This repository contains the course materials for this module taught at the Department of Mathematics of the University of York in Spring 2017.

Students on the module are encouraged to fork the repository so that they can modify the course materials for their own purposes. Also we would appreciate pull requests for suggested corrections and improvements.

We will not give standard lectures on the material. Instead the lecture slots will be discussion sessions where we talk through the material together with the help of the lecture slides. Students are required to read through a specified section of the lecture notes before each session.

There will be no brownie points for pretending to understand something. Instead there will be praise for raising questions about the material. Such questions will benefit not only the person asking the question but also the person attempting to answer the question, because there is no better way to sharpen one's understanding than by answering probing questions. So I see the lecture discussions as a competition of who can generate the most discussion, not of who can understand the material the fastest.

Instead of the one one-hour timetabled computer practical every week at 9am on Fridays, we will mix computer work into our discussion sessions whenever we find it appropriate. The aim is to implement any methods on the computer as soon as they are introduced.

Students will install R and RStudio on their notebook computers at the start of the module and bring it with them to all sessions or work on one of the supplied notebook computers.

Richard and I will prepare one or more R labs each week. These are worksheets with commented code examples and explanations as well as exercises. Students should work through the examples and then build on them to write code solving the exercises.

Following standard practice in the maths department, there will be four problem sheets. However, rather than setting a single deadline for each problem sheet, I want students to attempt each problem as soon as the material comes up in their reading. The deadline for handing in the written solution for a question will then be at the start of the session on the Tuesday following the session in which we discussed the material. That gives students at least six days to do the problems after the material has been discussed.

The module contains two mini projects that count 10% and 15% towards the final module mark respectively.

The first mini-project will ask students to implement and explore numerical methods for a specified model equations without any reference to real-world applications.

In the second mini-project students will explore a real-world application. Students will be able to choose the application for their second mini-project themselves according to their interests. They should propose a published paper to base their project on. That paper should contain numerical results that the student will aim to reproduce and then write a report on the methods used and the challenges encountered.

The marking scheme will put emphasis on how well the student discusses the appropriateness and efficiency of the chosen method and the challenges posed by the application. It is not necessarily a problem if the student fails to reproduce the results from the paper as long as the student clearly describes what the problems are that prevent this.

We will dedicate time in the sessions to discussions of students' projects. Each student will present their application and the special features of the PDE that they will need to deal with. Other students should see if they can make helpful suggestions.

I recommend that you fork this repository before cloning your fork to your computer. Forking the repository creates your own copy of the repository on Github over which you have full control. To do this you just have to click the "Fork" button near the top-right of the page.

On the Github page of your forked repository you can then click the "Clone or download" button and copy the repository URL given there. You then open R Studio, do "New Project -> Version Control -> Git", paste in the repository URL and click "Create Project". This clones the repository onto your machine and creates an RStudio project at the same time.

From time to time you will want to pull the changes from my repository into your own fork. For this you need to let your repository know about the URL of my repository on Github. You can not do this from the RStudio GUI but need to open a console window. In the RStudio Git window click the drop-down menu "More". It has a picture of a gear. Click "Shell..."; this should open up a console. In the console type

git remote add upstream https://github.com/gustavdelius/NumPDE_2017.git

Now you can pull changes from my repository and merge them into your master branch with the command

git pull upstream master