J.P. McCarthy: Math Page

Test 2

Test 2, worth 15% and based on Chapter 3, will now take place Week 12, 30 April. There is a sample test in the notes and the test will be based on Chapter 3 only.

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.136, Q.1-3
• P. 143, Q. 1-4
• P. 125, Q. 1-4, P.172, Q.1
• P. 117, Q. 1-4
• P.112, Q. 1-5
• Sample Test 2, P.145

If you want to do more again, look at P.113, Q.6-9, P. 118, Q. 5-6, P. 125, Q.5. There is a Weekly Summary for the Chapter 3 Material on P.144.

If you read on there is some information below about solutions to these exercises.

Week 10

For those who were able to make it we had some tutorial time from 18:00-19:00 for parametric, implicit, and related rates differentiation. If you are really interested in understanding how does a curve have an equation, see here.

In class we looked at partial differentiation and error analysis. For those who could not make it, here is video of the partial differentiation material and here are the slides from the error analysis (the video died shortly after we started error analysis).

We only started a revision of Antidifferentiation to start Chapter 4 on (Further) Integration. I have this section completed here.

Week 11

We will have some tutorial time from 18:00-19:00 for further differentiation (i.e. for Test 2, after Easter).

We are under pressure for time but I have made the decision that we will be better off completing our review of antidifferentiation before starting Chapter 4 proper. This might put us under time pressure later on but I believe it is the correct thing to do.

We will look at Integration by Parts, completing the square, and work.

Read the rest of this entry »

VBA Assessment 1 & Written Assessment 1 – Results

VBA Assessment 1 Results have been emailed and I hope to have your Written Assessment 1 Results to ye Wednesday or Thursday.

Week 10

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

In VBA we implemented same.

Week 11 — 2nd 20% VBA Assessment

I will be in B242 from 08:30 – 09:00 to help with any questions, ideally the p. 146 tutorial equations. This is extra time that I am making myself available but it is just an option for you.

This tutorial time will continue in B242 until 09:55.

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

To understand how your student numbers generate constants (see below) see this VBA Test 2 from 2017 (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).

Your VBA 2 Assessment will consist of three questions:

• shooting method
• finite differences; steady state temperature uninsulated rod (more P. 90)
• Laplace’s Equation

Formulae will be provided in the VBA 2 Assessment.

See last weeks’ Summary for more detail on the VBA 2 assessment.

Week 12 — 40% Written Test — After Easter

There will be no 12:00 class but I will be in B242 from 08:00 until about 08:40 for any last minute questions.

The second part of the Test will take place in your VBA slot. I have to tell you in advance what questions are coming up so let us say

1. Second Order Problem Using Heun’s Method
2. Heat Flux Density at a Point (p.101)
3. Heat Equation

Each group will get questions with only minor variations from the sample questions p. 111 (more Q. 1 on P.55).

Formulae will be provided in the Written Assessment 2.

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.

Final Concept MCQ League Table

Unfortunately with my illness this kind of ran of steam so this is the final standings.

Please ask questions in the lab about questions you have gotten wrong.

VBA Assessment 1 & Written Assessment 1 – Results

I have been very ill over the last two weeks but have gotten some meds from the doctor and hope to get these back to you ASAP.

Weeks 8 & 9

I missed the 09:00 class on the Tuesday of Week 8 with illness.

In the afternoon, we did two examples: of the Shooting Method and of Finite Differences (for the temperature along a rod). Please see Shooting_and_FiniteDifferences_Examples.

In Week 9, we started looking at partial differential equations by looking at Laplace’s Equation.

In VBA, in Week 8 we had MCQ VI and we did the Boundary Value Problems lab.

In VBA, in Week 9 we did the Laplace Equation Lab (which also had some 1-d boundary value stuff). I will email on a VBA file of the 1-D finite differences problem.

This completes the examinable VBA material. The Heat Equation that we cover in Week 10 will not be examinable. 

Week 10

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

In VBA we will implement same.

Read the rest of this entry »

Weeks 8 & 9

Week 8 was a disaster. We missed out on Monday due to St Patrick’s Day. We missed out on Wednesday morning because of my man flu. Thursday I had to go to Dublin for a funeral.

Week 9 we managed to get everything done so that you can now do Assignment 2.

We had two tutorials in Week 9

Week 10

We have two additional classes:

Monday 09:00, B189

Thursday 14:00, E6

So we have six classes

Monday x 2

Wednesday x 2

Thursday x 2

The following classes will be tutorials:

Monday x 2

Wednesday 09:00

Thursday 14:00

Wednesday 14:00 and Thursday 10:00 will be lectures, focused on Systems of Differenial Equations.

Read the rest of this entry »

Week 8

We finished looking at Related Rates and then looked at Implicit Differentiation. Video here.

Week 9

I cried off with illness. I’m on some medication and so hope to feel better by the weekend so next Tuesday should be grand.

I think it will be very difficult for us to catch up this missed class. We could come in during Easter but the Doodle poll suggests that this will not be possible.

What I am suggesting instead is that I make up these three hours by having three hours of tutorial time over Weeks 10-12. I will do this by being in B188 from 18:00 rather than 19:00 and using 18:00-19:00 as tutorial time. If you cannot make this time so be it (although if you can get in at 18:15, 18:30 or even 18:45 please do so).

We are also going to have our review class in Week 13.

This means we will not have Test 2 until AFTER Easter.

Read the rest of this entry »

Assignment 1 – Results

Have been emailed to you. Some remarks to common mistakes.

Week 7

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

We had about 30 minutes of tutorial time on Thursday.

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.

Read the rest of this entry »

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:

• Revision of Differentiation
• Operators

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.

Student Resources

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

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.

Read the rest of this entry »

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.

Student Resources

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

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:

• Revision of Differentiation
• Operators

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.

Student Resources

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