Numerical integration
02-03-2016, 04:52 PM
Post: #1
 alealessietto Junior Member Posts: 4 Joined: Feb 2016
Numerical integration
Hi, I'm new on this forum. Sorry for my english, but I'm italian and I don't speak english very well. However, I study chemical engineering. I've bought HP PRIME and now I have a problem. How can I resolve a numerical integration??
Alessio
02-03-2016, 04:55 PM
Post: #2
 DrD Senior Member Posts: 1,133 Joined: Feb 2014
RE: Numerical integration
Hi.

It takes awhile to get used to where things are, and what they do, but have you discovered the "template" key, [units C]? That may be helpful for you.

-Dale-
02-03-2016, 05:03 PM
Post: #3
 alealessietto Junior Member Posts: 4 Joined: Feb 2016
RE: Numerical integration
Thank you for your answer, but I'm sorry, I don't know what is the "template" key, [units C]. Can you help me?
02-03-2016, 05:17 PM (This post was last modified: 02-03-2016 05:18 PM by DrD.)
Post: #4
 DrD Senior Member Posts: 1,133 Joined: Feb 2014
RE: Numerical integration
That is the alpha key C. Just to the right of the Toolbox key. I think it is described on page 13 of the user guide, which you may be able to bring up via the emulator: Help | User Guide. It's called the Math Template Key.
02-03-2016, 05:30 PM
Post: #5
 alealessietto Junior Member Posts: 4 Joined: Feb 2016
RE: Numerical integration
Umh, You mean the symbol of defined integration? I use that symbol when I have to solve a definite integral between two values.
However I meant: can you resolve numerical integral with HP Prime? For example it is possible to solve nonlinear equations in a numerical way with fsolve.
For numerical integration I mean: https://en.wikipedia.org/wiki/Numerical_integration
02-03-2016, 05:38 PM
Post: #6
 DrD Senior Member Posts: 1,133 Joined: Feb 2014
RE: Numerical integration
I guess, I didn't understand. You might try the forum search feature, with "non linear equations" in the entry field. This topic has been discussed previously, and (I think) there have been some related firmware changes, so make sure you have the latest updates. That's about all I can offer, good luck!

-Dale-
02-03-2016, 05:55 PM
Post: #7
 alealessietto Junior Member Posts: 4 Joined: Feb 2016
RE: Numerical integration
hoping someone could help me! I need to solve that problem!
02-03-2016, 06:39 PM
Post: #8
 Arno K Senior Member Posts: 470 Joined: Mar 2015
RE: Numerical integration
Perhaps you mean something like:
Code:
 #cas simpsonint(g,a,b,n):= BEGIN local l,l1; IF even(n) THEN IF (type(g)==DOM_SYMBOLIC  OR type(g)== DOM_FUNC)   THEN     l:=MAKELIST(X,X,a,b,(b-a)/n);      IF type(g)==DOM_SYMBOLIC THEN      g:=unapply(g,x);      END;    l:=apply(g,l);    l1:=MAKELIST(even(X)+1,X,1,n+1);  return (2*DOT(l,l1)-g(a)-g(b))*(b-a)/(3*n);    ELSE return ("f must be symbolic or function!");   END;  // return 0; ELSE return "n must be even!"; END; END; #end #cas trapezregel(g,a,b,n):= BEGIN local l; IF (type(g)==DOM_SYMBOLIC  OR type(g)== DOM_FUNC)   THEN     l:=MAKELIST(X,X,a,b,(b-a)/n);      IF type(g)==DOM_SYMBOLIC THEN      g:=unapply(g,x);      END;    l:=apply(g,l);    return (2*ΣLIST(l)-g(a)-g(b))*(b-a)/(2*n);    ELSE return ("f must be symbolic or function!");   END; END; #end #cas rightsum(g,a,b,n):= BEGIN local l; IF (type(g)==DOM_SYMBOLIC  OR type(g)== DOM_FUNC)   THEN     l:=MAKELIST(X,X,a,b,(b-a)/n);      IF type(g)==DOM_SYMBOLIC THEN      g:=unapply(g,x);      END;    l:=apply(g,l);    return (ΣLIST(l)-g(a))*(b-a)/n;    ELSE return ("f must be symbolic or function!");   END; END; #end #cas leftsum(g,a,b,n):= BEGIN local l; IF (type(g)==DOM_SYMBOLIC  OR type(g)== DOM_FUNC)   THEN     l:=MAKELIST(X,X,a,b,(b-a)/n);      IF type(g)==DOM_SYMBOLIC THEN      g:=unapply(g,x);      END;    l:=apply(g,l);    return (ΣLIST(l)-g(b))*(b-a)/n;    ELSE return ("f must be symbolic or function!");   END; END; #end EXPORT NumericIntegr() BEGIN local a,N,f,b; N:=12; a:=1;b:=3; f:='X^2';    if input(      {{f,[8],{20,70,0}},      {a,[0],{20,30,1}},      {b,[0],{20,30,2}},      {N,[0],{20,30,3}}},            "Enter Data",      {"f(X)=", "a= ", "b= ","N= "       },      {        "Enter the function, upper case X!",        "Enter the starting point",        "Enter the endpoint",        "Enter the amount of intervals"             },      {f,a,b,N}    ) then f:=lower(string(f)); PRINT(); PRINT("Simpsonsumme:   "+simpsonint(f,a,b,N)); PRINT("Trapezsumme:    "+trapezregel(f,a,b,N)); PRINT("Rechtecklinks:  "+leftsum(f,a,b,N)); PRINT("Rechteckrechts: "+rightsum(f,a,b,N)); return  end; END;
but I did not implement an adaptive method.
Arno
02-03-2016, 08:32 PM
Post: #9
 ndzied1 Member Posts: 115 Joined: Apr 2014
RE: Numerical integration
Maybe this will help.

First make sure you are in Home mode (1). Then press the template key (2). Then select the integration template from the touch screen (3).

Then enter a function to integrate into the template.

At this point, I usually hit Enter to make a copy of the equation (1). The press Shift/Eval (2/3) to numerically evaluate the integral.

02-04-2016, 10:22 AM (This post was last modified: 02-04-2016 10:25 AM by retoa.)
Post: #10
 retoa Member Posts: 168 Joined: Jan 2015
RE: Numerical integration
[attachment=3093]If you work in home you will find directly the numerical result (using capital letters) without the need of "eval"
The precision depends on the settings, I have floating 3.

Se lavori in modalità home (usando variabili maiuscole) invece che in CAS ottieni direttamente il risultato numerico, senza dover utilizzare il tasto "eval".
La precisione del risultato dipende dalle impostazioni, io ho impostato floating 3.

Attached File(s) Thumbnail(s)

02-04-2016, 11:04 AM
Post: #11
 ndzied1 Member Posts: 115 Joined: Apr 2014
RE: Numerical integration
It looks like you are in Textbook mode and I am in RPN mode. Some other settings could affect this as well.
02-04-2016, 12:31 PM
Post: #12
 retoa Member Posts: 168 Joined: Jan 2015
RE: Numerical integration
You are right, I didn't notice you were in RPN mode.
In RPN I have to press the "eval" key to see the numeric result.
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