Thursday, Frirday 10th, 11th March: finished a maths asssignment, going to Lake District

I didn't feel too good on these two days. So I didn't do anything too exciting.

I tried to finish an assignment about numerical methods. The first question caused me a few problems. Solving an "eigenvalue problem" for an ordinary differential equation. y'' + f(x)y' + g(x)y = lambda y. Solutions may exist only for some lambda. So you can use some finite difference approximations for y'' and y', then write it in matrix form as an eigenvalue problem. The problem was that there were only complex solutions for the eigenvalues. I haven't done things with eigenvalues for a while, so I'm not sure what happened. Maybe complex solutions were okay.

The second question went well. Had to solve a boundary value problem ODE with matlab. So you have conditions y(a) and y(b) instead of y(a) and y'(a) or something like that. The 'shooting method' works by just guessing some value for y'(a), solving that repeatedly, trying to minimize the difference between the true value y(b) and the one obtained with the guess for y'(a). The guess is altered to minimize the difference. Eventually you find a solution that satisfies all conditions pretty well. The difference is a function with input parameter being the guess. So you can just use Newton's method or midpoint rule to get close to the root of that function.

In the afternoon after submitting my assignment I walked to Beeston to get some food ready for the weekend. I also got a needle and some cotton so that I could reattach a button to my pants (a.k.a. trousers). I hadn't done this for years so it was good fun.

This weekend I had signed up to go to the Lake District with the rambling society. We had to gather by the Portland Building at 17:00 friday ready for the bus to leave at 17:30.

We took a very strange route for half the trip. We drove along normal roads. I guess the motorway must have been closed because that would have been a lot quicker. We stopped at a town called Wetherby for dinner. It looks like a very nice town. I got some chips. They were quite good. On the journey, the committee people had written a quiz for us all to do. I didn't really know any of the answers. They were mostly questions about English stuff. One question about Australian stuff: what is Ian Thorpe's birthday? I have no idea who would know this.

We got to the hostel at Keswick at about 22:30 or maybe 23. We got inside. People did a bit of loitering, and then we went to bed. Keswick is about 43km south of the border to Scotland, according to Google Earth. On the west coast. Above Liverpool and those places.