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.

Maple Test

I will give ye a sample Maple Test next week and ye will have your Maple Test in Week 12.

Study

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

Please find a reference for some of the prerequisite material here.

Week 9

We started our study of Laplace Methods

Weeks 10

More work on Laplace Methods: including a total review of partial fractions. I have also done out solutions of the Winter 2012 Laplace questions so that ye can see how I mark these questions. I hope to scan this here either today Friday 12 April 2013 or maybe early next week.

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 the an inverse Laplace transform.

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.

Revision

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

The worked solutions of all the Winter 2012 stuff we covered is here.

Please find a reference for some of the prerequisite material here.

Week 7

In Week 7 we looked at approximate integration. The notes that I gave you had a slightly different notation to the one used in the mathematical tables. Here are these notes except in a notation that is consistent with the mathematical tables. A corollary of this is that there will be no questions on errors in approximate integration.

Week 8

In Week 8 we did Euler’s method and we also did some Newton-Raphson and indeed Euler in the Maple Lab.

Weeks 9 – 12

Eight and half good hours of Laplace Methods — a Maple Lab and an open book Maple test. I will send you a sample Maple test early this week.

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 Euler Method.

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

The test will be held next week 13 March. Please find a sample attached (you will also be given these tables although you can use your own tables also if they are clean). This sample is not a guide to the questions or their marks but only the layout of the test:

• Answer all questions
• 1 hour test 19:10 – 20:10
• Q.1 Integration by Parts, Q. 2 Partial Fractions Q.3 Partial Differentiation Q. 4 Differentials and Error Analysis Q. 5 Root Approximation

We will have the test from 19:10 – 20:10. After the break we will start a proper look at approximate integration.

There are some students with a very busy Week 7: those students with physics or a heavily pregnant spouse. Ye will have an opportunity to sit the test at 20:15 on Thursday 21 March which is in Week 8. Ideally you should email me if you fall into this bracket. If you are sitting the test in Week 8 you don’t need to turn up next Wednesday until 20:30.

Revision

Please feel free to ask me questions via email or even better on this webpage.

Week 6

In Week 6 we did some revision, namely the sample test. After this we used Maple to help us revise partial differentiation.

Week 7

Test and then a proper look at approximate integration.

Week 8

Finish off numerical methods and maybe start Laplace methods. We will do some numerical methods stuff in Maple.

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

A test will be held in Week 7, 13 March 2013. Please find a sample attached (you will also be given these tables). This sample is not a guide to the questions or their marks but only the layout of the test:

• Answer all questions
• 1 hour test 19:10 – 20:10
• Q.1 Integration by Parts, Q. 2 Partial Fractions Q.3 Partial Differentiation Q. 4 Differentials and Error Analysis Q. 5 Root Approximation

I understand that a few of ye have a very heavy schedule in Week 7. If and only if this is the case I am considering giving ye an opportunity to sit the test on Thursday evening 21 March at 19:10. Please email me if you fall into this bracket.

Revision

We will do some revision next week but really you should be trying exercises yourself. Please feel free to ask me questions via email or even better on this webpage.

Week 5

In Week 5 we looked at differentials and how they help in error analysis. We looked at the Bisection & Newton-Raphson Methods for approximating solutions of equations. We began looking at methods of approximate, numerical integration.

Week 6

In Week 6 we will do some revision, namely the sample test. I would strongly advise you to try the sample test before this class to see what you can do and what you can’t do. After this we will have a Maple session.

Week 7

We will have the test from 19:10 – 20:10. After the break we will start a proper look at approximate integration.

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 4

In Week 4 we looked at Multivariable Calculus and Partial Differentiation . We are going to use this stuff for error analysis. We did some Partial Fractions & Partial Differentiation in our Maple lab.

Next Week

We will begin to look at error analysis — very important for the analysis of physics experiments/data. We will hopefully begin some Numerical Methods.

Test

The test will be held in Week 7 (13 March). I will send ye a sample next Friday and the test we be on the material covered in weeks 1-5 inclusive. We will do some revision in Week 6 before Maple.

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 3

In Week 3 we looked at Partial Fractions. They provide us with a way of integrating rational functions and will be very important later for when we study Laplace Methods.

Next Week

We will look start Multivariable Calculus and perhaps begin to look at its application to error analysis — very important for the analysis of physics experiments/data. We will do some Partial Fractions & Multivariable Calculus in our Maple lab.

Additional Notes

I skipped over some of the more complicated Partial Fractions stuff that we don’t need for exams. For completeness I have put it here.

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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.

Maple Assessment

I have decided to allocate the Maple marks as follows:

• 5 x Maple Labs @ 2% each
• Maple Exam @ 5%

This means that if you participate in all of the Maple labs you will have 10%. If you have done this you should be well able for the Maple Exam in Week 12. More information on this in Week 10.

Week 1

In Week 1 we explained the kind of thing that we would be looking at in this module. We did a quick review of integral calculus.

Week 2

In Week 2 we looked at Integration by Parts: this is the start of the new material. In Maple we did some basic plotting, differentiation and integration.

Next Week

We will look at Partial Fractions and possibly start Multivariable Calculus.

Notes

I have given out 13 sets of the notes. I received the E12 from most people: if you didn’t bring it this week you may bring it next week. I now have five more copies of the notes ready for the people who were left without (one week on/off, two day students, one lad who had the money and another lad who was in with me last year). If you did not attend either of the first two lectures please email me so I can another set of notes printed cheers.

I said that to those that I should have had notes for that I would give ye a set of Week 2 notes… here they are: Lecture Two.

Your continuous assessment results are down the bottom. You are identified by the last three digits of your student number.

Sample

Find the inverse Laplace transforms of the following functions:

Note that as soon as we step inside the exam hall we write down the following rule that is on the tables but not nearly in as nice a form:

.

(i)

.

Solution

This looks quite tricky but all it needs is a little trick. Multiply out  by hand (or by memory or by the Binomial Theorem (in tables)) to get:

.

Now taking advantage of the linearity of the inverse Laplace transform (I’m just going to write  instead of . To get a nice inverse Laplace transform symbol I have to type \mathcal{L}^{-1} — along with some dollar signs and I’m sick of it! — no keyboard shortcuts on this page — the notes have shortcuts.)

.

Now using the tables;

.

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