Le mathématicien Peter Woit explique la formule de Euler (en anglais) pour l'univ

At Not Even Wrong: Various and Sundry, Peter Woit writes:

"The semester here (ed.: Mathematics department at Columbia University in New York) is finally underway, and I’m getting back to work on my quantum mechanics and mathematics book (latest version available here). Current plan is to have a final version by next spring, with publication by Springer late next year. This semester I’m teaching Calculus II, a subject where there’s only one thing I really dislike about pretty much all textbooks, their refusal to use Euler’s formula. Since I couldn’t find an online source I was completely happy with, I spent some of the last couple days writing up some notes for the students on Euler’s Formula and Trigonometry, which maybe someone else will find useful."

Et aussi:

"In the US Euler’s formula is not part of the standard secondary school curriculum. Even worse, it’s not part of the calculus curriculum at the college level. I hope this is not true in most other countries.

One fundamental problem (besides that of not having a crucial, powerful tool) is that without using Euler’s formula, there’s no sensible way of understanding why the addition formulas (and thus most trig identities) are true. As a result, students are led to believe that mathematics is about some list of formulas you should memorize without understanding why they are true.

Another way of getting the same thing (cos(ϑ) + i sin(ϑ) is a rotation by ϑ), while avoiding complex numbers would have been to use two by two rotation matrices, but that requires introducing matrix multiplication.

I don’t really understand why the US math curriculum makes this choice not to use Euler’s formula. It seems to be that the logic is “to understand Euler’s formula you need to understand complex functions of a complex argument, and we can’t talk about that until a complex variables course”"

... pour cette contribution, ... la première depuis bien longtemps.
Cordialement, G. Lorang

Mais je vous en prie. Par contre il aurait fallu laisser les hyperlinks, cela permettrait d'aller droit au contenu.

C'est effectivement un endroit calme et un tantinet mélancolique ici.

... changé à votre post. Chez moi les liens marchent.
Cordialement, G. L.