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MATH7019: Week 3

October 3, 2014 in MATH7019 | 2 comments

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.

Repeat Students — particularly EXAM ONLY

There have been some changes made to MATH7019

– Second Order Linear Ordinary Differential Equations have been moved to MATH7021 and are no longer studied in MATH7019

 – The chapter on Curve Fitting from MATH7021 has been introduced into MATH7019 however forward difference methods have been dropped altogether. The correlation coefficient has been added to this chapter. This material is being done first and will be completed by or in Week 3.

 – Cantilevers have been added to the section on beam equations

 – Regarding the chapter on Further Calculus, reviews of calculus topics have been spread out throughout the module

 – No change to the chapter on Statistics

To find out the exact syllabus please consult the module descriptor.  

Manuals

The manuals are priced at  €14 and are available in the Reprographic Centre.

Week 3

In Week 3 we finished talking about Least Squares Curve Fitting and started the second chapter on Differential Equations.

Week 4

In Week 4 we will continue with second chapter on Differential Equations — with a particular emphasis on Beam Equations.

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.

Based on the results of the Quick Test, I have already advised some of ye to attend the Academic Learning Centre.

Assessment 1

Assessment 1 will have a hand-in date of October 17. Expect to see the assignment early in Week 3.

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.

Read the rest of this entry »

MATH7019: Week 2

September 26, 2014 in MATH7019 | Leave a comment

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.

Repeat Students — particularly EXAM ONLY

There have been some changes made to MATH7019

– Second Order Linear Ordinary Differential Equations have been moved to MATH7021 and are no longer studied in MATH7019

 – The chapter on Curve Fitting from MATH7021 has been introduced into MATH7019 however forward difference methods have been dropped altogether. The correlation coefficient has been added to this chapter. This material is being done first and will be completed by or in Week 3.

 – Cantilevers have been added to the section on beam equations

 – Regarding the chapter on Further Calculus, reviews of calculus topics have been spread out throughout the module

 – No change to the chapter on Statistics

To find out the exact syllabus please consult the module descriptor.  

Manuals

The manuals are priced at  €14 and are available in the Reprographic Centre.

Week 2

In Week 2 we worked with Least Squares curve fitting, spoke about the correlation coefficient and started looking at Log-Linear Least Squares.

Week 3

In Week 3 we will finish talking about Least Squares Curve Fitting and start the second chapter on Differential Equations — with a particular emphasis on Beam Equations.

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.

Based on the results of the Quick Test, I have already advised some of ye to attend the Academic Learning Centre.

Assessment 1

Assessment 1 will have a hand-in date of October 17. Expect to see the assignment early in Week 3.

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.

Read the rest of this entry »

MATH7019: Week 1

September 17, 2014 in MATH7019 | Leave a comment

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.

Repeat Students — particularly EXAM ONLY

There have been some changes made to MATH7019

– Second Order Linear Ordinary Differential Equations have been moved to MATH7021 and are no longer studied in MATH7019

 – The chapter on Curve Fitting from MATH7021 has been introduced into MATH7019 however forward difference methods have been dropped altogether. The correlation coefficient has been added to this chapter. This material is being done first and will be completed by or in Week 3.

 – Cantilevers have been added to the section on beam equations

 – Regarding the chapter on Further Calculus, reviews of calculus topics have been spread out throughout the module

 – No change to the chapter on Statistics

To find out the exact syllabus please consult the module descriptor.  

Manuals

The manuals are not yet completed as far as I know. They will be priced at around €14 and will be available in the Reprographic Centre.

Week 1

In week one we spoke in general terms about curve fitting. We introduced Lagrange Interpolation and started talking about Least Squares curve fitting.

Week 2

In Week 2 we will finish talking about Least Squares Curve Fitting.

Tutorials

Tutorials start properly next week. Friday at 10 am in B240.

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.

Assessment 1

Assessment 1 will have a hand-in date of October 17. Expect to see the assignment late in Week 2 or early in Week 3.

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 why we do least squares.

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!

Additional Notes: E-Books

If you look in the module descriptor, you will see there is some suggested reading. Of course I think my notes are perfect but if you can look here, search for ‘glyn advanced modern engineering math’ you will see that the library have an E-Book resource.

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“

MATH7019: Week 12

December 9, 2013 in MATH7019 | 1 comment

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

Finally completed: here.

Week 12

In Week 12 we will finished the module by looking at Hypothesis Testing and Control Charts.

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 09:00 B212
  • Review Lecture Tuesday 14:00 B212
  • Review Lecture Wednesday 11:00 B212
  • Review Tutorial Thursday 15:00 B228

The Review Lectures will be conducted as follows (from Monday 9 December)

  1. Students can ask any question and I will answer it on the whiteboard. If we run out of questions
  2. I will start going through the Autumn 2013 paper (which was given out in the Thursday 28 December tutorial). If we finish this paper
  3. I will help ye one to one.

The Review Tutorials will be conducted as follows

  1. Students can ask any question and I will answer it on the whiteboard. If we run out of questions
  2. I will help ye one to one

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 What is a Confidence Interval?

MATH7019: Week 11

November 29, 2013 in MATH7019 | Leave a comment

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 A Probability Solutions

The CFO of a large civil engineering company is concerned about the number of sick days taken by its 2,000 construction workers and hires a business analyst to monitor the situation.

Question 1(a)

Historic records suggest that workers take an average of 5 sick days out of 220. The analyst assumes that the number of days missed in a year of 220 days has a Binomial Distribution. Calculate the probability that

Let X be the number of sick days that a worker takes in a year. The question says that  X is binomially distributed. The number of trials,  n, is 220 and the probability of a sick day… well if it is 5 out of 220 then it is  \displaystyle \frac{5}{220}=\frac{1}{44} and we have that  X\sim \text{Bin}[220,1/44].

i. a worker takes three or more sick days in a year

We are looking for for the probability that X is three or more

\mathbb{P}[X\geq 3]=\mathbb{P}[\text{not-}(X=0\text{ or }X=1\text{ or }X=2)]

=1-\mathbb{P}[X=X=0\text{ or }X=1\text{ or }X=2]

=1-(\mathbb{P}[X=0]+\mathbb{P}[X=1]+\mathbb{P}[X=2])

\displaystyle 1-\left({220\choose 0}\left(\frac{1}{44}\right)^0\left(\frac{43}{44}\right)^{220}+{220\choose 1}\left(\frac{1}{44}\right)^1\left(\frac{43}{44}\right)^{219}\right.

\displaystyle \left.+{220\choose 2}\left(\frac{1}{44}\right)^2\left(\frac{43}{44}\right)^{218}\right)

=1-(0.0063602+0.032541+0.08286)=0.8782

ii. a worker takes no sick days in a year.

We are looking for the probability that X is zero. We have actually found this above

\displaystyle \mathbb{P}[X=0]=0.00636.

Read the rest of this entry »

MATH7019: Week 10

November 25, 2013 in MATH7019 | Leave a comment

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 and Sample

Test 2 will take place on Thursday 28 November at 17:00, in B228. Please find a sample to give you an idea of the format.  The test will also come with a set of tables and formulae which is at the back of the “Normal Distribution” handout.

Course Notes

Finally completed: here.

Week 10

In Week 10 we started to look at the Poisson and Normal distributions.

Week 11

In Week 11 we will look at Sampling Theory and start Hypothesis Testing.

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 deep question about the normal distribution.

MATH7019: Week 9

November 14, 2013 in MATH7019 | Leave a comment

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 and Sample

Test 2 will take place on Thursday 28 November at 17:00, in B228. Please find a sample to give you an idea of the format. I will give you a copy of this on Monday. The test will also come with a set of tables and formulae which you will get with Monday’s notes.

Course Notes

At the moment they look like this.

Week 9

In Week 9 we started our work on probability after looking at some more non-homogenous second order linear differential equations with boundary conditions. We have so far just looked at the Binomial distribution.

Week 10

In Week 10 we will look at the Poisson and Normal distributions.

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 question about how many times you should win the lotto.

MATH7019: Week 8

November 7, 2013 in MATH7019 | Leave a comment

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

At the moment they look like this.

Week 8

In Week 8 we finished our work on beam analysis and looked at some more non-homogenous second order linear differential equations with boundary conditions.

Week 9

In Week 9 we will start our work on probability.

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 question about a moving load.

MATH7019: Week 7

November 1, 2013 in MATH7019 | Leave a comment

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

At the moment they look like this.

Week 7

In Week 7 we continued our work on beam analysis and looked at Macauley’s Method.

Week 8

In Week 8 we will finish our work on beam analysis. When we finish the beams we will do two more examples of non-homogenous ordinary second order linear differential equations with boundary/initial conditions.

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 question about how \int \delta(x-a)\,dx=H(x-a)+C.

MATH7019: Week 6

October 25, 2013 in MATH7019 | Leave a comment

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

Results pending.

Course Notes

At the moment they look like here.

Week 6

In Week 6 we began our study of beam analysis.

Week 7

In Week 7 we will continue our work on beam analysis and indeed look at Macauley’s Method. When we finish the beams we will do two more examples of non-homogenous ordinary second order linear differential equations with boundary/initial conditions.

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 by yours discussing the Delta Function \delta(x)?