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Line integral and curvilinear integral - salvomic - 05-15-2015 08:17 PM
hi all,
here there are two programs (CAS) to calculate Line integral (for vectorial functions fields) and Curvilinear Integral (for scalar functions).
intcur: INPUT a scalar function (x,y,z), a parametric form of a curve [r(t), r(t), r(t)], lower and high bound and the programs returns curvilinear integral
intlin: INPUT a vectorial function, a parametric form of a curve (as above), lower and high bound and the program returns linear integral.
These programs work with 2 or 3 components (parametric expression: [r1(t), r2(t), r3(t)] or [r1(t), r2(t)])...
Examples:
1.0 to find the curvilinear integral of z in a circle (parametric: x=COS(t), y=SIN(t), z=t) from 0 to 2π
intcur(z, [COS(t), SIN(t), t], 0, 2*π) -> 2*√2*π^2
2. to find the line integral of F=‹x*SIN(y), y› along the path ‹t, t^2› from -1 to 2
intlin([x*SIN(y), y], [t, t^2], -1,2) -> (15/2)+(COS(1)-COS(4))/2
Enjoy!
Salvo Micciché
Code:
#cas
intcur(args):=
BEGIN
local argv,argc, a, b;
local f, r, dr, ft, s,t;
purge(t);
argv:=[args];
argc:=size(argv);
IF argc !=4 THEN
return "Input:f(x,y,z), [r(t),r(t),r(t)] ,low, high";
ELSE
f:=argv(1);
r:=argv(2);
a:=argv(3);
b:=argv(4);
dr:=diff(r,t);
s:= size(argv(2));
ft:= IFTE( s==3, subst(f,[x,y,z]=r), subst(f,[x,y]=r) );
return int(dot(ft,l2norm(dr)),t,a,b);
END;
END;
#end...
Code:
#cas
intlin(args):=
BEGIN
local argv, argc, a, b;
local f, r, dr, ft,s, t;
purge(t);
argv:=[args];
argc:=size(argv);
IF argc !=4 THEN
return "Input:[x,y,z], [r(t),r(t),r(t)] ,low, high";
ELSE
f:=argv(1);
r:=argv(2);
a:=argv(3);
b:=argv(4);
dr:=diff(r,t);
s:= size(argv(2));
ft:= IFTE( s==3, subst(f,[x,y,z]=r), subst(f,[x,y]=r) );
return int(dot(ft,dr),t,a,b);
END;
END;
#endEDIT: put above a slightly new code, in which t is a local variable that's now purged first to being used in the integral calculus, to avoid to leave a global variable in CAS Vars.