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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.
Manuals
The manuals are priced at €14 and are available in the Reprographic Centre. Please purchase these ASAP.
Week 2
In Week 2 we learned how to differentiate with respect to first principles and also how to differentiate sums of differentiable functions.
Week 3
In Week 3 we will look at differentiating products, quotients (fancy word for fractions) and compositions.
Tutorials
The tutorial split is
ON EVEN WEEKS (e.g. this is Week 2 so is even)
– Group A’s tutorial is Tuesday at 13:00 in B145
– Group B’s tutorial is Friday at 09:00 in B185
ON ODD WEEKS (e.g. next week is Week 3 so is odd)
– Group A’s tutorial is Friday at 09:00 in B145
– Group B’s tutorial is Tuesday at 13:00 in B145
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 and there are sample tests in the notes.
Quick Test: 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.
I have already advised some of ye to go to the ALC for specific help.
Study
Please feel free to ask questions about the exercises via email or even better on this webpage — especially those of us who struggled in the test.
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.
Manuals
The manuals are priced at around €14 and are available in the Reprographic Centre. You will need these notes for Monday.
Week 1
In week one we spoke about the questions that the derivative and the definite integral were originally formulated to answer. Namely how do we find the tangent to a curve and how do we find the area of ‘curvy’ region.
Week 2
In Week 2 we will look at calculating some derivatives.
Tutorials
Tutorials start properly this week:
- Tuesday 13:00 in B145
- Friday 09:00 in B185
We will discuss the split on Monday.
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 and there are sample tests in the notes.
Quick Test: 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.
When I get the Quick Tests corrected I will be advising some of ye to go to the ALC for specific help.
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 about tangents to curves.
Maple Online & 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!
Calculators
Although Assessment 1 is to be taken without the use of calculators, subsequent assessments will have no such ban. 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 12
In Week 12 we spoke about differential equations. Most of next year’s maths will be taken up studying these ubiquitous engineering maths equations.
Week 13: Review Week
I will be available to any and all students (Groups A & B) at the following (usual) times and (usual) venues:
- Review Lecture Monday 16:00 B263
- Review Lecture Tuesday 09:00 B149
- Review Tutorial Tuesday 17:00 B165
- Review Lecture Thursday 11:00 B188
- Review Tutorial Friday 09:00 B188
The Review Lectures will be conducted as follows (from Monday 9 December)
- Students can ask any question and I will answer it on the whiteboard. If we run out of questions
- I will start going through the Autumn 2013 paper (which was given out in Thursday 28 December Lecture). If we finish this paper
- I will help ye one to one.
The Review Tutorials will be conducted as follows
- Students can ask any question and I will answer it on the whiteboard. If we run out of questions
- I will help ye one to one
Additional Notes
Find a possibly useful reference here.
Academic Learning Centre
Those in danger of failing need 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.
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 about why we need to talk about the root-mean-square value of a function.
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 11
In Week 11 about the applications of integration to volume & work as well as to the mean & root-mean-square values of a function. Essentially these are four formulae:
Volume of Revolution ![\displaystyle =V=\int_a^b\pi [f(x)]^2\,dx](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%3DV%3D%5Cint_a%5Eb%5Cpi+%5Bf%28x%29%5D%5E2%5C%2Cdx&bg=ffffff&fg=545454&s=0&c=20201002)
Work 
Mean Value of a Function 
Root-Mean-Square Value of a Function ![\displaystyle =f_{\text{rms}}=\sqrt{\frac{1}{b-a}\int_a^b[f(x)]^2\,dx}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%3Df_%7B%5Ctext%7Brms%7D%7D%3D%5Csqrt%7B%5Cfrac%7B1%7D%7Bb-a%7D%5Cint_a%5Eb%5Bf%28x%29%5D%5E2%5C%2Cdx%7D&bg=ffffff&fg=545454&s=0&c=20201002)
*I will get onto you very soon about this — they might be put on the exam paper.
Week 12
In Week 12 we will talk about differential equations. Most of next year’s maths will be taken up studying these ubiquitous engineering maths equations.
As of this moment there will be NO class on Friday 6 December. There is a small chance that I will make myself available at this time… ye will get an email about this before Tuesday.
Week 13: Review Week
I will be available to any and all students (Groups A & B) at the following (usual) times and (usual) venues:
- Review Lecture Monday 16:00 B263
- Review Lecture Tuesday 09:00 B149
- Review Tutorial Tuesday 17:00 B165
- Review Lecture Thursday 11:00 B188
- Review Tutorial Friday 09:00 B188
The Review Lectures will be conducted as follows (from Monday 9 December)
- Students can ask any question and I will answer it on the whiteboard. If we run out of questions
- I will start going through the Autumn 2013 paper (which was given out in Thursday 28 December Lecture). If we finish this paper
- I will help ye one to one.
The Review Tutorials will be conducted as follows
- Students can ask any question and I will answer it on the whiteboard. If we run out of questions
- I will help ye one to one
Additional Notes
Find a possibly useful reference here.
Academic Learning Centre
Those in danger of failing need 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.
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 about why we need to talk about the root-mean-square value of a function.
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.
Test 2 Results
To be honest I haven’t started correcting. I will have these before Friday.
Week 10
In Week 10 spoke about partial fractions and how to calculate areas using integration.
Week 11
In Week 11 we will talk about volumes and work using integration.
Additional Notes
Find a possibly useful reference here.
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.
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 one person wanted to know where the area of a circle 
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.
Test 2
Test 2 will take place this week. 9 am Friday 22 November in B240. Ye have a sample in your notes.
Week 9
In Week 9 we started looking at how to evaluate definite integrals that need a substitution.
Week 10
In Week 10 we will talk about partial fractions and how to calculate areas using integration.
Additional Notes
Find a possibly useful reference here.
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.
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. We have only scratched the surface with trigonometric substitutions as you can see here.
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.
Test 2 Notice
Test 2 will take place in Week 10. Probably at 9 am Friday 22 November in B240. Ye have a sample in your notes.
Week 8
In Week 8 we started looking at the important technique of integration by substitution.
Week 9
In Week 9 we will begin to learn how to evaluate definite integrals that need a substitution.
Additional Notes
Find a possibly useful reference here.
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.
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. I am fairly sure you are not reading this. If you are well done and look at this.
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 7
In Week 7 we started looking at integration.
Week 8
In Week 8 we will begin to learn how to evaluate definite integrals.
Additional Notes
Find a possibly useful reference here.
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.
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 awesome answer that explains in great detail everything we did this week.
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.
Test 1
I have the test results. I will bring the tests with me to the next two tutorials: one of which you will attend.
You are identified by the last four digits of your student number.
| S/N | Test 1 |
| 0826 | 90.5 |
| 3811 | 85.7 |
| 7813 | 85.7 |
| 6828 | 85.7 |
| 2521 | 83.3 |
| 6247 | 83.3 |
| 7718 | 78.6 |
| 2942 | 78.5 |
| 7113 | 76.2 |
| 4224 | 76.2 |
| 7472 | 73.8 |
| 2828 | 66.7 |
| 5625 | 64.3 |
| 9704 | 64.3 |
| 5686 | 64.3 |
| 7002 | 64.3 |
| 2263 | 64.3 |
| 8226 | 61.9 |
| 9290 | 61.2 |
| 9372 | 59.5 |
| 1047 | 59.5 |
| 8734 | 54.8 |
| 4136 | 52.4 |
| 4649 | 52.4 |
| 4918 | 47.6 |
| 7807 | 47.6 |
| 4203 | 47.6 |
| 2802 | 47.6 |
| 0418 | 45.2 |
| 4953 | 38.1 |
| 3513 | 38.1 |
| 0833 | 31 |
| 1034 | 28.6 |
| 8558 | 26.2 |
| 7604 | 9.5 |
The below is a scatter graph of Test 1 scores vs missed days. The correlation is strong and a statistician would call the effect of missed days on your test score to be large. Of course this doesn’t surprise me in the least. The fitted line says roughly that the average test score is given by 
where 
is the number of days missed. In other words: missing seven lectures and tutorials means that your score is nearly 30 percentage points lower than what it would have been had you had perfect attendance.
where is the number of days missed. In other words: missing seven lectures and tutorials means that your score is nearly 30 percentage points lower than what it would have been had you had perfect attendance.Additional Notes
Find a useful reference here.
Week 6
In Week 6 we finished looking at differentiation constrained optimisation problems.
Week 7
In Week 7 we will begin the second part of the module: the intimately linked concept of integration.
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.
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 about maximising the strength of a rod.
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.
Test 1
The first 15% test has been POSTPONED and now will take place at 4 pm Monday 21 October in B263 (Week 6). 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.
- Differentiation from First Principles
- Tangent Lines
- Differentiate by Rule
- Differentiate by Rule
- Differentiate by Rule
- Rates of Change
- Rate of Change/ Geometry of Graph
Additional Notes
Find a useful reference here.
Week 5
In Week 4 we learned how to find the maxima and minima of functions.
Week 6
In Week 6 we will finish the first part of the module by looking at constrained optimisation problems.
J.P. McCarthy: Math Page 
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