From 1d0bb72e19fe1327a8fa454154a464fbb154f2eb Mon Sep 17 00:00:00 2001 From: joshuab <> Date: Wed, 30 Jun 2010 20:32:41 +0000 Subject: fixed numbering --- Problem Set 1.page | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'Problem Set 1.page') diff --git a/Problem Set 1.page b/Problem Set 1.page index cf96a80..8464f37 100644 --- a/Problem Set 1.page +++ b/Problem Set 1.page @@ -6,7 +6,7 @@ - Show that the Cauchy-Riemann equations are equivalent to the following PDE: -$df/dx + i df/dy = 0$ + $df/dx + i df/dy = 0$ You might want to use this fact in the problems below, though it's not necessary. @@ -19,11 +19,11 @@ You might want to use this fact in the problems below, though it's not necessary - Show that the product of two holomorphic functions is holomorphic. - Try to extend the following functions of a real variable to holomorphic functions defined on the entire complex plane. Is it always possible to do so? What goes wrong? - - $\sinh(z), \cosh(z)$ + a. $\sinh(z), \cosh(z)$ - $\frac{z^3}{1 + z^2}$ - $\sin(z), \cos(z)$ - $\sqrt{z}$ - $\log z$ - $\mathrm{erf}(z)$, the antiderivative of the gaussian $e^{-z^2/2}$ - - $e^{1/z}$ + - $e^{1/z}$ What is the growth rate of the magnitude of these functions as $z \to \infty$ along the real axis? The imaginary axis? How does the argument change? -- cgit v1.2.3