Mumbai university > Electronics and telecommunication engineering, Electronics engineering > Sem 3 > Applied mathematics 3

Marks : 05

Years : MAY 2016

F(z) is an analytic function, Hence by C.R.equation

$\dfrac {du}{dr}=\dfrac 1r\dfrac {dv}{d\theta}, But \space U=r^3\cos p\theta, v=\r^p \sin 3\theta \\ 3r^2\cos p\theta=\dfrac 1r [r^P \cos 3\theta.3] \\ r^2\cos p\theta =r^{p-1} \cos 3\theta \\ \Rightarrow 2=p-1 \space\space \space i.e. p=3 \\ Or \space P=3$