Teaching MPPSC Assistant Professor Mock Test Series 2025 Engineering Mathematics Complex Variables Analytic Functions
Polar form of the Cauchy-Riemann equations is
1
\(\dfrac{\partial u}{\partial r} = r \dfrac{\partial v}{\partial \theta} \ \text{and} \ \dfrac{\partial v}{\partial r}=-r \dfrac{\partial u}{\partial\theta }\)
2
\(\dfrac{\partial u}{\partial r} = \dfrac{1}{r} \dfrac{\partial v}{\partial \theta} \ \text{and} \ \dfrac{\partial v}{\partial r}=-\dfrac{1}{r} \dfrac{\partial u}{\partial\theta }\)
3
\(\dfrac{\partial u}{\partial r} = \dfrac{1}{r} \dfrac{\partial v}{\partial \theta} \ \text{and} \ \dfrac{\partial v}{\partial r}=-r \dfrac{\partial u}{\partial\theta }\)
4
\(\dfrac{\partial u}{\partial r} = r \dfrac{\partial v}{\partial \theta} \ \text{and} \ \dfrac{\partial v}{\partial r}=- \dfrac{1}{r} \dfrac{\partial u}{\partial\theta }\)