Help for a "Surface and Flux integrals" program

11042017, 11:04 AM
Post: #21




RE: Help for a "Surface and Flux integrals" program
(11042017 10:56 AM)Arno K Wrote: If I use f(x,y)=x^2+y^2 and substite x=u*cos(v), y=u*sin(v),z=u^2 and integrate u from 0 to 1, v=0 to 2*PI I get (1/60)*(sqrt(5)*25*π+π), the same is provided by the prime, so some thing with that substitution must be wrong. Clearly my integral then has u^3*sqrt(...) which explains the difference, but where does it result from. I think that should be f(x,y,z) = 1 

11042017, 11:08 AM
(This post was last modified: 11042017 11:09 AM by Arno K.)
Post: #22




RE: Help for a "Surface and Flux integrals" program
So there it is, the parametrization totally reflects the considered surface, there is no need to integrate f(x,y)=x^2+y^2, using f=1 provides 1/6*(√5*5*ππ), that is correct. So my program does what it shall, as I like to have some help on the calc I think I will leave it as is, that is input in a list so that the help can be printed.
Arno 

11042017, 11:17 AM
Post: #23




RE: Help for a "Surface and Flux integrals" program
(11042017 10:54 AM)AlexFekken Wrote: What exactly is the calculation that you carried out on the Prime that gave an incorrect result? I get the result in the attached image, approx = 166.856756133 ∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11042017, 11:21 AM
Post: #24




RE: Help for a "Surface and Flux integrals" program
(11042017 11:08 AM)Arno K Wrote: So there it is, the parametrization totally reflects the considered surface, there is no need to integrate f(x,y)=x^2+y^2, using f=1 provides 1/6*(√5*5*ππ), that is correct. So my program does what it shall, as I like to have some help on the calc I think I will leave it as is, that is input in a list so that the help can be printed. That's right: the parametrisation, including range of integration, determines the surface while f describes the function that you want to integrate. A priori the two are totally unrelated. The same is true for the flux integral (where n is part of the surface definition and it will automatically come out of the parametrisation). 

11042017, 11:24 AM
(This post was last modified: 11042017 11:26 AM by AlexFekken.)
Post: #25




RE: Help for a "Surface and Flux integrals" program  
11042017, 11:24 AM
Post: #26




RE: Help for a "Surface and Flux integrals" program
(11042017 10:56 AM)Arno K Wrote: If I use f(x,y)=x^2+y^2 and substite x=u*cos(v), y=u*sin(v),z=u^2 and integrate u from 0 to 1, v=0 to 2*PI I get (1/60)*(sqrt(5)*25*π+π), the same is provided by the prime, so some thing with that substitution must be wrong. Clearly my integral then has u^3*sqrt(...) which explains the difference, but where does it result from. I think it should be correct also (surface integral for that function). Using 1 (constant function) the program returns the value of the area, that is also correct... (11042017 11:08 AM)Arno K Wrote: So there it is, the parametrization totally reflects the considered surface, there is no need to integrate f(x,y)=x^2+y^2, using f=1 provides 1/6*(√5*5*ππ), that is correct. So my program does what it shall, as I like to have some help on the calc I think I will leave it as is, that is input in a list so that the help can be printed. I think so. For now you could put it, if you want, into the Library, maybe someone else would like to collaborate and ameliorate it. At the moment the program permits to calculate: surface integral (and integral of the area, putting 1 as function) and flux integral (putting a vector in the first element). For the different parametrisation we could discuss about how it's the best way to do it without complicate the program itself... ∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11042017, 11:27 AM
Post: #27




RE: Help for a "Surface and Flux integrals" program
(11042017 11:24 AM)AlexFekken Wrote:(11042017 11:17 AM)salvomic Wrote: I get the result in the attached image, approx = 166.856756133You have got rho and theta in the wrong order: swap the integration intervals. ahh, ok I was following the order of the book (drho, dtheta), I forgot that in the Prime is correct the inverse... Swapping them it's ok. ∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11042017, 11:34 AM
Post: #28




RE: Help for a "Surface and Flux integrals" program
(11042017 11:27 AM)salvomic Wrote: I was following the order of the book (drho, dtheta), I forgot that in the Prime is correct the inverse... I don't know which book you are looking at but the convention is pretty standard: the integration symbols (with intervals) and differentials act as opening and closing pairs of brackets. I.e. the first range corresponds to the last variable, etc... I can't remember ever seeing a book where this was different. 

11042017, 11:39 AM
Post: #29




RE: Help for a "Surface and Flux integrals" program
I think the help can be implemented in the comments, then the list can be omitted. As the program works like it shall I will add some comments and then put it in the software forum.
Arno 

11042017, 11:46 AM
(This post was last modified: 11042017 05:49 PM by salvomic.)
Post: #30




RE: Help for a "Surface and Flux integrals" program
(11042017 11:34 AM)AlexFekken Wrote: I don't know which book you are looking at but the convention is pretty standard: the integration symbols (with intervals) and differentials act as opening and closing pairs of brackets. I.e. the first range corresponds to the last variable, etc... I can't remember ever seeing a book where this was different. The book is this one, from Andrea Bacciotti (Torino University), it's more precise (I studied also with it), but in this specific examples (perhaps a typo) there was dρdθ... In my other Italian books there is often dθdρ, but not always, however you're right: the differentials are as they would be "closed brackets", yes. EDIT: The trick (and the difficulty) tu solve these integrals stay mostly in a correct determination of the bounds and the order of differentials. Often, in fact, it's convenient to pass from the cartesian to polar (or cylindric) or spheric parametrisation. Doing so, the Arno's program works well, very well. ∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11042017, 11:47 AM
(This post was last modified: 11042017 05:45 PM by salvomic.)
Post: #31




RE: Help for a "Surface and Flux integrals" program
(11042017 11:39 AM)Arno K Wrote: I think the help can be implemented in the comments, then the list can be omitted. As the program works like it shall I will add some comments and then put it in the software forum. thanks a lot! It'll be useful to other users, I'm sure. EDIT: the idea is use some markers in the comments: simply \\ Help \\ About program, help, and so on... \\ \Help or \\ !Help \\ About program, help, and so on... \\ /Help ∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11062017, 04:37 PM
Post: #32




RE: Help for a "Surface and Flux integrals" program
(11042017 11:39 AM)Arno K Wrote: I think the help can be implemented in the comments, then the list can be omitted. As the program works like it shall I will add some comments and then put it in the software forum. Arno, as we have privately discussed, to avoid problems with the exportation of u and v vars in CAS variables, in the code it would be better to insert u,v in the local statement and then the two lines purge(u); and purge(v). The code would be this: Code:
What you you think about? Salvo ∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11062017, 05:56 PM
(This post was last modified: 11062017 06:24 PM by Arno K.)
Post: #33




RE: Help for a "Surface and Flux integrals" program
I had tried that with a local u statement at the beginning, then the program refuses to work. I tried that and your order works, nice find. Local in front and purge at the end does not work, that is what I tried this morning.
Arno 

11062017, 06:06 PM
Post: #34




RE: Help for a "Surface and Flux integrals" program
(11062017 05:56 PM)Arno K Wrote: I had tried that with a local u statement at the beginning, then the program refuses to work. It's strange... here it works with Code: BEGIN I'm trying now in HC and in VC with Code:
∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11062017, 06:25 PM
Post: #35




RE: Help for a "Surface and Flux integrals" program
(11062017 06:06 PM)salvomic Wrote:(11062017 05:56 PM)Arno K Wrote: I had tried that with a local u statement at the beginning, then the program refuses to work. I edited my post from above 

11062017, 06:32 PM
Post: #36




RE: Help for a "Surface and Flux integrals" program
∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11062017, 06:37 PM
Post: #37




RE: Help for a "Surface and Flux integrals" program
No no, now it works, but I am not that contented with implementing of local variables and then purging them to avoid their occurance in memorymanager.
Arno 

11062017, 06:49 PM
Post: #38




RE: Help for a "Surface and Flux integrals" program
(11062017 06:37 PM)Arno K Wrote: No no, now it works, but I am not that contented with implementing of local variables and then purging them to avoid their occurance in memorymanager. I know, you are right, that's only a workaround, but the occurrence in memory manager leaves there variables that after some time could interfere with other commands or programs... We need a real solution :) Salvo ∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

11062017, 06:57 PM
Post: #39




RE: Help for a "Surface and Flux integrals" program
Yes, we do!


11062017, 07:43 PM
(This post was last modified: 11062017 07:46 PM by parisse.)
Post: #40




RE: Help for a "Surface and Flux integrals" program
If you need symbolic variables inside a user function, the cleanest way to do that is to declare the variable(s) local, and then purge their initial content (initial content is "Unitialized local variable") so that the local var eval to itself. You can also assume the variable to be DOM_SYMBOLIC (it has the same effect).


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