matlab对离散曲线积分 matlab实现曲线积分

MATLAB语言并未直接提供曲线积分和曲面积分的现成函数。以下是曲线积分函数：

function I = path_integral(F,vars,t,a,b)

%path_integral

%第一类曲线积分

% I = path_integral(f, [x,y], t, t_m, t_M)

% I = path_integral(f, [x,y,z], t, t_m, t_M)

% Examples:

% 计算int_l(z^2/(x^2+y^2))ds, l是如下定义的螺线

% x=acost, y=asint, z=at, 0<=t<=2*pi, a>0

% MATLAB求解语句

% syms t; syms a positive;

% x=a*cos(t); y=a*sin(t); z=a*t;

% f=z^2/(x^2+y^2);

% I=path_integral(f,[x,y,z],t,0,2*pi)

%

%第二类曲线积分

% I = path_integral([P,Q], [x,y], t, a, b)

% I = path_integral([P,Q,R], [x,y,z], t, a, b)

% I = path_integral(F, v, t, a, b)

% Examples:

% 曲线积分int_l( (x+y)/(x^2+y^2)*dx - (x-y)/(x^2+y^2)*dy ),

% l为正向圆周x^2+y^2=a^2

% 正向圆周的参数函数描述： x=acost, y=asint, (0<=t<=2pi)

% MATLAB求解语句

% syms t; syms a positive;

% x=a*cos(t); y=a*sin(t);

% F=[ (x+y)/(x^2+y^2), -(x-y)/(x^2+y^2) ];

% I=path_integral(F,[x,y],t,2*pi,0)

if length(F)==1

I = int(F*sqrt(sum(diff(vars,t).^2)),t,a,b);

else

F = F(:).';

vars = vars(:);

I = int(F*diff(vars,t),t,a,b);

end