Question

13. Show using a picture and the Jacobian determinant that if we convert from rectangular coordinates (x, y) to polar coordinates (r,0), then

Answer 1

" Show using a picture and the Jacobian determinant of we convert from rectangular coordinates (x, y) to polar coordinates (r, theta) then dx dy = r dr d theta For polar conversion, we write x = r cos theta and y = r sin theta (from the figure) If we change from Cartesian coordinates (x, y) to polar coordinates (r, theta) then Jacobian is partial differential (x, y)/partial differential (r, theta) =