You are currently browsing the category archive for the ‘MATH7021’ category.

## 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:

1. have I answered the question that was asked?
2. does my answer make sense?
3. 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..

## 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.

## 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.

## 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..

## 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.

More information in last week’s Weekly Summary.

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.

## Student Resources

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

## 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.

Read the P.51 and P.52 instructions carefully. You will be submitting an Excel file, 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 first 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 $c_i$ and $P$ they are calculated in MATH7021A1 – Student Data.

We have now covered enough in class for you to do all of the Assignment. I recommend that you start ASAP.

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.

Regarding Q. 1.3.5, Assignment 1, on P.62 of the manual. The intention with Q. 1.3.5 (b) 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 part (b) 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 (c) if you do six iterations and do not yet have convergence.

## Assignment 1

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

Read the P.51 and P.52 instructions carefully. You will be submitting an Excel file, 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 first 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 $c_i$ and $P$ they are calculated in MATH7021A1 – Student Data.

We have now covered enough in class for you to do all of the Assignment. I recommend that you start ASAP.

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 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 also had about ten minutes of tutorial time with this.

On Wednesday we showed the following video, which shows how the approximations to the solution iterate:

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 12:00  Friday 1 March (Week 5).

Read the P.51 and P.52 instructions carefully. You will be submitting an Excel file, 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 rst 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 $c_i$ and $P$ they are calculated in MATH7021A1 – Student Data.

We have now covered enough in class for you to do all of the Assignment except for Q. 1.3.5. 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 started Monday with some Gaussian Elimination Concept MCQs. We probably should have waited until we finished the Gaussian Elimination examples, which we did straight afterwards.

Wednesday am we had some tutorial time — and then Wednesday pm began to look at applications of linear systems to traffic and pipe flow.

On Thursday we finished the section on pipe flow and had a little more 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 hopefully have another Concept MCQ. Wednesday pm we will have more tutorial time (and do the Concept MCQ if necessary).

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.

## 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..