diff --git a/.gitignore b/.gitignore
index 4df3da5..aebaece 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,3 +4,4 @@
 *.toc
 *.synctex.*
 *.fls
+*.out
diff --git a/ana3.tex b/ana3.tex
index acacc0d..42a07c1 100644
--- a/ana3.tex
+++ b/ana3.tex
@@ -1,6 +1,8 @@
 \documentclass{lecture}
 
 \begin{document}
+\newcommand{\K}{\mathrm{K}}
+\newcommand{\qnorm}[1]{\left\Vert#1\right\Vert^2}
 \section{Fourier-Entwicklung}
 \begin{definition}[Periodische Funktionen]
     $f: \R \to \K$ heißt $L$-periodisch $(L >0)$ falls $f(x+L) = f(x)$, $\forall x \in \R (\implies f(x+kL) = f(x),\; \forall k\in \Z)$.
diff --git a/analysisII.pdf b/analysisII.pdf
index ccb9af9..15a186e 100644
Binary files a/analysisII.pdf and b/analysisII.pdf differ
diff --git a/lecture.cls b/lecture.cls
index a97356c..9219ad0 100644
--- a/lecture.cls
+++ b/lecture.cls
@@ -139,7 +139,5 @@
 % remove page before chapters
 \let\cleardoublepage=\clearpage
 
-%josuas fault, ana3.tex addons
-\newcommand{\K}{\mathrm{K}}
-\newcommand{\qnorm}[1]{\left|\left|#1\right|\right|^2}
-\newcommand{\norm}[1]{\left|\left|#1\right|\right|}
\ No newline at end of file
+%josua
+\newcommand{\norm}[1]{\left\Vert#1\right|\Vert}
\ No newline at end of file