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## Homework Statement

w(r,[tex]\theta[/tex])= u(rcos [tex] \theta [/tex]),rsin([tex] \theta[/tex])) for some u(x,y)

express [tex]

\frac{ \partial w}{\partial r} [/tex] and [tex] \frac{ \partial w}{ \partial \theta} [/tex] in terms of [tex] \frac{ \partial u}{ \partial x} [/tex] and [tex] \frac{ \partial u}{ \partial y} [/tex]

## Homework Equations

rewrite the following PDE and initial conditions in terms of w,r and [tex]\theta[/tex] and solve

y[tex] \frac{ \partial u}{ \partial x} [/tex] - x[tex] \frac{ \partial u}{ \partial y} [/tex] = 1 where u(x,0) = 0 for 0<x<[tex]\infty[/tex]

## The Attempt at a Solution

[tex] \frac{ \partial w}{ \partial r} [/tex] = [tex] \frac{ \partial u}{ \partial x} [/tex] . [tex] \frac{ \partial x}{ \partial r} [/tex] + [tex] \frac{ \partial u}{ \partial y} [/tex] . [tex] \frac{ \partial y}{ \partial r} [/tex]

and

[tex] \frac{ \partial w}{ \partial \theta} [/tex] = [tex] \frac{ \partial u}{ \partial x} [/tex] . [tex] \frac{ \partial x}{ \partial \theta} [/tex] + [tex] \frac{ \partial u}{ \partial y} [/tex] . [tex] \frac{ \partial y}{ \partial \theta} [/tex]

but im not sure about part b...