*Problem Find area surface *

x = ( 1-u )(3+cos v)cos(2pi*u)

y = ( 1-u )(3+cos v)sin(2pi*u)

z = 4u + ( 1-u )sinv.

D={(u,v)|0<=u<=1,0<=v<=2pi}

http://i1203.photobucket.com/albums/bb396/kidstar079/Capture-1.png

mycode

{ syms u v;

x = (1-u).*(3+cos(v)).*cos(pi*u);

y = (1-u).*(3+cos(v)).*sin(pi*u);

z = 8*u+( 1-u ).*sin(v);

F=[x,y,z];

ru=diff(F,[u]);

rv=diff(F,[v]);

ruv=ru.*rv;

druv=sqrt(ruv(1).^2+ruv(2).^2+ruv(3).^2);

S=int(int(druv,u,0,1),v,0,2*pi)

}

Answer 1

[bym]

you are going to need:

a =feval(symengine,'linalg::crossProduct',ru,rv)%  .* is not cross product!
b =feval(symengine,'norm',a,2)

once you get the integrand (b) then I would suggest you evaluate it numerically rather than symbolically. You can use

   MatlabFunction()

to turn it into a function to pass to

dblquad

[justin Taylor]

syms u v;

x = (1-u).*(3+cos(v)).*cos(pi*u);

y = (1-u).*(3+cos(v)).*sin(pi*u);

z = 8*u+( 1-u ).*sin(v);

% find area surface .

F=[x,y,z];

ru=diff(F,u);

rv=diff(F,v);

rurv=feval(symengine,'linalg::crossProduct',ru,rv);% .* Khong can dau .

ds= feval(symengine,'norm',rurv,2);

a=int(ds,u,0,1/2);

f=inline('a')

S=subs(f,2*pi)-subs(a,0)

% Plot .

n = 50;

[u,v] = meshgrid(linspace(0,1,n),linspace(0,2*pi,n));

x = (1-u).*(3+cos(v)).*cos(pi*u);

y = (1-u).*(3+cos(v)).*sin(pi*u);

z = 8*u+( 1-u ).*sin(v);

surf(x,y,z)

[Walter Roberson]

You cannot subs() in to an inline function, only in to a symbolic variable.

On the other hand, inline('a') is just going to be a routine that takes a single parameter and returns it, since inline('a') passes the literal string 'a' to inline() rather than passing the value of a. But inline(a) is not going to work either, as inline() cannot be applied to symbolic objects.

You never use S after you calculate it, so there would not seem to be any point in calculating it, and thus no point in calculating f or a or ds or rurv or rv or F.

[justin Taylor]

syms u v;

x = (1-u).*(3+cos(v)).*cos(pi*u);

y = (1-u).*(3+cos(v)).*sin(pi*u);

z = 8*u+( 1-u ).*sin(v);

% find area

F=[x,y,z];

ru=diff(F,u);

rv=diff(F,v);

rurv=feval(symengine,'linalg::crossProduct',ru,rv);% .* Khong can dau .

ds= feval(symengine,'norm',rurv,2);

S=int(int(ds,u,0,1/2),v,0,1);

[justin Taylor]

What proplem i meet ?

[Walter Roberson]

The dot product produces a single expression as its result, not a vector.

norm() must be applied to a matrix, a vector, a polynomial (which is a specific MuPad data type), or a "polynomial expression" (which is an expression in which the variables only enter in terms with integer exponents.) As indicated above, rurv is not a matrix or vector, and it was not constructed as a MuPad polynomial data type, so the only possibility left is a polynomial expression. The dot product, rurv, however, has many sin() and cos() terms involving the variables, so it is not a polynomial expression. Thus, norm() cannot be applied to it. See http://www.mathworks.com/help/toolbox/mupad/stdlib/norm.html

[bym]

the expression is for the _cross_ product not _dot_ product.

[Walter Roberson]

Some day I will learn, "Never feed them after Midnight". ;-)