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| author | joshuab <> | 2010-06-30 20:32:41 +0000 |
|---|---|---|
| committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-06-30 20:32:41 +0000 |
| commit | 1d0bb72e19fe1327a8fa454154a464fbb154f2eb (patch) | |
| tree | 22a6d38371988530eca1a27109e1c6ac94386207 | |
| parent | 6bab71cee6c9ea96486bb24499bb1f2f022c8719 (diff) | |
| download | afterklein-wiki-1d0bb72e19fe1327a8fa454154a464fbb154f2eb.tar.gz afterklein-wiki-1d0bb72e19fe1327a8fa454154a464fbb154f2eb.zip | |
fixed numbering
| -rw-r--r-- | Problem Set 1.page | 6 |
1 files changed, 3 insertions, 3 deletions
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? |