diff --git a/Lectures_my/NumMet/2016/Lecture11/mchrzasz.tex b/Lectures_my/NumMet/2016/Lecture11/mchrzasz.tex
index 90d8dcd..ceea9f9 100644
--- a/Lectures_my/NumMet/2016/Lecture11/mchrzasz.tex
+++ b/Lectures_my/NumMet/2016/Lecture11/mchrzasz.tex
@@ -220,7 +220,7 @@
 \begin{center}
 	\begin{columns}
 		\begin{column}{0.9\textwidth}
-			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Linear equation systems: exact methods}
+			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Chaos in ODEs}
 		\end{column}
 		\begin{column}{0.2\textwidth}
 		  %\includegraphics[width=\textwidth]{SHiP-2}
@@ -242,48 +242,41 @@
 \vspace{1em}
 %		\footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\
 \vspace{0.5em}
-	\textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 10 October, 2016}
+	\textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 16 November, 2016}
 \end{center}
 \end{frame}
 }
 
 
-\begin{frame}\frametitle{Linear eq. system}
+\begin{frame}\frametitle{Classical mechanics formulation}
 
-\ARROW This and the next lecture will focus on a well known problem. Solve the following equation system:
+\ARROW This you should know by heart:\\{~}\\
+\begin{columns}
+\column{0.33\textwidth}
+\ARROW Newton:
 \begin{align*}
-A \cdot x =b,
-\end{align*} 
-\ARROWR $A = a_{ij} 	\in \mathbb{R}^{n\times n}$ and $\det(A) \neq 0$\\
-\ARROWR $b=b_i \in  \mathbb{R}^n$.\\
-\ARROW The problem: Find the $x$ vector.
+\overrightarrow{F} = \frac{d \overrightarrow{p}}{dt}
+\end{align*}
+\column{0.33\textwidth}
+\ARROW Lagrange:
+\begin{align*}
+\mathcal{L}=T-V\\
+\frac{\partial \mathcal{L} }{ \partial x} - \frac{d}{dt} \frac{\partial \mathcal{L}}{\partial \dot{x}}=0
+\end{align*}
+\column{0.33\textwidth}
+\ARROW Hamilton:
+\begin{align*}
+\mathcal{H}=T+ V\\
+\frac{d p}{d t}=-\frac{\partial \mathcal{H}}{\partial x}\\
+\frac{d x }{d t}= \frac{\partial \mathcal{H}}{\partial p}
+\end{align*}
 
+\end{columns}
 
+\ARROW Now what are advantages of each one?
 
 \end{frame}
 
-\begin{frame}\frametitle{Error digression}
-\begin{small}
-\ARROW There is enormous amount of ways to solve the linear equation system.\\
-\ARROW The choice of one over the other of them should be gathered by the {\it condition} of the matrix $A$ denoted at $cond(A)$.
-\ARROW If the $cond(A)$ is small we say that the problem is well conditioned, otherwise we say it's ill conditioned.\\
-\ARROW The {\it condition} relation is defined as:
-\begin{align*}
-cond(A) = \Vert A \Vert \cdot \Vert A^{-1} \Vert
-\end{align*}
-\ARROW Now there are many definitions of different norms... The most popular one (so-called ''column norm''):
-\begin{align*}
-\Vert A \vert_1 = \max_{1 \leq j \leq n} \sum_{i=1}^n \vert a_{i,j} \vert,
-\end{align*}
-where $n$ -is the dimension of $A$, $i,j$ are columns and rows numbers.
-
-
-
-\end{small}
-\end{frame}
-
-
-