Assignment 2 Problem 4

108 days ago by renaldorini

f(x,y)=x/(x^2+y^2); g(x,y)=derivative(f,x) u(x,y)=derivative(g,x) h(x,y)=derivative(f,y) v(x,y)=derivative(h,y) 
       
print(u+v) 
        
(x, y) |--> 8*x^4/(x^2 + y^2)^3 + 8*x^2*y^2/(x^2 + y^2)^3 -
12*x^2/(x^2 + y^2)^2 + 2/(x^2 + y^2)
(x, y) |--> 8*x^4/(x^2 + y^2)^3 + 8*x^2*y^2/(x^2 + y^2)^3 - 12*x^2/(x^2 + y^2)^2 + 2/(x^2 + y^2)
#Therefore, f(x,y) is harmonic 
       
f(x,y)=x^2/(x^2+y^2); g(x,y)=derivative(f,x) u(x,y)=derivative(g,x) h(x,y)=derivative(f,y) v(x,y)=derivative(h,y) 
       
print(u+v) 
        
(x, y) |--> 8*x^4/(x^2 + y^2)^3 + 8*x^2*y^2/(x^2 + y^2)^3 -
12*x^2/(x^2 + y^2)^2 + 2/(x^2 + y^2)
(x, y) |--> 8*x^4/(x^2 + y^2)^3 + 8*x^2*y^2/(x^2 + y^2)^3 - 12*x^2/(x^2 + y^2)^2 + 2/(x^2 + y^2)
#Therefore, this f(x,y) is harmonic