I hated the magnetism maths at A’Level physics
If it’s any consolation, really sorting it out does get very tough indeed. I spent long enough with it, both as an undergraduate and then teaching it myself, that I eventually got a pretty good grip. But if you ever come across anyone who’s got a clear explanation of the practical consequences of gauge invariance of the magnetic vector potential then I’d be keen to hear it. (I reckoned the finals examiners simply wouldn’t ask about that, and sure enough they didn’t.)
The water’s very deep here https://en.wikipedia.org/wiki/Magnetic_potential#Magnetic_vector_potential.
The staggering thing is that we now have a couple of very useful mathematical tools - vector calculus and tensor calculus - to make this more tractable. Neither of these had been invented when Maxwell was working. He had to grind through the whole thing longhand ! Genius.
A level was ok, but magnetics at uni was very tough. To the point that they made it multiple choice as even clever people (unlike me) struggled.
These days, I wish I’d put more effort into it!
Will we get a super conductor at room temp ?
Oh how droll
Not unless someone makes another breakthrough like they did with the cuprates (which came out of more-or-less nowhere) or finds a cheap and easy way of recreating the conditions in the core of Jupiter so we can use metallic hydrogen (ha ha).
I thought it was Andre Previn
I use some of these techniques in my work. Much of this really came into usage in my area of interest after I wrote my PhD. Much brain-ache was involved in gunning up the skills myself, as was the case with the asymptotic theory for the dynamic models I work on.
… and he is not at room temperature, as evidenced by his jumper.
This is the bible
I think the cover picture is meant to suggest that climbing the mountain will be easier than getting through the book. I still remember getting it off a library shelf 40 years ago and trying to work through the maths that convert the real-world experiments into Maxwell’s ‘curl H = Jf + dD/dt’. At one point he just says ‘integrating by parts yields …’ and then writes down the next line. I tried to do the integration. That was as far as I got. After a day and a half someone came up to me and asked if I was going to be much longer with the book. I handed it over. In the ensuing conversation he revealed that he was Alan Walton and his father had a Nobel prize in physics.
I don’t any more. Heavens, you could pull up trees with them though when the going got tough.
fixt for honesty. My brain is hurty thinking about this stuff.
C[quote=“Valvebloke, post:113, topic:92”]
I think the cover picture is meant to suggest that climbing the mountain will be easier than getting through the book. I still remember getting it off a library shelf 40 years ago and trying to work through the maths that convert the real-world experiments into Maxwell’s ‘curl H = Jf + dD/dt’. At one point he just says ‘integrating by parts yields …’ and then writes down the next line. I tried to do the integration.
I recall reading a paper by Cox, Ingersoll and Ross in the 1985 edition of Econometrica. I waded through many pages of algebra to reach some prose which basically finished with a line ending “which of course [turns page] is a Bessel function of the second kind”.
After 15 minutes of quiet swearing and utter despair, I went off to the math library to bone up on Bessel functions. It took a further two weeks of hard slog to read and (sort of) understand this paper. I don’t miss those bleak winter afternoons being confronted with my complete and utter inadequacy.
Amazing how many financial instruments follow the maths of natural phenomena and physical models like heat flow through an iron bar, etc.
At least your feelings of inadequacy were limited to a few winter afternoons… mine seems to have extended my whole life after reading these last few posts.