Help for a "Surface and Flux integrals" program
11-03-2017, 05:53 PM (This post was last modified: 11-04-2017 10:05 AM by salvomic.)
Post: #1
 salvomic Senior Member Posts: 1,379 Joined: Jan 2015
Help for a "Surface and Flux integrals" program
hi,
I need some help to implement for the Prime a simple CAS programs to calculate Surface Integrals and Flux Integrals (Surface integrals with vector fields)

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

Flux integral:
$\int _\sigma F\cdot \mathbf{n} \, dS = \iint_{\sigma }(f_1(\sigma _1(u, v),\sigma _2(u, v),\sigma _3(u, v))I_1)+f_2(\sigma _1(u, v),\sigma _2(u, v),\sigma _3(u, v))I_2+f_3(\sigma _1(u, v),\sigma _2(u, v),\sigma _3(u, v))I_3) dudv$
(where $$F = (f_1, f_2, f_3)$$)

Where also:
$I_1(u,v) = det\begin{pmatrix} \frac{\partial \sigma _2}{\partial u}(u,v) & \frac{\partial \sigma _2}{\partial v}(u,v)\\ \frac{\partial \sigma _3}{\partial u}(u,v) & \frac{\partial \sigma _3}{\partial v}(u,v)\\ \end{pmatrix} \, ; I_2(u,v) = det\begin{pmatrix} \frac{\partial \sigma _3}{\partial u}(u,v) & \frac{\partial \sigma _3}{\partial v}(u,v)\\ \frac{\partial \sigma _1}{\partial u}(u,v) & \frac{\partial \sigma _1}{\partial v}(u,v)\\ \end{pmatrix} \, ; I_3(u,v) = det\begin{pmatrix} \frac{\partial \sigma _1}{\partial u}(u,v) & \frac{\partial \sigma _1}{\partial v}(u,v)\\ \frac{\partial \sigma _2}{\partial u}(u,v) & \frac{\partial \sigma _2}{\partial v}(u,v)\\ \end{pmatrix}$

Which are parts of: $$I = (I_1, I_2, I_3)$$

I would like to start (or follow) from this program in the Prime Software Library that has a simple syntax (for linear and curvilinear integrals):
INPUT 4 parameters: 1. a function (scalar / vectorial), 2. parametrisation of a curve, 3. lower bound, 4. upper bound;
and a control for arguments (2 or 3) and for the case there is no input (and then the program show a little help)...

I'd think to extend these concepts (from (curvi)linear integrals to surface and flux), using a parametrisation of the surface like "u, v, σ(u, v)"...
$\sigma (u, v) : \left\{\begin{matrix} x_{1}=\sigma_{1}(u, v)) \\ x_{2}=\sigma_{2}(u, v)) \\ x_{3}=\sigma_{3}(u, v)) \end{matrix}\right. \,\, , (u,v) \in A \subset \mathbb {R}^2$
But I've no clear idea at the moment, ehm :-)

Salvo

EDIT: edited typo in laTeX formulas (thanks Alex!)...

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
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 Messages In This Thread Help for a "Surface and Flux integrals" program - salvomic - 11-03-2017 05:53 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-03-2017, 10:26 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-03-2017, 10:57 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-03-2017, 11:16 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-03-2017, 11:23 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-04-2017, 12:06 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 07:51 AM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-03-2017, 11:41 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-03-2017, 11:49 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-03-2017, 11:47 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 09:14 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 10:21 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 10:38 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 10:50 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 10:54 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 11:17 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 11:24 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 11:27 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 11:34 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 11:46 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 09:50 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 10:08 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 10:40 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 10:44 AM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-04-2017, 10:56 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 11:04 AM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-04-2017, 11:08 AM RE: Help for a "Surface and Flux integrals" program - AlexFekken - 11-04-2017, 11:21 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 11:24 AM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-04-2017, 11:39 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-04-2017, 11:47 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-06-2017, 04:37 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-06-2017, 05:56 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-06-2017, 06:06 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-06-2017, 06:25 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-06-2017, 06:32 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-06-2017, 06:37 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-06-2017, 06:49 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-06-2017, 08:57 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-06-2017, 09:13 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-06-2017, 06:57 PM RE: Help for a "Surface and Flux integrals" program - parisse - 11-06-2017, 07:43 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 11-06-2017, 08:44 PM RE: Help for a "Surface and Flux integrals" program - parisse - 11-07-2017, 07:13 AM RE: Help for a "Surface and Flux integrals" program - salvomic - 11-07-2017, 08:32 AM RE: Help for a "Surface and Flux integrals" program - Arno K - 12-02-2017, 05:02 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 12-02-2017, 05:04 PM RE: Help for a "Surface and Flux integrals" program - Arno K - 12-02-2017, 05:23 PM RE: Help for a "Surface and Flux integrals" program - salvomic - 12-02-2017, 05:38 PM

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