J.P. McCarthy: Math Page

20% VBA Assessment 1, 8-11 March

Please see Canvas for more information.

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

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

Week 6

We had a Chapter 2 Concept MCQ on Wednesday.

On Monday we looked at The Engineer’s Transform” — the Laplace Transform. We will look at the first shift theorem.

On Wednesday we looked at how the Laplace Transform interacts with differentiation.

On Thursday, in a double class, we covered partial fractions. We had a bare ten minutes of tutorial time looking at the cover up method.

Week 7

We will spend time on the inverse Laplace transform. We may or may not have tutorial time… we will probably have some on Thursday.

Extra Tutorials

There will be two extra tutorials in room B180:

• 13:00-14:00, Tuesday 22 March
• 13:00-14:00, Tuesday 29 March

Assignment 2

Assignment 2 will have a hand-in time and date of 11:00 6 April. Assignment 2 is in the manual. Once we get someway into the examples on p.132 you should be able to make a start.

Study

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

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

20% Written Assessment 1, 1 March

Please see Canvas for more information.

20% VBA Assessment 1, 8-11 March

Please see Canvas for more information.

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

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

15% Assignment 1

This has a revised deadline. Please see Canvas and email.

There is one typo in Problem F:

…but you need to ask yourself is it worth your time to keep going for the sake of one mark (out of 62 out of 35%) that is 0.56 percentage points towards your final grade.

It should be 15% and 0.24 percentage points.

Week 5

On Monday we drove further into Chapter 2, the method of undetermined coefficients for linear differential equations. We more-or-less have it all covered, but we need to see more examples.

On Wednesday we had some concept MCQ on Chapter 1, and then did the last bit of the Chapter 2 theory.

On Thursday most were absent (doing Assignment 1 I presume), but we finished Chapter 2 and had maybe an hour and twenty minutes of tutorial time on Chapter 2. There will be no further (dedicated/recommended) tutorial time on Chapter 2.

Week 6

Things are getting more serious now as we start Chapter 3. We must work hard on this material:

1. because without doing so you could be very, very lost on 15% Assignment 2 (and 35% exam question), and
2. because if you are going into Level 8 Structural Engineering it will be assumed that you are competent with the Chapter 3 material

Chapter 3 is about “The Engineer’s Transform” — the Laplace Transform. We will look at the first shift theorem, and how the Laplace Transform interacts with differentiation. We will start looking at partial fractions.

There will be no tutorial time. We will have a Chapter 2 Concept MCQ on Wednesday.

Extra Tutorials

There will be two extra tutorials in room B180:

• 13:00-14:00, Tuesday 22 March
• 13:00-14:00, Tuesday 29 March

Assignment 2

Assignment 2 will have a hand-in time and date of 11:00 6 April. Assignment 2 is in the manual. Once we get someway into the examples on p.132 you should be able to make a start.

Study

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

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

20% Written Assessment 1, 1 March

Please see Canvas for more information.

Week 4

We could avoid the implicit differentiation of -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

• , ,
• , ,
• , .

The function 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 depends on ; so above we have , then , then . How exactly that works we will not get into but we will say:

1. It is still true that the local Heun errors are , and so
2. The global Heun error is , 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

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

15% Assignment 1

Should probably be underway by you. This has a (provisional) hand in time and date of 11:00 Thursday 24 February. Please see Canvas.

There is one typo in Problem F:

…but you need to ask yourself is it worth your time to keep going for the sake of one mark (out of 62 out of 35%) that is 0.56 percentage points towards your final grade.

It should ne 15% and 0.24 percentage points.

Gaussian Elimination Tutor

If you download Maple (see Student Resources), there is a Maple Tutor that is easy to use and will help you with Gaussian Elimination. Open up Maple and go to Tools -> Tutors -> Linear Algebra -> Gaussian Elimination.

Week 4

I spoke on academic integrity for Assignment 1 (see also Canvas information) but was not yet able to do the Chapter 1 “concept MCQ” (hopefully Wednesday in Week 5).

We drove into Chapter 2, the method of undetermined coefficients for linear differential equations. We more-or-less have it all covered, but we need to see more examples.

We had only 25 minutes of tutorial time — on homogeneous second order differential equations on Thursday.

Week 5

We will move to finish Chapter 2. Any remaining classes will be given over to tutorial time on Chapter 2.

Study

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

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..