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 13

### Catch Up/Revision of Lab 8 Material

The final assessment, based on Lab 8, takes place 11:00, Tuesday 12 May.

If you have not yet done so, you will undertake the learning described in Week 10. Perhaps you should also look at the theory exercises described in Week 10.

The final 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}

so if you want to send on this work for feedback please do so.

If you 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.

Submit work — VBA or Theory, catch-up or revision — based on Week 10 to the Lab 8 VBA/Theory Catch-up/Revision II assignment on Canvas by midnight 9 May. If you have any further questions, I am answering emails seven days a week. Email before midnight Monday 11 May to be guaranteed a response Tuesday 12 May. I cannot guarantee that I answer emails sent on Tuesday (although of course I will try).