green's theorem
97 views (last 30 days)
Show older comments
Verify Green’s theorem for the vector field𝐹=(𝑥2−𝑦3)𝑖+(𝑥3+𝑦2)𝑗, over the ellipse 𝐶:𝑥2+4𝑦2=64
6 Comments
Walter Roberson
on 8 Jul 2023
@Gayathri I do not understand how that will help prove Green's theorem?
I am also unclear as to which variable the integration is with respect to?
Answers (1)
Mehul Mathur
on 11 Jan 2022
clear
clc
syms x y t
F=input('Enter the vector function M(x,y)i+N(x,y)j in the form [M N]: ');
M(x,y)=F(1); N(x,y)=F(2);
r=input('Enter the parametric form of the curve C as [r1(t) r2(t)]: ');
r1=r(1);r2=r(2);
P=M(r1,r2);Q=N(r1,r2);
dr=diff(r,t);
F1=sum([P,Q].*dr);
T=input('Enter the limits of integration for t [t1,t2]: ');
t1=T(1);t2=T(2);
LHS=int(F1,t,t1,t2);
yL=input('Enter limits for y in terms of x: [y1,y2]: ');
xL=input('Enter limits for x as constants: [x1,x2]: ');
y1=yL(1);y2=yL(2);x1=xL(1);x2=xL(2);
F2=diff(N,x)-diff(M,y);
RHS=int(int(F2,y,y1,y2),x,x1,x2);
if(LHS==RHS)
disp('LHS of Greens theorem=')
disp(LHS)
disp('RHS of Greens theorem=')
disp(RHS)
disp('Hence Greens theorem is verified.');
end
0 Comments
See Also
Categories
Find more on Numbers and Precision in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!