...Cartesian to polar coor? 1. Show that the following expressions can be simplified by changing coordinates: from Cartesian to polar coordinates (x, y)->(r,? ), which gives us u(x, y)-> g(r,? ).
x^2(u''(resp to x))+2xy(du^2/dxdy)+y^2(u''(resp to y))=r^2(g''(resp to r))
i know u'(resp to x)=(dg/dr)(dr/dx)+(dg/? )(d? /dx),
what is u''(resp to x) and what is (du^2)/(dxdy),
To solve this question,should I just express the LHS as function as g,r,? then it will equal to RHS?
this is really bothers me ,somone please help!
x^2(u''(resp to x))+2xy(du^2/dxdy)+y^2(u''(resp to y))=r^2(g''(resp to r))
i know u'(resp to x)=(dg/dr)(dr/dx)+(dg/? )(d? /dx),
what is u''(resp to x) and what is (du^2)/(dxdy),
To solve this question,should I just express the LHS as function as g,r,? then it will equal to RHS?
this is really bothers me ,somone please help!