If you would like to submit anonymous feedback on this module/lecturer, you may do so here. This link will be open until Friday May 11 2018.

On Monday we finished the module by looking at triple integrals.

The Wednesday 09:00 lecture will be a tutorial. In this class and your usual tutorial we will look at the P.182, P. 192, P. 163, & P.116 exercises. If these are completed you will be recommended to revise either by trying Chapter 1 & 2 exercises or perhaps by looking at the Summer 2017 paper.

As next Monday is a bank holiday, we will begin the Summer 2017 Paper (in your notes) revision on Thursday.

In the Wednesday 09:00 lecture we will continue working on the Summer 2017 Paper and hopefully finish it before the end of the Thursday 10:00 lecture.

If we finish the Summer 2017 paper early, any extra time (probably just Thursday but maybe Wednesday if we go fast) will be dedicated to one-to-one help.

Wednesday’s tutorial will go ahead as normal with one-to-one help.

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

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

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If you would like to submit anonymous feedback on this module/lecturer, you may do so here. This link will be open until Friday May 11 2018.

Assignment 2 has been corrected and your results emailed to you.

We spent three lectures looking at double integrals, in particular their application to second moments of area. We set of integration over a cylinder by looking at polar coordinates.

In the Wednesday tutorial we worked on the p. 163 (primarily) and p. 182 exercises.

On Monday we will finish the module by looking at triple integrals.

We will therefore have three tutorials where we will look at the P.182, P. 192, P. 163, & P.116 exercises. If these are completed you will be recommended to revise either by trying Chapter 1 & 2 exercises or perhaps by looking at the Summer 2017 paper.

We will go through last year’s exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one.

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

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

]]>

If you would like to submit anonymous feedback on this module/lecturer, you may do so here. This link will be open until Friday May 11 2018.

We looked at the normal distribution.

In Maple looked at Binomial and Poisson random variables.

The Maple Test should take no more than one hour but I am giving ye extra time. For various reasons, I have decided to schedule next week’s class as:

- 19:05 – 20:25: Sampling and Control Charts
- 20:25 – 20:45: Break
- 20:45 – 22:00: Maple Test

The Maple Test will be open book. You have a sample Maple Test (this is also in the notes) with solutions (*the first with(Statistics) should be with(LinearAlgebra)). The Maple Test will not include anything from Chapter 2 (Lab 4).

We will speak about sampling in more detail and also introduce control charts.

We will hold a review class on Wednesday 9 May in the usual room. First off, the *layout* of your exam is the same as Autumn 2016 (in the back of your notes): do question one worth 50/100 and two out of questions two, three, four; each worth 25/100.

I will field any questions ye might have at this time and if there are no questions we will do this exam paper. The best possible thing for your study is to do this exam paper and then on Wednesday see how you got on.

If you have missed a lab you have two options: either download Maple onto your own machine (instructions may be found here) or come into CIT at another time to use Maple.

Go through the missed lab on your own, doing *all* the exercises in Maple. Save the worksheet and email it to me.

The deadline for Maple Catch up is Friday May 11 2018.

Questions you can do include:

**After Week 11:**P. 124, Q. 1-10 (this is loads: more is Q. 11-21)**After Week 10:**P. 102, Q. 1-4; P. 107, Q. 1-7; P. 111, Q. 1-12 (this is loads: more is Q. 13-16); P. 115, Q. 1-15**After Week 9:**P. 92, Q. 1-10 (not too important); P. 96, Q. 1-6 (this is loads: more is Q. 7-13)**After Week 8*:**P. 89, Q. 1-3**After Week 7*:**P. 89, Q. 1 (a), (b); Q. 2 (b); Q. 3 (b)**After Week 6*:**P. 74, Q. 1-4; P. 77, Q. 1-3**After Week 5*:**P.44, Q. 1-3, Q. 4-5 more abstract. P.47, Q. 1-3, Q. 4 more abstract. P.56, Q. 1-3, Q. 4 more abstract. P.69, Q. 9 is an important question. A version might be

Use only

determinantsto determine if the following homogeneous system of linear equations has non-zero solutions:

**After Week 4:**P. 41, Q. 1-4**After Week 3:**P. 28, Q. 1-5, 6-9 have answers with Q. 7 a harder question. P. 34 exercises.**After Week 2:**P. 18 Q. 2**After Week 1:**P. 18 Q. 1, 3 – 6. Harder questions are 7 and 8. For those who do not yet have the manual, see here.

I am not suggesting you should do *all *of these. It is recommended by the module descriptor that you do two hours of independent and directed learning every week but of course this isn’t feasible for everyone.

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

]]>We did a lot of probability — reliability block diagrams, the binomial distribution, the Poisson distribution.

Those who missed the class I recorded some of it here.

Ironically I recorded the same lectures in 2016 as you can see here.

We will look at the normal distribution and talk about sampling.

In Maple we will look at Binomial and Poisson random variables.

We will speak about sampling in more detail and also introduce control charts.

The Maple Test will be open book. You have a sample Maple Test with solutions (*the first with(Statistics) should be with(LinearAlgebra)). The Maple Test will not include anything from Chapter 2.

We will hold a review class on Wednesday 9 May in the usual room. First off, the *layout* of your exam is the same as Autumn 2016 (in the back of your notes): do question one worth 50/100 and two out of questions two, three, four; each worth 25/100.

I will field any questions ye might have at this time and if there are no questions we will do this exam paper. The best possible thing for your study is to do this exam paper and then on Wednesday see how you got on.

If you have missed a lab you have two options: either download Maple onto your own machine (instructions may be found here) or come into CIT at another time to use Maple.

Go through the missed lab on your own, doing *all* the exercises in Maple. Save the worksheet and email it to me.

Questions you can do include:

**After Week 10:**P. 102, Q. 1-4; P. 107, Q. 1-7; P. 111, Q. 1-12 (this is loads: more is Q. 13-16); P. 115, Q. 1-15**After Week 9:**P. 92, Q. 1-10 (not too important); P. 96, Q. 1-6 (this is loads: more is Q. 7-13)**After Week 8*:**P. 89, Q. 1-3**After Week 7*:**P. 89, Q. 1 (a), (b); Q. 2 (b); Q. 3 (b)**After Week 6*:**P. 74, Q. 1-4; P. 77, Q. 1-3**After Week 5*:**P.44, Q. 1-3, Q. 4-5 more abstract. P.47, Q. 1-3, Q. 4 more abstract. P.56, Q. 1-3, Q. 4 more abstract. P.69, Q. 9 is an important question. A version might be

Use only

determinantsto determine if the following homogeneous system of linear equations has non-zero solutions:

**After Week 4:**P. 41, Q. 1-4**After Week 3:**P. 28, Q. 1-5, 6-9 have answers with Q. 7 a harder question. P. 34 exercises.**After Week 2:**P. 18 Q. 2**After Week 1:**P. 18 Q. 1, 3 – 6. Harder questions are 7 and 8. For those who do not yet have the manual, see here.

I am not suggesting you should do *all *of these. It is recommended by the module descriptor that you do two hours of independent and directed learning every week but of course this isn’t feasible for everyone.

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

]]>Assignment 2 has a hand-in date of 17:00 23 April: the Monday of Week 11. Assignment 2 is in the manual, P. 149..

The Monday lecture was another tutorial on the P.116 exercises. In the Wednesday lectures we worked on systems of differential equations. In the Thursday lecture we worked on systems of differential equations exercises.

In the Wednesday tutorial we continued with the full Laplace Transform questions.

In the Monday and Wednesday lectures we will make a start on the final chapter by looking at double integrals.

In the Wednesday tutorial we will work on the p. 163 and p. 182 exercises. This work will continue on Thursday.

On Monday and Wednesday we will finish looking at double integrals and then triple integrals.

In the Wednesday tutorial we will work on the p.182, p.192, and p.186 exercises. This work will continue on Thursday.

We will go through last year’s exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one.

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

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

]]>

We looked at finite differences for the Heat Equation. This completes the examinable written material.

In VBA we implemented same.

In the 09:00 class we will have a revision session, geared towards the 20% VBA Assessment 2. This will look at the *20% VBA Assessment 2 Tutorial* Sheet It might therefore be a good idea to go through this before next week.

In the 12:00 class we will have a revision session, geared towards the 40% Written Assessment 2. This will look at the *40**% Written Assessment 2 Tutorial* Sheet It might therefore be a good idea to go through this before next week.

Formulae will be provided in the VBA 2 Assessment.

To understand how your student numbers generate constants (see below) see this VBA Test 2 from last year (do *not *read this as a sample – it included e.g. the Heat Equation which you will not be examined on (in VBA) and the Laplace’s Equation might be slightly simpler than what ye will have).

See last week’s Weekly Summary for the Format of the VBA Assessment 2.

The 40% Written Test is to be split in two.

The first part of the Written Test is the Theory Element (worth 20%). It will take place in B242 at 09:00, Tuesday 1 May.

From the *40**% Written Assessment 2 Tutorial* Sheet, you will receive

- one question from
*Runge-Kutta Exercises*[10%] - 3/4 questions from
*Other Theory Exercises*[10%]

This Theory Element is designed to take 30 minutes. You will be allowed up to 55 minutes.

The second part of the Written Test is the Calculations Element (worth 20%). It will take place during your Week 12 VBA slot. Like the *40**% Written Assessment 2 Tutorial* Sheet, you will receive

- A damped harmonic oscillator, with for all groups but will be different for groups A, B, and C [8%]
- A Heat Flux Density Vector Question, with different temperature distributions for groups A, B, and C. [4%]
- A Heat Equation Question. With different values for groups A, B, and C [8%]

This Calculation Element is designed to take 45 minutes. You will be allowed up to an hour and 55 minutes.

There will be no 12:00 class on Tuesday 1 May.

Study should consist of

- doing exercises from the notes
- completing VBA exercises

Assignment 2 has a hand-in date of 17:00 23 April: the Monday of Week 11. Assignment 2 is in the manual, P. 149.

If you were absent today and want to view your submission next week please email me.

We said a few things about damped harmonic oscillators on Monday and the rest of the week was spent working on the p.116 exercises.

The Monday lecture will be another tutorial on the P.116 exercises. In the Wednesday and Thursday lectures we will work on systems of differential equations.

In the Wednesday tutorial we will continue with the p.116 exercises.

In the Monday and Wednesday lectures we will make a start on the final chapter by looking at double integrals.

In the Wednesday tutorial we will work on the p. 163 and p. 182 exercises. This work will continue on Thursday.

On Monday and Wednesday we will finish looking at double integrals and then triple integrals.

In the Wednesday tutorial we will work on the p.182, p.192, and p.186 exercises. This work will continue on Thursday.

We will go through last year’s exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one.

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

]]>

We made a good start on probability, talking about random variables, independence, mutual exclusivity, conditional probability, and tree diagrams.

You can read about the child paradox here.

We will have a lot of probability to do — reliability block diagrams, the binomial distribution, the Poisson distribution.

You have a sample Maple Test with solutions (*the first with(Statistics) should be with(LinearAlgebra)). The Maple Test will not include anything from Chapter 2.

We do not have enough probability done to have a Maple Lab until…

We will look at the normal distribution and talk about sampling.

We will speak about sampling in more detail and also introduce control charts.

The Maple Test will be open book and you will have already received a sample test with solutions.

We will hold a review class on Wednesday 9 May in the usual room. First off, the *layout* of your exam is the same as Autumn 2016 (in the back of your notes): do question one worth 50/100 and two out of questions two, three, four; each worth 25/100.

I will field any questions ye might have at this time and if there are no questions we will do this exam paper. The best possible thing for your study is to do this exam paper and then on Wednesday see how you got on.

If you have missed a lab you have two options: either download Maple onto your own machine (instructions may be found here) or come into CIT at another time to use Maple.

Go through the missed lab on your own, doing *all* the exercises in Maple. Save the worksheet and email it to me.

Questions you can do include:

**After Week 9:**P. 92, Q. 1-10 (not too important); P. 96, Q. 1-6 (this is loads: more is Q. 7-13)**After Week 8*:**P. 89, Q. 1-3**After Week 7*:**P. 89, Q. 1 (a), (b); Q. 2 (b); Q. 3 (b)**After Week 6*:**P. 74, Q. 1-4; P. 77, Q. 1-3**After Week 5*:**P.44, Q. 1-3, Q. 4-5 more abstract. P.47, Q. 1-3, Q. 4 more abstract. P.56, Q. 1-3, Q. 4 more abstract. P.69, Q. 9 is an important question. A version might be

Use only

determinantsto determine if the following homogeneous system of linear equations has non-zero solutions:

**After Week 4:**P. 41, Q. 1-4**After Week 3:**P. 28, Q. 1-5, 6-9 have answers with Q. 7 a harder question. P. 34 exercises.**After Week 2:**P. 18 Q. 2**After Week 1:**P. 18 Q. 1, 3 – 6. Harder questions are 7 and 8. For those who do not yet have the manual, see here.

I am not suggesting you should do *all *of these. It is recommended by the module descriptor that you do two hours of independent and directed learning every week but of course this isn’t feasible for everyone.

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

]]>We finished talking about Laplace’s Equation and started talking about the Heat Equation.

In VBA we looked at finite difference methods for Laplace’s Equation. This completes the examinable VBA material. The Heat Equation that we cover in Week 10 will *not* be examinable.* *

We will look at finite differences for the Heat Equation. This completes the examinable written material.

In VBA we will implement same.

In the 09:00 class we will have a revision session, geared towards the 20% VBA Assessment 2.

In the 12:00 class we will have a revision session, geared towards the 40% Written Assessment 2.

Formulae will be provided in the VBA 2 Assessment.

To understand how your student numbers generate constants (see below) see this VBA Test 2 from last year (do *not *read this as a sample – it included e.g. the Heat Equation which you will not be examined on and the Laplace’s Equation might be slightly simpler than what ye will have).

The VBA 20% Assessment 2 format will be as follows.

Specifically,

; , ,

for some , , and step-size determined by your student number.

I want Euler Shooting Method approximations to for .

You can use:

- An Excel Worksheet, or
- Excel’s
*Goal Seek,*or - A VBA program

but you have to use a Shooting Method (technically *Goal Seek* takes loads of shots so I am happy to call it a shooting method).

It is up to you to understand which method is easiest for you.

*Use a shooting method to solve the following with :*

, , .

*Solution: *The preliminary work is to turn this into a system of first order initial value problems. To do so introduce a new variable for the first derivative (as it happens is the shear).

Let together with the initial value .

If is the first derivative of with respect to then

so that we have

.

We have no initial value for so we just guess for the moment… say .

Please see the first worksheet of *Shooting Method for Bending Moment* (it will be emailed) for the implementation of Euler’s Method for the system:

; ,

; ,

The first shot with produced , an undershoot (we are trying to get ).

We try again with a larger , say . This produces an overshot of .

Now use equation (3.38) on p. 130 of the notes to find the correct :

.

Now see the worksheet where the Euler Method is run with this value and the resulting graph (I am happy with just the values but if you can input the graph). Note this value of yields as required.

(Usually in engineering we plot underneath the -axis… don’t worry about this.)

Very similar set-up to the previous except we don’t have to take any shots and instead ask Excel to try a load of shots.

See Worksheet 2 of *Shooting Method for Bending Moment.*

So perhaps just put as a placeholder.

Now do Goal Seek (see p. 131). This produces and .

Again the set up is similar but we run the Euler Method via VBA.

See Worksheet 3 of *Shooting Method for Bending Moment* (or moreover the code behind the worksheet).

We have to take two shots and use equation (3.38) to get . Finally, we must run the program one more time.

Specifically,

; and

for some , , , and . These constants will be determined by your student number.

Use a Finite Difference Method with a mesh size (determined by your student number) [Sample: Lab 7, p.134, Problem 2], to produce approximations to for .

I have actually sent ye an email on 11 April with a worked example of this.

Specifically,

for the temperature at the point of a rectangular plate with boundary conditions given by , where is the boundary/perimeter of the rectangular plate .

The boundary temperature will be given in terms of your student number.

The above equation, Laplace’s equation, can instead by framed as the Mean Value Property which can be approximated using the ‘four adjacent gridpoint average’ once the rectangular plate is *meshed *using a square grid.

Sample Question: Lab 7, Problem 1, P. 133

I have not yet decided the format of the 40% Written Test but am toying with the idea of splitting the Test in two.

The problem with this is that I can do the first part of the test at 09:00 on the Tuesday in B242 but A183L is too small to conduct an assessment in.

I might consider putting the second part of the test into your VBA slot.

To ensure some kind of fairness, this would work as follows:

The first part of the Test would take place at 09:00 . It would be designed to be easily completed in 30-40 minutes. It would be geared more towards theoretical questions.

The second part of the Test would take place in your VBA slot. I would have to tell you in advance what questions are coming up, e.g. maybe

- Q. 1 Second Order Problem Using Heun’s Method
- Q. 2 Euler Shooting Method
- Q. 3 Heat Equation

Each group would get questions with only minor variations from the sample questions. I will confirm this next week.

Study should consist of

- doing exercises from the notes
- completing VBA exercises