Keep in mind at all times:

“Any and all work, submitted at any time, will receive feedback.”

“Do not hesitate to contact me with questions at any time. My usual modus operandi is to answer all queries in the morning but sometimes I may respond sooner.”

## Week 12/13

### 11:00 Tuesday 28 April, Week 12: Assessment Based on Lab 7

Students can submit work — VBA or Theory, catch-up or revision — based on Week 9 Lab 7 VBA/Theory Catch-up/Revision II assignment by today, Saturday 25 April.

If you have any further questions, I am answering emails seven days a week. Email before midnight Monday 27 April to be guaranteed a response Tuesday 28 April. I cannot guarantee that I answer emails sent on Tuesday morning (although of course I will try).

### Catch Up/Revision of Lab 8 Material

If you have not yet done so, you will undertake the learning described in Week 10.

If you feel like doing even more theory work on top of this, you will be asked to consider looking at the theory exercises described in Week 10.

If you have already conducted this learning, and submitted a Lab 8 either back before 6 April, or after, I will invite you, if necessary, to take on board the feedback I gave to that submission, and resubmit a corrected version for further feedback.

Students will be able submit work — VBA or Theory, catch-up or revision — based on Week 10 to a Lab 8 VBA/Theory Catch-up/Revision assignment on Canvas (due dates 3 May and 9 May).

## Week 14

### 11:00 Tuesday 12 May, Week 14: Assessment Based on Lab 8

This assessment will ask you to do the following:

Consider:

$\displaystyle k\cdot \frac{\partial^2 T}{\partial x^2}=\frac{\partial T}{\partial t}$      (1)

For one (i.e. $x_1$ or $x_2$ or $x_3$) or all (i.e. general $x_i$), use equations (2) and (3) to write (1) in the form:

$T^{\ell+1}_i=f(T_j^\ell),$

i.e. find the temperature at node $i$ at time $\ell+1\equiv(\ell+1)\cdot \Delta t$ in terms of the temperatures at the previous time $\ell\equiv \ell\cdot \Delta t$. You may take $\Delta t=0.5$.

\begin{aligned} \left.\frac{dy}{dx}\right|_{x_i}&\approx \frac{y(x_{i+1})-y(x_i)}{\Delta x}\qquad(2) \\ \left.\frac{d^2y}{dx^2}\right|_{x_i}&\approx \frac{y(x_{i+1})-2y(x_i)+y(x_{i-1})}{(\Delta x)^2}\qquad(3) \end{aligned}