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There are a number of ways of explaining why you cannot divide by zero. Here are my two favourites.

## Any Set of Numbers Collapses to a Single Number

How old are you? Zero years old.

How tall are you? Zero metres old.

How many teeth do you have? Zero.

How many Superbowls has Tom Brady won? Zero

Yep, if you allow division by zero you only end up with one number to measure everything with.

## Week 10

We looked at finite differences for the Heat Equation.

In VBA we implemented same.

## Easter

You will receive regular correspondence from me over the next week or so such as sample VBA Assessment 2, sample 40% Written Assessment, sample solutions of both, better programs.

Some of you need to put in a serious effort to get yourselves up to scratch or you will fail this module. It is up to you to be organised and be keeping an eye on the email correspondence.

Feel free to email me any questions that you might have. If you put in the effort I will reciprocate.

## Week 9

We did a little revision of the earlier material.

In VBA we will look at finite difference methods for Laplace’s Equation.

## Week 10

We will look at finite differences for the Heat Equation.

In VBA we will implement same.

**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.**

## Week 8

We started looking at partial differential equations, in particular Laplace’s Equation and its solution using finite differences.

In VBA we looked at the shooting method.

## Week 9

We will complete our study of Laplace’s Equation and introduce the Heat Equation.

In VBA we will look at finite difference methods for Laplace’s Equation.

**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.**

## Written Assessment — Results

I expect to have these to you by the end of Monday, 20 March, Week 8.

## VBA Assessment — Results

I also expect to have these to you by the end of Monday, 20 March, Week 8.

## Week 7

We started looking at the shooting method and finite differences.

In VBA we had our first assessment.

## Week 8

We start looking at partial differential equations, in particular Laplace’s Equation and its solution using finite differences.

In VBA we will look at the shooting method and finite differences for boundary value problems.

**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.**

## Written Assessment — Results

I expect to have these to you by the end of Monday, 20 March, Week 8.

## Week 6

We started looking at Boundary Value Problems.

In VBA we looked at implementing Runge-Kutta Methods.

## Week 7

We start looking at the shooting method and finite differences.

In VBA we had our first assessment.

## 20% Written Assessment 1

The first written assessment takes place Tuesday 7 March at 09:00 in B242.

Here you can see type of questions which you will have to be able to answer in the first test.

The questions are divided into P, M and D:

- P are pass questions and test your ability to implement methods and show basic understanding.
- M are merit questions and test your ability to solve slightly harder problems as well as understand error.
- D are distinction questions and test your ability on solve hard problems, generalised problems as well show a deeper understanding.

Your Test will have, roughly,

- 30 Marks of P questions
- 40 Marks of M questions
- 10 Marks of D questions

See here for some worked examples.

## 20% VBA Assessment 1

The first VBA Assessment takes place Tuesday 14 March in A285 at the usual times.

“I have decided that you will not be allowed any resources other than the library of code and formulae at the end of the assessment. Furthermore the digits of your student number will be used to personalise your assessment(!). Also there will be an Assessment A and an Assessment B.”

The VBA assessment tests your ability to write programs to tackle a specific problem. If you do everything correctly, you can use Euler’s Method only but the most you can get is 80%. To get more than 80% (and get marked out of 100%) you will have to implement Heun’s Method.

There will be two problems.

### Problem 1: First Order Initial Value Problem with Parameters [80%]

If you are comfortable writing a VBA program that implements Heun’s Method, and your program is correct, you get 70% by doing Part B ii. There is an additional 10% available if you can use the program to analyse the problem.

If you are comfortable writing a VBA program that implements Euler’s Method, and your program is correct, you get 55% by doing Part B i. There is an additional 10% available if you can use the program to analyse the problem.

If you can implement Heun’s Method on a worksheet (given parameters), you can get 20% by doing Part A i.

If you can implement Euler’s Method on a worksheet (given parameters), you can get 15% by doing Part A i.

### Problem 2: Second Order Initial Value Problem without Parameters [20%]

This is in a non-VBA environment.

5% for writing the second order initial value problem as two first order problems.

15% for solving the system on a worksheet using Heun’s Method.

10% for solving the system on a worksheet using Euler’s Method.

More detailed information outline (including practise questions).

A sample (with a messy Problem 1) with Excel and VBA work sent to you as an attachment.

LEARNING CODE ‘OFF’ IS A RECIPE FOR DISASTER.

You need to understand what you are doing.

## Week 5

We introduced the full Runge-Kutta Theory.

In VBA we look at second order systems using Euler’s Method

## Week 6

We start looking at Boundary Value Problems.

In VBA we look at implementing Runge-Kutta Methods.

## Written Assessment 1

- P are pass questions and test your ability to implement methods and show basic understanding.
- M are merit questions and test your ability to solve slightly harder problems as well as understand error.
- D are distinction questions and test your ability on solve hard problems, generalised problems as well show a deeper understanding.

- 30 Marks of P questions
- 40 Marks of M questions
- 10 Marks of D questions

## Week 4

We spoke some more about Huen’s Method. We will also see how to handle second order differential equations.

In VBA we implemented Huen’s Method.

## Week 5

We will introduce the full Runge-Kutta Theory.

In VBA we look at a second order system. We will use Euler’s Method and/or Huen’s Method.

## Week 3

We finished our work on Taylor Series and used it to analyse the Euler Method, and improve the Euler Method to a Three Term Method.

We explained the problem with the Three Term Taylor Method and changed tack to look at Huen’s Method.

In VBA we finished off our Euler Method problem and some of us wrote a Newton Cooling programme.

## Week 2

We developed the Euler Method for approximating the solution of differential equations. As we will need Taylor Series to analyse the error in this approximation — and improve Euler’s Method — we started looking at that.

In VBA we started programming the Euler Method to solve the problem of a damper.

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