**Problem 1B-06**:** Partial differentiation involving
two-dimensional polar coordinates

(a) A function F is expressed in two dimensional polar coordinates as F(r, θ). Calculate the partial differentials in rectangular coordinates, ∂F/∂x, and ∂F/∂y.

(b) A function G is expressed in two dimensional rectangular coordinates as G(x, y). Calculate the partial differentials in polar coordinates, ∂G/∂r and ∂G/∂θ.

Scroll down for solution

**Solution:**

(a) From Problem 1B-4, we know

Using Eq.(1) and Eq.(1A), we have

Since

Similarly

Substituting Eqs.(3), (5) and (6) into Eq.(2), we have

(b)

<-Previous page | Table of contents | Next page-> |