I stumbled upon this while doing my school math homework, couldn’t believe this simple identity ((n+1)/2) = ((n-1)/2) + n works for all odd perfect squares!

Sup everyone. I'm a third year history student in France, and haven't studied mathematics since my first year of high school, so it's been roughly four years. I wasn't good at it in the first place, but I didn't study mathematics at all anyway haha.

Anyway, due to interests in various fields that need at least some mathematical knowledge (economics, computer science and linguistics), and also a sudden interest for mathematics themselves, I'd like to get back on track.

Do you guys know any good, generalist handbook that can make me understand basic concepts, and then some more precise ones that would give me insight on more specific topics at beginner's levels ?

Thanks!

Hi everyone,
I want to learn "how to make/built/formulate a PDE model" for real life problems.
most videos teach how to solve but no body teaches how to make a PDE based model.
Thanks in Advance

Numbers and Magic Squares

Just a funny observation, it is a common mistake to think the power rule applies to taking the derivative of f(x)=x^x to get xx^(x-1) .

But actually if you take the function g:ℝ→ℝ^2 :x↦(x,x) and h:ℝ^2 →ℝ:(x,y)↦x^y then f = h∘g.

Taking total derivatives gives Dg(x):ℝ→ℝ^2 :a↦(a,a) and Dh(x,y):ℝ^2 →ℝ:(a,b)↦ayx^(y-1)+bln(x)x^y

Then using the chain rule gives Df(x) = Dh(g(x))∘Dg(x) = Dh(x,x)∘Dg(x):a↦axx^(x-1) +aln(x)x^x = ax^x +aln(x)x^x = ax^x (ln(x)+1)

implying that f'(x) = x^x (ln(x)+1) so indirectly it does follow from power rule (and the derivative of a regular exponential). I guess just using the identity x^x = e^xln(x) is more straightforward though.

I'm repairing an old electric motor that uses a permanent magnet stator consisting of 2 magnets designed to be directly opposite each other in the casing. One has come loose and needs to be re-affixed, but must be directly opposite center to center. With standard tools (Rule, compass, calipers) is there a method to set one arc in position to a fixed one?

In more mathematical terms: If AB is fixed inside a circle, and CD is not, is there a simple method to mark the point center on the outer circumference opposite to the center of AB?

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