Archive for Vector Calculus

On Grinds

Posted in Literature, mathematics with tags , , , , on July 24, 2020 by telescoper

When I moved to Ireland a couple of years ago, one of the words I discovered had a usage with which I was unfamiliar was grind. My first encounter with this word was after a lecture on vector calculus when a student asked if I knew of anyone who could offer him grinds. I didn’t know what he meant but was sure it wasn’t the meaning that sprang first into my mind so I just said no, I had just arrived in Ireland so didn’t know of anyone. I resisted the temptation to suggest he try finding an appropriate person via Grindr.

I only found out later that grinds are a form of private tuition and they are quite a big industry in Ireland, particularly at secondary school level. School students whose parents can afford it often take grinds in particular subjects to improve their performance on the Leaving Certificate. It seems to be less common for third level students to pay for grinds, but it does happen. More frequently university students actually offer grinds to local schoolkids as a kind of part-time employment to help them through college.

The word grind can also refer to a private tutor, i.e. you can have a maths grind. It can also be used as a verb, in which sense it means `to instil or teach by persistent repetition’.

This sense of the word grind may be in use in the United Kingdom but I have never come across it before, and it seems to me to be specific to Ireland.

All of which brings me back to vector calculus, via Charles Dickens.

In Hard Times by Charles Dickens there is a character by the name of Mr Thomas Gradgrind, a grimly utilitarain school superintendent who insisted on teaching only facts.

Thomas Gradgrind (engraving by Sol Eytinge, 1867).

If there is a Mr Gradgrind, why is there neither a Mr Divgrind nor a Mr Curlgrind?

Vector Calculus Weather

Posted in mathematics, The Universe and Stuff with tags , , on October 12, 2018 by telescoper

As it happens I did a lecture today about vector fields as part of my module on vector calculus. Whenever I did similar lectures in the past I used the day’s weather map as an illustration, so this morning I downloaded what turned out to be a particularly dramatic example. The curl of the velocity field around the weather system off the west coast of Ireland this morning was definitely non-zero…

Storm Callum turned out to be not as damaging as feared. Apparently it was rather windy in Maynooth overnight, but I slept right through it.

A (Physics) Problem from the Past

Posted in Cute Problems, Education, The Universe and Stuff with tags , , , , , on September 25, 2012 by telescoper

I’ve been preparing material for my new 2nd year lecture course module The Physics of Fields and Flows, which starts next week. The idea of this is to put together some material on electromagnetism and fluid mechanics in a way that illustrates the connections between them as well as developing proficiency in the mathematics that underpins them, namely vector calculus. Anyway, in the course of putting together the notes and exercises it occurred to me to have a look at the stuff I was given when I was in the 2nd year at university, way back in 1983-4. When I opened the file I found this problem which caused me a great deal of trouble when I tried to do it all those years ago. It’s from an old Cambridge Part IB Advanced Physics paper. See what you can make of it..

(You can click on the image to make it larger…)