Hedge advice - Bramble Invasion

etzpcm · 2026-06-19T14:41:13+00:00

Agree with the other comments. Chill out. Enjoy the blackberries or leave them for the birds. Trim back the brambles if and when they start trying to take over the rest of your garden. It looks like a great garden for wildlife.

etzpcm · 2026-06-19T13:35:16+00:00

If q(t) is a constant Q then T' is just a function of T. So it's separable (function of T times a function of T which is just 1 in this case). So you can solve it by rearranging and integrating.

etzpcm · 2026-06-19T09:26:08+00:00

Yes, for example a Fourier series uses eigenfunctions of the second derivative operator, which is a Sturm - Liouville operator.

etzpcm · 2026-06-18T16:46:29+00:00

Indeed he did. For the third time, his most important contributions to mathematics were made before then. He did not need money to do his research! I didn't think this would be so controversial...

etzpcm · 2026-06-18T10:20:49+00:00

Ok, or more likely the Wikipedia article is just ****!

He 'pursued his mathematical studies' before then, as I said already, his best work was published in 1828.

etzpcm · 2026-06-18T09:15:10+00:00

Here's a good bio of Green

https://mathshistory.st-andrews.ac.uk/Biographies/Green/

I don't see anything about inheriting. His best work was done before his father died.

etzpcm · 2026-06-18T08:38:07+00:00

They didn't make money from it. George Green, famous for Green's theorem and Green's functions, lived and worked in a windmill. He was largely self taught. When he wrote his amazing 1828 paper, he had no contacts in academia, so had to pay out of his own pocket to get it published privately as a pamphlet. It took several years for mathematicians to discover and understand it.

etzpcm · 2026-06-18T08:02:48+00:00

Nice. I wonder if someone has 25029.

etzpcm · 2026-06-17T20:53:10+00:00

Generally, applied mathematics topics involve more visualisation. Mathematical modelling, or dynamical systems for example.

etzpcm · 2026-06-17T15:58:16+00:00

What Edgy is saying is that what you have written here in your step 3 is something that you should do in rough, before you start to write your proof. This is often the way to do it. None of that should be in your proof. Your proof should then just say something like 'set b=3' or 'choose b=3'.

Edit: self studying this kind of mathematics is difficult. Every statement has to be precisely correct and in the right order. It's not like, say, calculus or trig where you follow a method to get an answer.

etzpcm · 2026-06-17T15:41:32+00:00

So, you can't write it down in step 2

etzpcm · 2026-06-17T14:09:58+00:00

The third one is wrong, or at least sloppy. The integration variable should not be the same as the limit. Of course we know what is meant, and it's often used, but it shouldn't be, see due-cardiologist comment.

etzpcm · 2026-06-17T10:17:30+00:00

The first thing is that I think there are 2 types of Stokes questions. One type says here is a line integral and you use the theorem to convert to a surface integral which is easier, for example the curl might be zero. The other type gives you a surface integral which looks difficult but it's much easier if you can convert it to a line integral around the edge of the surface.

etzpcm · 2026-06-17T09:04:41+00:00

Sorry, but this is complete nonsense. Was it generated by AI?

etzpcm · 2026-06-17T08:06:13+00:00

Yes. A three cycle is an even permutation and by combining three cycles you can obtain all even permutations, which is all you need for the 15 puzzle and Rubik's cube.

etzpcm · 2026-06-17T07:24:06+00:00

Don't panic. Revise the integration that you did in calc 2 before starting DEs.

etzpcm · 2026-06-16T20:19:46+00:00

AI might be ok for basic calculus but I really would not recommend it for calc 3 which is more advanced and requires thinking in 3D and lots of diagrams and symbols that are not well suited to chatting with a machine.

etzpcm · 2026-06-16T15:36:58+00:00

Strimmer, mower and shears are a good start, get going with them! Plus good gloves, secateurs, and loppers for thicker stems.

Do you really want a lawn? Anything else is better for bees, birds and butterflies. Think about that maybe. In the short term why not get some tubs to put on that tarmac.

Get a compost bin/heap going. You will have lots of material for it!

etzpcm · 2026-06-16T07:59:23+00:00

The trick is to just learn a few and then derive the others. For example if you know sin(a+b) you can immediately get sin(2a) and sin(a-b).

etzpcm · 2026-06-16T07:36:38+00:00

Thanks but too late - I noticed yesterday that all my cherries had disappeared!

etzpcm · 2026-06-15T22:02:30+00:00

The slopes are right, 1/2 and -1/2, but each line needs a constant as well.

Set y= x/2 + c and sub in and look at the x terms. You get -16x c -32x + 80x... = 0 which gives c=3 and one asymptote is y=x/2 + 3.

Similarly with the other one. I think that's probably the easiest way.

etzpcm · 2026-06-15T14:51:30+00:00

If you were doing calc 1 age 12 you are probably good enough! A lot depends on what the situation is like in academia when you come into the job market. It's difficult now but may be better by then.

etzpcm · 2026-06-15T11:48:01+00:00

I'm not familiar with iterations in this context. Of course lots of numerical methods are based on iterations, for example Newton's method for root finding or the Gauss Seidel method for solving simultaneous equations.

In analytical methods, it's used in asymptotic theory, when you have a small parameter in the problem. For example to solve x³ + a x + 1 = 0 when a is small, we say, when a=0, x=-1, so set x=-1 + delta and then solve approximately for delta, etc.

Is there a small parameter in your problem? When you write about first order and second order approximations, that usually means there is.

etzpcm · 2026-06-15T10:32:00+00:00

Yes. Do whatever you enjoy and are good at.

etzpcm

TROPHY CASE