Prove that the Cauchy-Riemann equations in polar coordinates are given in the following way: $ru_{r}=v_{\theta}$ ; $rv_{r}=-u_{\theta}$
2952
Cauchy-Riemann equations in polar form.
25996
Using the definition of Riemann integrability, prove that $f $is Riemann integrable on $[0,1]$
75501
Proof using Cauchy Integral Theorem
45682
Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$
128159
the Riemann integrability of inverse function
31027
Ahlfors "Prove the formula of Gauss"
9143
Solve $u_{xx}-3u_{xt}-4u_{tt}=0$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$
67747
divergence in polar coordinates
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
153158
how to get $dx\; dy=r\;dr\;d\theta$
60230
Prove that $\frac{1+\sin\theta+i\cos\theta}{1+\sin\theta-i\cos\theta}=\sin\theta+i\cos\theta$
57191
Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk - Rouché theorem
142821
Why?$\int_0^1\int_{u(t)}^{u(t)+w(t)} f(t,v(t)) dv dt = \int_0^1 f(t,u(t)+\theta w(t))w(t) dt; ~~\theta\in[0,1] $
69020
Complex analysis : If $z =re^{i\theta}$, then prove that $|e^{iz}| =e^{-r\sin\theta}$
54196
When is a function satisfying the Cauchy-Riemann equations holomorphic?
6843
Explain $\iint \mathrm dx\,\mathrm dy = \iint r \,\mathrm \,d\alpha\,\mathrm dr$
47977
If $u$ is harmonic and bounded in $0 < |z| < \rho$, show that the origin is a removable singularity