diff --git a/Lectures_my/MC_2016/Lecture9/mchrzasz.log b/Lectures_my/MC_2016/Lecture9/mchrzasz.log index 5d05a7d..9dee18c 100644 --- a/Lectures_my/MC_2016/Lecture9/mchrzasz.log +++ b/Lectures_my/MC_2016/Lecture9/mchrzasz.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 30 APR 2016 16:15 +This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 3 JUN 2016 10:55 entering extended mode restricted \write18 enabled. %&-line parsing enabled. diff --git a/Lectures_my/MC_2016/Lecture9/mchrzasz.pdf b/Lectures_my/MC_2016/Lecture9/mchrzasz.pdf index e8f7f4a..db1fe0c 100644 --- a/Lectures_my/MC_2016/Lecture9/mchrzasz.pdf +++ b/Lectures_my/MC_2016/Lecture9/mchrzasz.pdf Binary files differ diff --git a/Lectures_my/MC_2016/Lecture9/mchrzasz.synctex.gz b/Lectures_my/MC_2016/Lecture9/mchrzasz.synctex.gz index be3db69..de444e1 100644 --- a/Lectures_my/MC_2016/Lecture9/mchrzasz.synctex.gz +++ b/Lectures_my/MC_2016/Lecture9/mchrzasz.synctex.gz Binary files differ diff --git a/Lectures_my/MC_2016/Lecture9/mchrzasz.tex b/Lectures_my/MC_2016/Lecture9/mchrzasz.tex index 383569f..e64d1ff 100644 --- a/Lectures_my/MC_2016/Lecture9/mchrzasz.tex +++ b/Lectures_my/MC_2016/Lecture9/mchrzasz.tex @@ -431,7 +431,7 @@ \end{align*} \ARROW To solve this equation we need to expand the $\nu(x,t)$ funciton in the Taylor series: \begin{align*} -\nu(x,t) + \frac{\partial \nu(x,t)}{\partial t} \Delta t = p \nu(x,t) - p \frac{\partial\nu(x,t) }{\partial x} \Delta x + \frac{1}{2} p \frac{\partial^2 \nu(x,t)}{\partial x^2} (\Delta x)^2\\ + q \nu(x,t) - q \frac{\partial\nu(x,t) }{\partial x} \Delta x + \frac{1}{2} q \frac{\partial^2 \nu(x,t)}{\partial x^2} (\Delta x)^2 +\nu(x,t) + \frac{\partial \nu(x,t)}{\partial t} \Delta t = p \nu(x,t) - p \frac{\partial\nu(x,t) }{\partial x} \Delta x + \frac{1}{2} p \frac{\partial^2 \nu(x,t)}{\partial x^2} (\Delta x)^2\\ + q \nu(x,t) + q \frac{\partial\nu(x,t) }{\partial x} \Delta x + \frac{1}{2} q \frac{\partial^2 \nu(x,t)}{\partial x^2} (\Delta x)^2 \end{align*} \ARROW From which we get: \begin{align*}