## Week 3

We backtracked a little and found the Maclaurin Series

$\displaystyle \ln(\sec x)\approx \frac{1}{2}x^2+\frac{1}{12}x^4$.

We then did some further study on the Euler Method. The global error with the Euler Method is $\mathcal{O}(h)$ and we need to reduce this by coming up with a better method or adjusting the Euler Method.

We looked at the Three Term Taylor Method as a better method. To employ the Three Term Taylor Method we need implicit differentiation, which means more pen-and-paper work.

We could avoid implicit differentiation by looking at Huen’s Method, which is an adjustment of Euler’s Method in that it uses lines.

In VBA we finished off the Euler Method Lab 2 and looked at P. 122, Exercise 1. The first group also started P. 123, Exercise 2, but the later groups instead used the time for some theory revision.

## Week 4

We will finish off the Three Term Taylor Method Example we didn’t finish and talk again about Heun’s Method.

We will also introduce second order differential equations and how to attack them numerically.

In VBA we have MCQ III and look at Lab 3, on Heun’s Method.

## Assessment

The following is a proposed assessment schedule:

1. Week 6, 20% First VBA Assessment, Based (roughly) on Weeks 1-4
2. Week 7, 20 % In-Class Written Test, Based (roughly) on Weeks 1-5
3. Week 11, 20% Second VBA Assessment, Based (roughly) on Weeks 6-9
4. Week 12, 40% Written Assessment(s), Based on Weeks 1-11

## Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises