the Week 6 assessment).

MCQ League

No change with the VBA Assessment,

Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises

Week 6

We had our written assessment on Tuesday and in the remote class we finished talking about Runge-Kutta Methods.

In VBA we (were supposed to) finish Lab 4, and also revise for the VBA Assessment

Week 7

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

In VBA we have VBA Assessment 1.

DME2C Lab 18 March

With the bank holiday, there will be no DME2C Lab in Week 8, but two in Week 9, with the additional lab held:

• 09:00, Monday, 21 March, C125.

Assessment

See Canvas for the assessment schedule. There will be more information on assessments the Friday of the week two before the assessment week (i.e. info on Friday of Week 4 about the Week 6 assessment).

MCQ League

Is updated. The last MCQ was not a great effort by me, apologies.

Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises

Week 5

We continued talking about second order differential equations and how to attack them numerically.

In VBA we worked towards Heun’s Method for second order differential equations.

Week 6

We will have our written assessment on Tuesday and in the remote class we will talk more about Runge-Kutta Methods.

In VBA we will finish Lab 4, and also revise for the VBA Assessment

Week 7

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

DME2C Lab 18 March

With the bank holiday, there will be no DME2C Lab in Week 8, but two in Week 9, with the additional lab held:

• Monday, 21 March, C125.

I will also set up a remote option for those who would prefer that.

Assessment

See Canvas for the assessment schedule. There will be more information on assessments the Friday of the week two before the assessment week (i.e. info on Friday of Week 4 about the Week 6 assessment).

MCQ League

Will be updated later on 25 February.

Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises

Week 4

We could avoid the implicit differentiation of $k$-Term-Taylor Methods by looking at Huen’s Method, which is an adjustment of Euler’s Method in that it uses lines.

We started talking about second order differential equations.

We also looked at calculating a Maclaurin Series

In VBA we did Heun’s Method. Unfortunately the storm messed up the Lab for DME2C and they need to do the lab remotely as per the email, as well as MCQIII.

Further Remark: Heun’s Method

There is a statement in the notes that Heun’s method is of order the second derivative. The exact situation with the Heun’s method error is fairly complicated. The errors depend not just on the nature of the solution but also the nature of the differential equation. For example, consider

• $\dfrac{dy}{dx}=2\sqrt{y(x)}$, $y(0)=1$,
• $\dfrac{dy}{dx}=\dfrac{2y(x)}{1+x}$, $y(0)=1$,
• $\dfrac{dy}{dx}=2x+2$, $y(0)=1$.

The function $y(x)=(x+1)^2$ is a solution of each of these, but only the third will yield zero errors with Heun. It turns out that the Heun’s method error depends in an important way on how the $F(x,y)$ depends on $y$; so above we have $F(x,y)=2\sqrt{y}$, then $F(x,y)=2y/(1+x)$, then $F(x,y)=2x+2$. How exactly that works we will not get into but we will say:

1. It is still true that the local Heun errors are $\mathcal{O}(h^3)$, and so
2. The global Heun error is $\mathcal{O}(h^2)$, and also
3. Heun’s method will have problems when the third derivative is large.

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.

Week 6

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

DME2C Lab 18 March

DME2C have already been impacted negatively by Storm Eunice. Rather than have them hit again with no lab on this day (for the university is closed for the bank holiday), we will have no DME2C Lab in Week 8, but two in Week 9, with the additional lab held:

• Monday, 21 March, C125.

I will also set up a remote option for those who would prefer that.

Assessment

See Canvas for the assessment schedule. There will be more information on assessments the Friday of the week two before the assessment week (i.e. info on Friday of Week 4 about the Week 6 assessment).

MCQ League

The standings after MCQIII will not be updated until next week.

Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises

Week 3

We then did some further study on the Euler Method. The global error with the Euler Method is $\mathcal{O}(h)$ and we need to reduce this by coming up with a better method or adjusting the Euler Method.

We looked at the Three Term Taylor Method as a better method. To employ the Three Term Taylor Method we need implicit differentiation, which means more pen-and-paper work.

In VBA we finished off the Euler Method Lab 2. Ideally everyone should have done up to p.130.

Some students did or started Exercise 1 and/or Exercise 2 on p. 130.

Read the rest of this entry »

Week 2

We looked at the Euler Method, and then started looking at big $\mathcal{O}$ notation, and Taylor Series.

In VBA we started programming the Euler Method.

Read the rest of this entry »

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 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

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.

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