Mumbai University > Information Technology, Computer Engineering > Sem 3 > Applied Mathematics 3

Marks: 8M

Year: Dec 2015

Part-1

Laplace equation in polar form in polar form is

$\frac{∂^2 u}{∂^2 r} + \frac{1}{r} \frac{∂u}{∂r} + \frac{1}{r^2} \frac{∂^2 u}{∂θ^2} =0$

We have

$u = [r+ \frac{a^2}{r}cosθ = (r + a^2 r^{-1} )cosθ$

Differentiating with respect to r

Therefore,

$\frac{∂u}{∂r} = (1 + (-1) a^2 r^{-2} )cosθ\\ \frac{∂u}{∂r} = (1 …