**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.

## 3 comments

Comments feed for this article

March 25, 2013 at 11:10 am

Student 31Would 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. McCarthyFirst 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

PawelThank you JP

Pawel