# Tagged Questions

47 views

### What is the potential function of the field $\left(\frac{-y}{x^2+y^2},\frac{x}{x^2+y^2}\right)$

The vector field is obviously conservative on every closed domain that doesn't encompass the point $(0,0)$, so there must be a potential function. I've got $\arctan(\frac{x}{y})$ for $x$ unequal to ...
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### How to prove the one-variable calculus definition of derivative extends to $\Bbb C$ *only* because $\Bbb C$ is a field?

I have been told the one-variable calculus definition of derivative extends to $\Bbb C$ only because $\Bbb C$ is a field. See : Higher dimensional analogues of the argument principle?  ...
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### Conservative field and potential functions

How can I prove that the field $F=\frac{-y}{x^2+y^2}dx + \frac{x}{x^2+y^2}dy$ is a conservative vector field, and isn't local conservative on the domain $U=(x-5)^{2/3}+(y-7)^{2/3}<1$? I tried to ...
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### Is it possible to do calculus on any field with a topology?

I'll try to make my point clear: when we consider the field of complex numbers $\mathbb{C}$ we can do calculus there because we have properties of a field and in the same time we have a topology to ...
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### Chracterizing quartic polynomials F such that $F, F',F''$ have only real rational roots.

When designing friendly problems for a calculus class one comes up with such a question. (The cubic case is relatively easy.) Of course one can generalize: Characterize degree $n$ polynomials such ...
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### probability inequality resolution finite field

I'm trying to find out whether my communication protocol should have redundant information padded, in order to help the receiver correct the error (error correction code, ECC) without needing a ...
I've seen it asserted in several places (e.g., Spivak's Calculus, p.3) that the fact that "parentheses can be freely rearranged" in expressions involving only addition ($+$) is based solely on (P1) ...