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.
| S/N | Mark |
| 08272 | 93 |
| 64673 | 90 |
| 91054 | 78 |
| 50902 | 70 |
| 79455 | 65 |
| 92344 | 61 |
| 92352 | 58 |
| 64674 | 48 |
| 93152 | 40 |
| 58171 | 30 |
| 92343 | 28 |
| 04346 | 28 |
| 92345 | 25 |
| 93150 | 25 |
| 92351 | 15 |
| 51215 | 0 |
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.
J.P. McCarthy: Math Page 
3 comments
Comments feed for this article
March 25, 2013 at 11:10 am
Student 31
Would you mind checking my Euler method exercise 3 answer please?
My answer is always 1.761639264, at the beginning I calculated manually, then I created a spreadsheet to test my answer – the same answer.
At this moment I don’t know what I’m doing wrong.
March 25, 2013 at 11:25 am
J.P. McCarthy
First of all it is clear that my answer must be wrong.
Let me explain why.
Euler’s Method approximates solutions of the ODE
Note that
is the slope. In this question we have
Now we also have
: that is at the ‘start’ we have 
when 
so at 
the slope is
that is positive: the function is increasing so, from
anyway, the function gets bigger than 1. Suppose at a short distance later, 
, we have
for some
. Then the slope, at 
is given by
and the function increases again and we have in fact that
for all 
.
So my answer is wrong.
Is your answer correct?
Yes it is; however the graph that you sent me has
vs 
rather than 
vs 
if you know what I mean.
Regards,
J.P.
March 25, 2013 at 4:32 pm
Pawel
Thank you JP
Pawel