Help for a "Surface and Flux integrals" program

[AlexFekken]

Hi Salvo (and Arno),

Nice to see some higher mathematics being implemented: I sincerely appreciate your work, so apologies if this seems like I am doing nothing more than nit-picking.

These are some typos that you might want to fix (and suggestions that you may or may not want to take up) if this is going to be the starting point for documentating your library:

1:

(11-03-2017 05:53 PM)salvomic Wrote:  \[ \int _\sigma dS = \iint_{A}f(\sigma _1(u,v),\sigma _2(u,v),\sigma _3(u,v))\sqrt{I_1^2+I_2^2+I_3^2}dudv \]

The f is missing on the left hand side:

\[ \int _\sigma f dS = \iint_{A}f(\sigma _1(u,v),\sigma _2(u,v),\sigma _3(u,v))\sqrt{I_1^2+I_2^2+I_3^2}dudv \]

And why not allow for vector functions f here as well? I realise that it is less common than a flux integral but the (component-wise) implementation would be trivial. Also, in my opinion, disitnguishing between 'regular' surface integrals and flux integrals more explicitly (e.g. by using a different function, like you did with your line and curvilinear integrals) might be a good thing.

2:

(11-03-2017 05:53 PM)salvomic Wrote:  \[
\int _\sigma F\cdot \mathbf{n} \, dS = \iint_{\sigma }(f_1(\sigma _1(u, v),\sigma _2(u, v),\sigma _3(u, v))I_1)+f_2(\sigma _1(u, v),\sigma _2(u, v),\sigma _3(u, v))I_2+f_3(\sigma _1(u, v),\sigma _2(u, v),\sigma _3(u, v))I_3) dudv
\]

Perhaps note that \[F = (f_1, f_2, f_3)\] for those less familiar with the maths.

3:

(11-03-2017 05:53 PM)salvomic Wrote:  \[ (u,v) \in A \supset \mathbb{R}^2 \]

The inclusion is the wrong way around:
\[ (u,v) \in A \subset \mathbb{R}^2 \]

You may also want to mention that A should be a rectangle, at least for the current implementation.

4:
Not really a typo, but for a better connect to the literature as well as the code it might be worth pointing out that \[I = (I_1, I_2, I_3)\] is the cross-product of the derivatives of \[ \sigma = (\sigma_1, \sigma_2, \sigma_3) \] w.r.t. u and v.