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Week 7
We continued looking at “The Engineer’s Transform” — the Laplace Transform.
We continued looking at partial fractions and then the inverse Laplace Transform.
We had one tutorial Wednesday PM where we worked on partial fractions.
Week 8
It is my intention to record lectures at home. I have a camcorder and a whiteboard in my home office.
I am going to, more or less as soon as possible, record at home enough lectures for you to be able to do the second assignment. This means I want to push forward up to p.132.
I expect ye to watch the lectures and to spend some time doing exercises. How much time you devote to exercises is up to you, but in theory you are supposed to spend 7 hours per week on MATH7021 between classes and independent learning.
Week 6
We finished off Chapter 2 on Monday and then had some tutorial time.
Wednesday, after an Undetermined Coefficients MCQ, 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.
Only those of us who finished Assignment 1 early got much tutorial time with Chapter 2. I will hope that we will get more tutorial time on Chapter 2 at a later date, but until then, I have developed the following for you to practise your differentiation which you need for Chapter 2 here:
It might not be the worst idea in the world to devote some time to this over Easter.
Assignment 1 – Results and Remarks
Have been emailed to you.
Week 5
We almost finished Chapter 2 on Wednesday. We must do a little more in Week 6.
I was absent Wednesday AM but instead we have an extra class, tomorrow, Thursday 09:00 in B185.
We thus have two hours of tutorial time tomorrow Thursday. You will be allowed work on Assignment 1. If you are ready for Assignment 1 you need to start looking at the Chapter 2 exercises.
Assignment 1
Assignment 1 now has a hand-in time and date of 18:00 Thursday 27 February (Week 5). Submit in class tomorrow or to A283.
- Work submitted after the deadline will be assigned a mark of ZERO. Hand up whatever you have on time.
Your Excel file must be submitted via CANVAS.
More information in the last two weekly summaries.
I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.
Assignment 1
Assignment 1 has a hand-in time and date of 11:00 Thursday 27 February (Week 5).
See the Week 2 Summary for more.
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.
Note in particular:
- Work submitted after the deadline will be assigned a mark of ZERO. Hand up whatever you have on time.
- Only Partial Pivoting has to be done using Excel.
- Note that if you are doing Gaussian Elimination by hand you must use exact fractions and square roots rather a decimal approximation.
- I advise that you do the questions out roughly first because small mistakes are inevitable.
THIS IS A LEARNING ACTIVITY NOT JUST A GRADED ACTIVITY. THE CHAPTER ONE EXAM QUESTION IS WORTH 24.5% OF YOUR FINAL GRADE WHILE THIS ASSIGNMENT IS WORTH JUST 15%. THINK ABOUT WHAT THIS MEANS.
Regarding Problem F, Assignment 1, on P.66 of the manual. The intention with Problem F really is for you to engage in some problem solving skills to come up with a clever way of implementing the Jacobi Method in Excel.
It should still be doable by hand but if it takes a large number of iterations to converge (to two significant figures), Excel is far more suitable.
It is possible that it could take a small number of iterations to converge to two significant figures (say two or three iterations) — which is no problem by hand — but potentially it could take more (at least six). I don’t really want people spending loads of time doing iterations by hand, so I will give 3/4 marks for Q. 2 if you do six iterations by hand. If you want to keep going – by hand – until convergence (to two significant figures) you can of course get the 4/4 marks – but you need to ask yourself is it worth your time to keep going for the sake of one mark (out of 60… out of 15% —- that is 0.25% of your final grade).
If it converges with fewer than six iterations then happy days for you, you can get 4/4.
If it doesn’t, you might be better off trying to come up with a way of doing the question in Excel if you really want all the marks.
You can still answer part Q. 3 if you do six iterations and do not yet have convergence.
Week 4
I was late on Monday… so we had a tutorial instead of a lecture.
We had another tutorial Wednesday AM.
We worked on Chapter 2 Wednesday PM and Thursday.
09:00 Wednesday 26 February
We will not have class 09:00 on Wednesday. Instead we will have class at 09:00 on Thursday, provisionally in B185. Watch this space.
Week 5
We will hopefully finish off our work on the method of undetermined coefficients between Monday and Wednesday PM. We will have two hours of tutorial on Thursday morning before the Assignment 1 deadline of 11:00.
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..
I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.
Assignment 1
Assignment 1 has a hand-in time and date of 11:00 Thursday 27 February (Week 5).
See the Week 2 Summary for more.
Week 3
On Monday, we looked at applications to temperature distribution, where the Jacobi Method is used to find approximate solutions to a diagonally dominant linear system. We had about ten minutes of tutorial time.
To understand more what is going on watch the following video, which shows how the approximations to the solution iterate:
On Wednesday we had two tutorials on Chapter 1, including a second Concept MCQ.
On Thursday we started work on Chapter 2 — the method of undetermined coefficients for solving linear odes.
Week 4
We will continue our work on Chapter 2 on Monday and Wednesday AM, then we will have two tutorials Wednesday PM and Thursday.
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..
I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.
Assignment 1
Assignment 1 has a hand-in time and date of 11:00 Thursday 27 February (Week 5).
Read the P.54 and P.55 instructions carefully. You will be submitting an Excel file, to Canvas, and written work (including a print out of your Excel work).
Note in particular:
- Work submitted after the deadline will be assigned a mark of ZERO. Hand up whatever you have on time.
- Only Partial Pivoting has to be done using Excel.
- Note that if you are doing Gaussian Elimination by hand you must use exact fractions and square roots rather a decimal approximation.
- I advise that you do the questions out roughly because small mistakes are inevitable.
The files you need to complete this assignment have been emailed to you. If you don’t want to calculate your 
We have now covered enough in class for you to do all of the Assignment except for Problem F. After Monday we will have enough covered in class.
WARNING!
This gives a good opportunity for collaboration but remember collaboration does not mean one student solving the problem and everyone else copying that student’s work. I demand originality of presentation here and you should at least understand what you hand up. If you are unsure of what I mean by this please email me immediately as if I have students who have clearly copied the answer word-for-word from another student they will all be sharing the marks.
Start early so you have enough time to complete the assignment properly and get good learning from it.
THIS IS A LEARNING ACTIVITY NOT JUST A GRADED ACTIVITY. THE CHAPTER ONE EXAM QUESTION IS WORTH 24.5% OF YOUR FINAL GRADE WHILE THIS ASSIGNMENT IS WORTH JUST 15%. THINK ABOUT WHAT THIS MEANS.
Week 2
We finished the Gaussian Elimination examples on Monday — then had some tutorial time Wednesday AM — and then Wednesday PM we will began to look at applications of linear systems to traffic and pipe flow.
We started Thursday with some Gaussian Elimination Concept MCQs.
Then we finished the section on pipe flow and had 10 minutes tutorial time.
Week 3
On Monday, we will look at applications to temperature distribution, where the Jacobi Method is used to find approximate solutions to a diagonally dominant linear system.
Wednesday am we will finish looking at Chapter 1, and possibly have another Concept MCQ. Wednesday pm we will have more tutorial time.
On Thursday we will start work on Chapter 2 — the method of undetermined coefficients for solving linear odes.
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..
I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.
Week 1
We started the first chapter on Linear Algebra. Essentially, for us, simultaneous equations. We looked at Gaussian Elimination including Partial Pivoting, which is required in the presence of rounding. We looked at three examples, and had a tutorial on Thursday.
Week 2
We will finish the Gaussian Elimination examples on Monday — then have some tutorial time Wednesday AM — and then Wednesday PM we will begin to look at applications of linear systems to traffic and pipe flow.
Assignment 1
Assignment 1 has a hand-in date of Thursday 27 February (Week 5). More information next week once the class list has settled down.
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..
Mathematics Exam Advice
- The first piece of advice is to read questions carefully. Don’t glance at a question and go off writing: take a moment to understand what you have been asked to do.
- Don’t use tippex; instead draw a simple line(s) through work that you think is incorrect.
- For equations, check your solution by substituting your solution into the original equation. If your answer is wrong and you know it is wrong: write that on your script.
If you do have time at the end of the exam, go through each of your answers and ask yourself:
- have I answered the question that was asked?
- does my answer make sense?
- check your answer (e.g. differentiate/antidifferentiate an antiderivative/derivative, substitute your solution into equations, check your answer against a rough estimate, or what a picture is telling you, etc)
Week 12
On Monday, and Wednesday PM, we finished the module by looking at triple integrals.
The Wednesday 09:00 lecture was a tutorial along with most of Wednesday PM and the Thursday class.
Assignment 2
Has been corrected and results emailed to you.
Some remarks on common mistakes here.
Week 11
We had a systems of differential equations tutorial Monday and before looking at double integrals.
Week 12
We will look at triple integrals and then have one or two tutorials on. Possibly Wednesday 09:00 for double integrals and Thursday for triple integrals.
Week 13
We will review the Summer 2018 paper.
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..
Week 10
We had two additional tutorials… actually four tutorials in total and two lectures; the lectures focused on Systems of Differential Equations.
Assignment 2
Assignment 2 now has a pushed back deadline of 12:00, 12 April: the Friday of Week 11. Assignment 2 is in the manual, P. 164. Usual warnings about copying apply.
Week 11
We will have a systems of differential equations tutorial Monday and then look at double integrals.
Week 12
We will look at triple integrals and then have one or two tutorials. Possibly Monday for double integrals and Thursday for triple integrals.
Week 13
We will review the Summer 2018 paper.
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..
J.P. McCarthy: Math Page 
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