## VBA Assessment 1 – Week 6

VBA Assessment 1 will take place in Week 6 (3 & 6 March) in your usual lab time. The following formulae will appear on the assessment. The following is the proposed layout of the assessment:

### Q. 1: Numerical Solution of Initial Value Problem [80%]

Examples of initial value problems that might be arise include:

• Damping $\displaystyle \frac{dv}{dt}=-\frac{\lambda}{m}v(t)$; $v(0)=u$

• The motion of a free-falling body subject to quadratic drag: $\displaystyle \frac{dv}{dt}=g-\frac{c}{m}v(t)^2$; $v(0)=u$

• Newton Cooling $\displaystyle \frac{d\theta}{dt}=-k\cdot (\theta(t)-\theta_R)$; $\theta(0)=\theta_0$

• The charge on a capacitor $\displaystyle \frac{dq}{dt}=\frac{E}{R}-\frac{1}{RC}q(t)$; $q(0)=0$

Students have a choice of how to answer this problem:

• The full, 80 Marks are going for a VBA Heun’s Method implementation (like Lab 3).
• An Euler Method implementation (like Lab 2), gets a maximum of 60 Marks.

You will be asked to write a program that takes as input all the problem parameters, perhaps some initial conditions, a step-size, and a final time, and implements Heun’s Method (or possibly Euler’s Method).

If you can write programs for each of the four initial value problems above you will be in absolutely great shape for this assessment.

### Q. 2: Using your Program [20%]

You will then be asked to use your program to answer a number of questions about your model. For example, see the questions to the Newton Cooling Problem on p.126.

## Week 4

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

We also introduced second order differential equations and saw how to attack them numerically. In particular we looked at a real pendulum.

In VBA we worked on Lab 3 and MCQIII. Those of us who did not finish the lab are advised to finish it outside class time, and are free to email me on their work if they are unsure if they are correct or not.

## MCQ League

Unless you are excelling, you are identified by the last five digits of your student number.

Please ask questions in the lab about questions you have gotten wrong. Students in red appear to not have a good handle on the material and should consider putting in extra time outside class in doing exercises (in the manuals).

Little change at the top again: ## Week 5

In the morning class we will finish looking at second order differential equations.

In the afternoon we will begin a quick study of Runge-Kutta Methods.

In VBA we have MCQ IV and look at Lab 4, on Second Order Differential Equations.

## Week 8

Unfortunately for us, St Patrick’s Day falls on a Tuesday.

I am unable to let these hours go: I will once again pre-record two video lectures, and the labs are postponed to Thursday 19 March:

For DME2A, who normally have their lab 15:00-17:00 on Tuesdays, will, this week only, have their lab:
• Thursday 15:00-17:00 in A214

For DME2B, who normally have their lab 10:00-12:00 on Tuesdays, will, this week only, have their lab:
• Thursday 11:00-13:00 in A269
DME2C will have their lab Friday morning as usual.
All students should watch the pre-recorded Week 8 lectures before their lab.

## Assessment

The following is a proposed assessment schedule. Please contact me if there are any problems with the Week 7 and 12 times.

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. Melbourn Hall, Tuesday 10 March, 09:30-10:30
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. Melbourn Hall, Tuesday 28 April, 15:00-17:00

## Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises