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.

Test 2

Test 2 — on Laplace Methods — will now be held at 13:00 on Tuesday 30 April in Week 12 in B190. I have a sample ready here — for q.1(a) let .

Week 10

We started line integrals which typically have applications to calculating the work done by a force.

Weeks 11 & 12

We will finish off line integrals and look at double integrals and triple integrals.

Week 13

We will probably review by going through the Winter 2012 paper.

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 rather technical question on the inverse Laplace transform.

Tutorials

Yes the following table should be A-L and M-Z not A-L and K-Z!

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 — on Laplace Methods — will be held on Monday 2 May in Week 12. I have a sample ready here — for q.1(a) let .

Week 9

Finished off Laplace. I gave ye the Laplace-Mega-Sheets (TM) also. We started line integrals.

Week 10

We will continue our work on line integrals.

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 on a line integral.

Tutorials

Yes the following table should be A-L and M-Z not A-L and K-Z!

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

Having spoken with Ted, Test 2 — on Laplace Methods — will now be held on Monday 29 April in Week 12 (rather than Week 11). I have a sample ready here — for q.1(a) let .

Weeks 7 & 8

Plenty of Laplace

Week 9

Finish off Laplace. I will give ye the Laplace-Mega-Sheet (TM) also.

More Explanations

Somebody told me the beauty of learning about maths off a video is that you can pause the lecturer. I found these online and I have to say I like these lectures a lot… not many examples but we do them in class even if you seem to think that I don’t!

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/

Ye would have covered lectures 11 to 14 last semester.

Lectures 19 & 20 are relevant for us. Lecture 22 and 23 are where this stuff ends up being really useful (not in MATH7021 unfortunately).

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 on an inverse Laplace transform.

Weeks 10 – 12

Multiple Integration.

Tutorials

Yes the following table should be A-L and M-Z not A-L and K-Z!

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 Results

You are identified by the last five digits of your student number. Two students never wrote down their name nor student number and should make themselves known to me.

Week 6

We defined what the Laplace transform is and found the Laplace transforms of some common functions. We proved that the Laplace transform is linear and this allowed us to find the Laplace transform of sine and cosine functions via the Euler Formula. We also proved the First Shift Theorem.

Week 7

Next week we will work slowly and deliberately developing our Laplace stuff in particular how well it behaves with respect to differential equations.

Tutorials

This week coming it is

13:30 Groups S1 and S3 (M-Z)

14:30 Groups S2 and S3 (A-L)

Yes the following table should be A-L and M-Z not A-L and K-Z!

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

Please find a sample – (bit of a mistake here — change all the s to plus rather than minus).

Week 5

We continued finished our work on the Jacobi Method and the similar Gauss Siedel Method.  We summarised the five methods that we developed for solving linear systems; weighing up the pros and cons of each. Finally we started our work on Laplace Methods by talking about infinite integrals.

Week 6

Next week we will work slowly and deliberately developing our Laplace stuff. We will also have our test on Thursday.

Tutorials

This week coming it is, and I will be enforcing it

13:30 Groups S2 and S3 (A-L)

14:30 Groups S1 and S3 (M-Z)

Yes the following table should be A-L and M-Z not A-L and K-Z!

Diagonally Dominant Systems

We use the Jacobi & Gauss-Siedel Methods for solving diagonally dominant linear systems. I wasn’t sure where diagonally dominant systems show up in Civil Engineering but a quick Google shows me that they come up in finite element analysis. This is a technique to numerically solve differential equations that we can’t solve exactly: in some sense most useful differential equations can’t be solved exactly and finite element analysis is a method for approximating solutions.

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.

Five students still owe me E10 for the notes. If this is a problem for you send me a confidential email. I don’t want to be chasing ye but if ye can’t get in touch with me I will have to.

Test 1

The test will be held in Week 6 (Thursday 7 March). Please find a sample – (bit of a mistake here — change all the s to plus rather than minus). The test will be on the material covered in weeks 1-4 inclusive so everything up to section 2.3 inclusive. The test will be 50 minutes long. The sample is to give you an idea of the format and length. However Q.1 will be on finite differences, Q. 2 will be on Least Squares, Q. 3 Gaussian Elimination and Q.4 Gaussian Elimination with Partial Pivoting. Lagrange Interpolation can sneak into Q. 1 or 2 while Cramer’s Rule can sneak into Q. 3 or 4.

Week 4

We continued our work on Gaussian elimination. We discussed Cramer‘s Rule; we explained why computers struggle with Gaussian elimination and learnt about Gaussian Elimination with Partial Pivoting. We started talking about the Jacobi Method: a way of quickly approximating solutions to linear systems: especially diagonally dominant ones.

Week 5

Next week we will develop the Jacobi Method and the similar Gauss Siedel Method. At this point we might stop and discuss the advantages and disadvantages of our five methods (Gaussian Elimination, Gaussian Elimination with Partial Pivoting, Cramer’s Rule, Jacobi Method, Gauss-Siedel Method). Depending on time we might begin talking about Laplace Methods…

Tutorials

Deadly serious: ye need to be A-standard on the first two chapters… they are doable for everyone with a bit of work. The later stuff will be challenging and will need a lot of work to reach a good standard.

This week it is

13:30 Groups S1 and S3 (M-Z)

14:30 Groups S2 and S3 (A-L)

Yes the following table should be A-L and M-Z not A-L and K-Z!

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.

Five students still owe me E10 for the notes. If this is a problem for you send me a confidential email.

Week 3

We started our work on linear algebra; specifically linear systems. We showed how to write a linear system in augmented matrix form and showed that the elementary row operations conserved the solutions. We loosed described the Gaussian elimination algorithm that would put the augmented matrix in reduced form. We said that solutions could have none, one or an infinite number of solutions and described how to tell from the reduced form. Depending on the scenario, the solutions are easily found via back-substitution.

Week 4

Next week we will continue to work on Gaussian elimination. We will discuss Cramer‘s Rule; we will see why computers struggle with Gaussian elimination and learn ways to get around this.

Tutorials

Deadly serious: ye need to be A-standard on the first two chapters… they are doable for everyone with a bit of work. The later stuff will be challenging and will need a lot of work to reach a good standard.

This week it is

13:30 Groups S2 and S3 (A-L)

14:30 Groups S1 and S3 (M-Z)

Yes the following table should be A-L and M-Z not A-L and K-Z!

Additional Notes

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.

Monday

No Maths on Monday ye have Geotech instead.

Continuous Assessment

You will have 15% tests in Weeks 6 & 11. It would be my intention that the Week 6 Test will cover material from the first four weeks and that the the Week 11 Test would cover material from weeks 5-9. Either way you will receive sample tests and additional information in Week 4 and Week 9 respectively.

Week 1

In the first week we had our introductions and looked at finite difference methods.

Week 2

In the second week we looked at Lagrange Interpolation and Least Squares Curve Fitting.

Next Week

We start Chapter 2: Linear Algebra.

Read the rest of this entry »

Exam Layout

Answer four questions: each worth the same marks.

1. Multiple Topics Question

(a) Interpolation (b) Linear Algebra (c) Laplace Methods

2. Interpolation

Finite Difference Methods, Least Squares, Lagrangian Interpolation

3. Linear Algebra

Gaussian Elimination with and without partial pivoting, Cramer’s Rule, Jacobi’s Method, Gauss-Siedel Method

4. Laplace Methods

Three differential equations

5.  Multiple Integration

line integrals, double integrals with applications including second moment of area, triple integrals.

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

We will have a lecture/tutorial on Tuesday 11 December from 18:00. We have to finish off multiple integration. I hope to do this in one hour. We will decide as a group when to have our break.

The different things I can do for the tutorial:

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 — which is more streamlined than other years:

Answer four questions: each worth the same marks.

1. Multiple Topics Question

(a) Interpolation (b) Linear Algebra (c) Laplace Methods

2. Interpolation

Finite Difference Methods, Least Squares, Lagrangian Interpolation

3. Linear Algebra

Gaussian Elimination with and without partial pivoting, Cramer’s Rule, Jacobi’s Method, Gauss-Siedel Method

4. Laplace Methods

Three differential equations

5.  Multiple Integration

line integrals, double integrals with applications including second moment of area, triple integrals.

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 Summer 2010 — which I will have printed out for ye.

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

Test 2 Results

You are identified by the last four digits of your student number: