## Assignment 1 – Results

Have been emailed to you.

## Week 7

We continued looking at partial fractions and then the inverse Laplace Transform.

## Week 8

We miss out on Monday due to St Patrick’s Day.

We will have two tutorials on Wednesday (p.121, p.112, p.103, p.100, p.99) before starting to look at Differential Equations on Thursday.

You will then be able to begin Assignment 2 after Thursday.

## Wednesday 20 March 2019, Week 8

As mentioned in previous weeks, I need to postpone the lecture of Tuesday 19 March, Week 8.

This will now take place the next night, Wednesday 20 March 2019.

Two students have indicated that they cannot attend this class: I will record as much of the class as possible but my camcorder usually doesn’t have the battery nor memory to record all 2.5 hours… but I’ll do my best.

## Outlook

As mentioned briefly in Week 6, 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 (see below) regularly.

## Week 7

We did a quick revision of differentiation before looking at Parametric Differentiation and starting to look at Related Rates.

If you want to look back here are two videos:

We mentioned briefly the Reuleaux Triangle and it’s use in the “Harry Watt Square Drill Bit”. See here for an animation of how this works.

## Week 8

We will finish looking at Related Rates and then look at Implicit Differentiation.

## Homework Exercises

If you do any of the suggested exercises you can give them to me for correction. Please feel free to ask me questions about the exercises via email or even better on this webpage.

I recommend strongly that everyone completes P.102, Q.1.

After that you can look at:

• P.102, Q. 2
• P.112, Q. 1-5

If you want to do more again, look at P.113, Q.6-9

## Test 2

Test 2, worth 15% and based on Chapter 3, will probably take place Week 11, 9 April. It might have to be pushed out to after Easter if we don’t make good progress on Chapter 3.

## Test 1 Results

…and marking scheme have been emailed to you.

## CIT Mathematics Exam Papers

These are not always found in your programme selection — most of the time you will have to look here.

## VBA Assessment 1 – Results

Last year I didn’t have these until Week 8.

## Written Assessment 1 – Results

Last year I didn’t have these until Week 9.

## Week 7

We looked at finite differences.

In VBA we have VBA Assessment 1.

## Week 8

We will do a (written) Shooting Method example and start looking at partial differential equations by looking at Laplace’s Equation.

In VBA we have MCQ VI and will do the Boundary Value Problems lab.

## Assignment 1 – Results

Last year the results were not made available until Week 8. I will do my best to have them to you comfortably before Week 8.

## Week 6

We had an Undetermined Coefficients Tutorial on Monday.

Tuesday, we started looking at “The Engineer’s Transform” — the Laplace Transform. We looked at the first shift theorem, and how the Laplace Transform interacts with differentiation. We started looking at partial fractions.

We had our Undetermined Coefficients Concept MCQ on Thursday. This showed up serious deficiencies in our ability to carry out differentiation. I may or may not come up with some interventional material.

## Week 7

We will continue looking at partial fractions and the inverse Laplace Transform. If we can finish Section 3.3 (doubtful) we will have tutorial time.

## Assignment 2

Assignment 2 will have a hand-in time and date of 12:00 8 April: the Monday of Week 11. Assignment 2 is in the manual, P. 164. Once we get someway into the examples on p.123 you should be able to make a start.

## 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.

## Study

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

## Exam Papers

These are not always found in your programme selection — most of the time you will have to look here.

## Tuesday 19 March 2019, Week 8

As mentioned in previous weeks, I need to postpone the lecture of 19 March, Week 8.

This will now take place the next night, Wednesday 20 March 2019.

Two students have indicated that they cannot attend this class: I will record as much of the class as possible but my camcorder usually doesn’t have the battery nor memory to record all 2.5 hours… but I’ll do my best.

## Outlook

As mentioned briefly in Week 6, 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 (see below) regularly.

## Week 6

We finished Chapter 2 by looking at Cramer’s Rule and then we did a Concept MCQ followed by tutorial time.

A video of a Cramer’s Rule Example

## Week 7

We will do a quick revision of differentiation. We will then look at Parametric Differentiation and Related Rates.

If you want to look ahead here are two videos:

## Homework Exercises

If you do any of the suggested exercises you can give them to me for correction. Please feel free to ask me questions about the exercises via email or even better on this webpage. Here are good exercises for Matrices. Feel free to try questions in the exercises that are not listed here (p.66, p.73, p.84,  or are in exam papers, see below):

• P.63, Q.1-4
• p.79, Q.1-2
• p.95, Q.3-5

## Test 2

Test 2, worth 15% and based on Chapter 3, will probably take place Week 11, 9 April. It might have to be pushed out to after Easter if we don’t make good progress on Chapter 3.

## Test 1 Results

…and marking scheme have been emailed to you.

## CIT Mathematics Exam Papers

These are not always found in your programme selection — most of the time you will have to look here.

## VBA Assessment 1

VBA Assessment 1 is taking place this week, Week 6.

Tuesday 14:20-16:00 will run 14:20-16:10

Friday 09:05-10:45 will run 09:05-10:55

In the Week 5 VBA we worked on Lab 3. Those of us who did not finish the lab are advised to finish it outside class time, and are free to email me on their work if they are unsure if they are correct or not.

## Written Assessment 1

Written Assessment 1 takes place Tuesday 12 March at 09:00 in the usual lecture venue.

Here is a copy of last year’s assessment. This should give you an idea of the length and format but not what questions are coming up – and replaces Section 1.6.1 of the manual.

However there are far more things I could examine.

Roughly, everything up to but not including Runge Kutta Methods (p.64). Some examples of questions I could ask include:

### ODEs in Engineering

p.13, Examples 1-4; p.15, Q.1-4

### General Theory

Example, p. 15; p.34 Example

### Maclaurin/Taylor Series

Examples 1 & 2 on p. 24; Q. 1 on p.27

### Euler Method

p.29, Examples 1-4; p. 38, Q.1-5, 8-9

### Three Term Taylor Method

p. 35, Examples 1-2; p.39, Q.7, 10-14

### Heun’s Method

p.38, Q. 6; p. 42, Examples 1-2l p. 47, Q.4-5

### Second Order Differential Equations

p.50, Example. p.51, Example. p.55, Q. 1-3, 5-14

When I say difficult, I mean difficult in comparison to the usual standard of Higher Level Leaving Cert Applied Maths Connected Particles Questions

## Question (a)

Consider the following:

A rectangular block moves across a stationary horizontal surface with acceleration $g/5$ (the question had $g/5$ m/s${}^2$ but the m/s${}^2$ is repeated as $g=9.8$ m/s${}^2$ and so includes the unit).

There is a serious problem with this question and that is that the asymmetry in the problem means that there is an ambiguity: is the block moving left to right or right to left? I am going to assume the block moves from left to right. One would hope not to see such ambiguity in an official exam paper.

Two particles of mass $M$ placed on the block, are connected by a taut inextensible string. A second string passes over a light, smooth, fixed pulley to a third particle of mass $2M$ which presses against the block as shown in the diagram.

### (i)

If contact between the particles and the block is smooth, find the magnitude and direction of the resultant forces acting on the particles.

#### Solution

Note firstly that there are two accelerations at play. The acceleration of the block relative to the horizontal surface, $g/5$, and the accelerations of the particles relative to the block, say $a$:

We draw all the forces (I lazily didn’t add arrows to the force vectors):

We know that the normal forces for the particles on top of the block because their vertical acceleration is zero and so the sum of the forces in that direction must be zero, and as the down forces are equal for both, necessarily the up forces must be equal too.

## Assignment 1

Assignment 1 has a hand-in time and date of 12:00 Friday 1 March (Week 5). Submit in class or to A283.

Work that is handed in late will be assigned a mark of ZERO so hand in what you have one time.

One final warning: do not give your work to others to copy. If there is a lack of originality of presentation I will be dividing marks between those who copy each other and the person who did the original work will be penalised along with those who copy them.

## Week 5

We finished our work on Chapter 2 — the method of Undetermined Coefficients — Wednesday PM. The Thursday class was (will be as I write) a tutorial.

## Week 6

On Monday we will have a tutorial on Undetermined Coefficients.

On Wednesday AM we will have a Concept MCQ, and then crack into Chapter 3, by looking at “The Engineer’s Transform” — the Laplace Transform.

## Study

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

## Exam Papers

These are not always found in your programme selection — most of the time you will have to look here.

## Tuesday 19 March 2019, Week 8

As mentioned in previous weeks, I need to postpone the lecture of 19 March, Week 8.

Three possibilities to catch up are:

• the next night, Wednesday 20 March 2019
• the Tuesday before Easter, Tuesday 16 April 2019
• the Wednesday after Easter, Wednesday 24 April 2019

Please fill in this Doodle poll by selecting all the days that you can attend.

Hopefully we can find a day that suits everyone but if people cannot make a day that is otherwise popular I will record the lecture.

## Test 1 – Results

I hope to have these out to you within 24 hours.

## Test 2

Test 2, worth 15% and based on Chapter 3, will probably take place Week 11, 9 April (or possibly Week 12, 30 April if we don’t go for a class Wednesday 20 March).

## Week 5

We had our test and then we talked about linear systems, and determinants.

## Week 6

We will finish Chapter 2 by looking at Cramer’s Rule. When we finish talking about Cramer’s Rule we will do a quick revision of differentiation, hopefully including some tutorial time.

## CIT Mathematics Exam Papers

These are not always found in your programme selection — most of the time you will have to look here.

## VBA Assessment 1

VBA Assessment 1 will take place in Week 6, (5 & 8 March) in your usual lab time.

Tuesday 10:05-11:45 will run 10:05 to 11:55

Tuesday 14:20-16:00 will run 14:20-16:10

Friday 09:05-10:45 will run 09:05-10:55

In the Week 5 VBA we worked on Lab 3. Those of us who did not finish the lab are advised to finish it outside class time, and are free to email me on their work if they are unsure if they are correct or not.

## Written Assessment 1

Written Assessment 1 takes place Tuesday 12 March at 09:00 in the usual lecture venue.

Here is a copy of last year’s assessment. This should give you an idea of the length and format but not what questions are coming up – and replaces Section 1.6.1 of the manual.

However there are far more things I could examine.

Roughly, everything up to but not including Runge Kutta Methods (p.64). Some examples of questions I could ask include:

### ODEs in Engineering

p.13, Examples 1-4; p.15, Q.1-4

### General Theory

Example, p. 15; p.34 Example

### Maclaurin/Taylor Series

Examples 1 & 2 on p. 24; Q. 1 on p.27

### Euler Method

p.29, Examples 1-4; p. 38, Q.1-5, 8-9

### Three Term Taylor Method

p. 35, Examples 1-2; p.39, Q.7, 10-14

### Heun’s Method

p.38, Q. 6; p. 42, Examples 1-2l p. 47, Q.4-5

### Second Order Differential Equations

p.50, Example. p.51, Example. p.55, Q. 1-3, 5-14