Question

If J1 is the Jacobian of u(x,y) and v(x,y) and J2 is the Jacobian of x(u,v) and y(u,v) then J1J2 *​

Answer 1

If J1 is the Jacobian of u(x, y) and v(x, y) and J2 is the Jacobian of x(u, v) and y(u, v) then J1J2 :

Explanation:

• j(u,vx,y) is the definition of Jacobian of u and v w.r.t x and y.
• ∣J∣=(1+v)(1+u)−uv=1+u+v
• The Jacobian of the transformation x=g(u, v) x = g ( u , v ) , y=h(u, v) y = h ( u , v ) is. ∂(x, y)∂(u, v)=∣∣ ∣ ∣∣∂x∂u∂x∂v∂y∂u∂y∂v∣∣ | ||