Category Archive

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.

Attendance

Frankly, as a group our attendance is abysmal. Not coming to tutorials and regularly missing lectures only means one thing: failure. Attending everything does not guarantee success but it is certainly necessary. You will not be getting much sympathy from me if you fail the test miserably having not attended class properly.

Test 1

The first 15% test will take place at 9 am FRIDAY 18 October in PF45 (Week 5). You can find a sample in the course notes, after the section on rates of change I think. It is a test that could arguably take 42 minutes but I’ll give ye from 9.05 — 10 am. You will be given a copy of these tables. Don’t worry I’ll scribble out the “UCC”!

Note that the format will be the same of this.

1. Differentiation from First Principles
2. Tangent Lines
3. Differentiate by Rule
4. Differentiate by Rule
5. Differentiate by Rule
6. Rates of Change
7. Rate of Change/ Geometry of Graph

Course Notes

The notes contain all the lecture material, all the exercises and exercise sheets as well as all of last year’s assessments and you will need them from Monday on. They cost €12 and are on sale in the copying centre. Also find a useful reference here.

Week 4

In Week 4 we worked on the Chain Rule and spoke applications of differentiation to rates of change. Finally we started talking about the duality between algebra & geometry.

Week 5

In Week 5 we will continue our work on the interplay between geometry & algebra and learn how to find the maxima/minima of functions.

Tutorials

Regarding the tutorial time split:

Academic Learning Centre

I would urge anyone having any problems with material that isn’t being addressed in the tutorials to use the Academic Learning Centre. As you can see the timetable is quite generous. You will get best results if you come to the helpers there with specific questions. You could also win a tablet device if you enter a competition that they are running.

Maple & Wolfram Alpha

If you are subscribed to CIT MathsOnline you will have free access to the mathematical software package Maple:

Self-enrolment for Maths Online

1.           Log into Blackboard Learn

2.           Click on the Courses tab button at the top of the screen. Go to Course Search and type Maths Online in the box.

3.           Once you’ve found the course, click on the action link button next to the course and click on Enrol. This should take you to the Self Enrolment page.

4.           Your Access Code is mathsonline (lower case, no spaces).

5.           After you’ve finished click Submit. You should now see a message that says your enrolment was successful.

Once you’ve enrolled, you can download Maple by selecting the Mathematical Software tab in the left hand column and following the instructions under the Maple item.

I myself am not a Maple expert but ‘grew up’ with another mathematical software package Mathematica. Mathematica powers the “computational knowledge engine” WolframAlpha. Go on ask it a question!

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question discussing whether increasing implies first derivative positive all the time.

Calculators

Please note the following taken from the CIT code of conduct for CIT examination candidates:

“Where a pocket calculator is used it must be silent, self-powered and non-programmable. 

It may not be passed from one candidate to another. Instructions for its use may not be 
brought into the Examination Hall. 
The term ‘programmable’ includes any calculator that is capable of storing a sequence of 
keystrokes that can be retrieved after the calculator is turned off or powers itself off. Note that the 
capacity to recall, edit and replay previously executed calculations does not render a calculator 
programmable, provided that this replay memory is automatically cleared when the calculator is 
powered off. Also, the facility to store numbers in one or more memory locations does not render 
a calculator programmable. 
Calculators with any of the following mathematical features are prohibited: 
• Graph plotting 
• Equation solving 
• Symbolic algebraic manipulation 
• Numerical integration 
• Numerical differentiation 
• Matrix calculations 
Calculators with any of the following features are prohibited 
• Data Banks 
• Dictionaries 
• Language translators 
• Text retrieval 
• Capability of remote communication“

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.

Course Notes

The notes contain all the lecture material, all the exercises and exercise sheets as well as all of last year’s assessments and you will need them from Monday on. They cost €12 and are on sale in the copying centre. Also find a useful reference here.

Test 1

The first 15% test will take place at 9 am FRIDAY 18 October in PF45 (Week 5). You can find a sample in the course notes, after the section on rates of change I think. It is a test that could arguably take 42 minutes but I’ll give ye from 9.05 — 10 am. You will be given a copy of these tables. Don’t worry I’ll scribble out the “UCC”!

Note that the format will be the same of this.

1. Differentiation from First Principles
2. Tangent Lines
3. Differentiate by Rule
4. Differentiate by Rule
5. Differentiate by Rule
6. Rates of Change
7. Rate of Change/ Geometry of Graph

Week 3

In Week 3 we learned how to differentiate quotients (fancy word for fractions) using the quotient rule and compositions  using the Chain Rule.

Week 4

In Week 4 we will continue our work on the Chain Rule and hopefully talk about applications of differentiation to rates of change.

Read the rest of this entry »

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.

Course Notes

The course notes are now on sale in the copying centre (beside the student centre). I would advise you to buy them ASAP. You will need to put money in your card to buy them (you can do this at the shop beside the canteen) and they cost E12. I would buy them Monday – although I will do photocopies for Monday & Tuesday. For Thursday you must have a copy of the notes as there will be no more photocopies. The notes contain all the lecture material, all the exercises, all of last years tests & exam as well as a small set of mathematical tables.

Week 2

In Week 2 we looked at differentiating some common functions. In particular we looked at the Product Rule.

Tutorials

Regarding the tutorial time split:

Academic Learning Centre

I would urge anyone having any problems with material that isn’t being addressed in the tutorials to use the Academic Learning Centre. As you can see the timetable is quite generous. You will get best results if you come to the helpers there with specific questions. You could also win a tablet device if you enter a competition that they are running.

Maple & Wolfram Alpha

If you are subscribed to CIT MathsOnline you will have free access to the mathematical software package Maple:

Self-enrolment for Maths Online

1.           Log into Blackboard Learn

2.           Click on the Courses tab button at the top of the screen. Go to Course Search and type Maths Online in the box.

3.           Once you’ve found the course, click on the action link button next to the course and click on Enrol. This should take you to the Self Enrolment page.

4.           Your Access Code is mathsonline (lower case, no spaces).

5.           After you’ve finished click Submit. You should now see a message that says your enrolment was successful.

Once you’ve enrolled, you can download Maple by selecting the Mathematical Software tab in the left hand column and following the instructions under the Maple item.

I myself am not a Maple expert but ‘grew up’ with another mathematical software package Mathematica. Mathematica powers the “computational knowledge engine” WolframAlpha. Go on ask it a question!

Week 3

In Week 3 we will learn how to differentiate quotients (fancy word for fractions) and compositions .

Continuous Assessment

As can be seen here in the Module Descriptor, there will be two 15% tests: one in Week 5 and one in Week 10. I hope to give you two week’s notice of each of these and also provide sample tests.

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage — especially those of us who struggled in the test.

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question regarding a more rigorous proof of the product rule (our argument was handwaving).

Calculators

Please note the following taken from the CIT code of conduct for CIT examination candidates:

“Where a pocket calculator is used it must be silent, self-powered and non-programmable. 

It may not be passed from one candidate to another. Instructions for its use may not be 
brought into the Examination Hall. 
The term ‘programmable’ includes any calculator that is capable of storing a sequence of 
keystrokes that can be retrieved after the calculator is turned off or powers itself off. Note that the 
capacity to recall, edit and replay previously executed calculations does not render a calculator 
programmable, provided that this replay memory is automatically cleared when the calculator is 
powered off. Also, the facility to store numbers in one or more memory locations does not render 
a calculator programmable. 
Calculators with any of the following mathematical features are prohibited: 
• Graph plotting 
• Equation solving 
• Symbolic algebraic manipulation 
• Numerical integration 
• Numerical differentiation 
• Matrix calculations 
Calculators with any of the following features are prohibited 
• Data Banks 
• Dictionaries 
• Language translators 
• Text retrieval 
• Capability of remote communication“

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

In week one we spoke about the questions that the derivative and the definite integral were originally formulated to answer. This led us onto a how to formulate the idea of a limit. We showed that the derivative correctly asked for the slope of a tangent to the line (i.e. the slope of the line).

Tutorials

Tutorials start properly this week:

• BIS/BEN: Tuesday 17:00 in PF45
• BIO: Friday 09:00 in PF45

We will discuss these times further on Monday.

Academic Learning Centre

I would urge anyone having any problems with material that isn’t being addressed in the tutorials to use the Academic Learning Centre. As you can see the timetable is quite generous. You will get best results if you come to the helpers there with specific questions. You could also win a tablet device if you enter a competition that they are running.

Week 2

In Week 2 we will look at differentiating some common functions.

Continuous Assessment

As can be seen here in the Module Descriptor, there will be two 15% tests: one in Week 5 and one in Week 10. I hope to give you two week’s notice of each of these and also provide sample tests.

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage — especially those of us who struggled in the test.

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question regarding the derivative of .

Calculators

Please note the following taken from the CIT code of conduct for CIT examination candidates:

“Where a pocket calculator is used it must be silent, self-powered and non-programmable. 

It may not be passed from one candidate to another. Instructions for its use may not be 
brought into the Examination Hall. 
The term ‘programmable’ includes any calculator that is capable of storing a sequence of 
keystrokes that can be retrieved after the calculator is turned off or powers itself off. Note that the 
capacity to recall, edit and replay previously executed calculations does not render a calculator 
programmable, provided that this replay memory is automatically cleared when the calculator is 
powered off. Also, the facility to store numbers in one or more memory locations does not render 
a calculator programmable. 
Calculators with any of the following mathematical features are prohibited: 
• Graph plotting 
• Equation solving 
• Symbolic algebraic manipulation 
• Numerical integration 
• Numerical differentiation 
• Matrix calculations 
Calculators with any of the following features are prohibited 
• Data Banks 
• Dictionaries 
• Language translators 
• Text retrieval 
• Capability of remote communication“

Test 2 Solutions

Please find the test 2 solutions and marking scheme here.

Exam Layout

Answer Q.1 [40 Marks] and two out of Q. 2, 3, 4 [30 marks each].

Q. 1 — 8 short questions each worth 5 marks each

Q. 2 — Differentiation with applications

Q. 3 — Integration with applications

Q.4 — Applications of differentiation and integration

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Week 13

I will run tutorial reviews in the usual lecture venues on

• Monday 10 December at 16:00*,
• Tuesday 11 December at 09:00,
• Thursday 11:00 and
• Friday 09:00.

*I had said in class that I would not do Monday but I’ve had a change of heart. Please email me if this is clashing with some assessment or other. Also please spread the word on Monday afternoon that I will hold this tutorial.

The different things I can do are:

1. Talk about exam layout
2. Answer questions
3. Do an exam paper
4. Help one-to-one

I can give the exam layout here:

Answer Q.1 [40 Marks] and two out of Q. 2, 3, 4 [30 marks each].

Q. 1 — 8 short questions each worth 5 marks each

Q. 2 — Differentiation with applications

Q. 3 — Integration with applications

Q.4 — Applications of differentiation and integration

I would prefer to answer questions on the board from people until there are no more.

If there are no questions I will start going through Winter 2010 — which I will have printed out for ye.

If we finish this (doubtful), I will start helping one-to-one.

Test 2 Results

Read the rest of this entry »

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Test 2 Results

Hopefully I should have these by Friday.

Additional Tutorial

An additional tutorial for MATH6015 has been arranged for today Tuesdays 17:00 – 18:00 in PF45. All may attend.

Lectures

We finished off the questions on volumes and work. We continue our work on the mean value of a function and the root-mean-square value of a function. The only topic left is ordinary differential equations.

Week 13

I will run tutorial reviews in the usual lecture venues on Tuesday 11 December at 09:00, Thursday 11:00 and Friday 09:00.

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Test 2

The second test will take place at 9 am next Friday 30 November. It is another 15% test that could arguably take 48 minutes but I’ll give ye from 9.05 — 10 am. Please find a sample.

Additional Tutorial

An additional tutorial for MATH6015 has been arranged for Tuesdays 17:00 – 18:00 in PF45.

To keep the numbers low at tutorials (so I can spend more time with ye) we have the following arrangement.

The BioEng students who have their lab in Week 10 (19 November 23 November) are known as GROUP I. Those who are doing their lab in Week 11 are known as GROUP II.

The following groups may attend the relevant tutorials:

Week 10

Tuesday 20 November: ALL

Week 11

Monday 26 November: Group I and BIS ONLY

Tuesday 27 November: ALL

Read the rest of this entry »

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Test 2 — POSTPONED

The second test will now take place at 9 am next Friday 30 November. It is another 15% test that could arguably take 48 minutes but I’ll give ye from 9.05 — 10 am. Please find a sample.

Additional Tutorial

An additional tutorial for MATH6015 has been arranged for Tuesdays 17:00 – 18:00 in PF45.

To keep the numbers low at tutorials (so I can spend more time with ye) we have the following arrangement.

The BioEng students who have their lab in Week 10 (19 November 23 November) are known as GROUP I. Those who are doing their lab in Week 11 are known as GROUP II.

The following groups may attend the relevant tutorials:

Week 10

Tuesday 20 November: ALL

Week 11

Monday 26 November: Group I and BIS ONLY

Tuesday 27 November: ALL

Week 12

Monday 3 December: Group II and BIS ONLY

Tuesday 4 December: ALL

Read the rest of this entry »

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

Attendance

Our attendance hasn’t been the best (although it is improving). You should know by now that missing lectures is a false economy.

Notes

So far we have covered up to and including Trigonometric Integration: MATH6015 Lecture Notes (with gaps).

Test 2!

The second test will take place at 9 am on Friday 23 November (Week 10). It is another 15% test that could arguably take 48 minutes but I’ll give ye from 9.05 — 10 am. Please find a sample. I will give ye a copy on Monday. You will be given a copy of these tables.

Note that the format will be the same of this: eight integrals that that could be a mix of everything and anything from the start of the chapter up to and including partial fractions.

Next Week

On Monday we will have a tutorial where we will work more on doing definite integrals (with limits) that need a substitution. In the rest of the week we shall learn about these partial fractions and also do the exam questions that I forgot to put in the notes (definite integrals that need a substitution, trigonometric integrals and partial fractions).