diff --git a/Lectures_my/NumMet/Lecture1/mchrzasz.log b/Lectures_my/NumMet/Lecture1/mchrzasz.log
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--- a/Lectures_my/NumMet/Lecture1/mchrzasz.log
+++ b/Lectures_my/NumMet/Lecture1/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)  18 SEP 2016 15:27
+This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1)  19 SEP 2016 11:11
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diff --git a/Lectures_my/NumMet/Lecture1/mchrzasz.pdf b/Lectures_my/NumMet/Lecture1/mchrzasz.pdf
index 1834b4a..e51b221 100644
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diff --git a/Lectures_my/NumMet/Lecture1/mchrzasz.tex b/Lectures_my/NumMet/Lecture1/mchrzasz.tex
index e180cee..30536ca 100644
--- a/Lectures_my/NumMet/Lecture1/mchrzasz.tex
+++ b/Lectures_my/NumMet/Lecture1/mchrzasz.tex
@@ -299,7 +299,7 @@
 \item Linear equation solving with elimination methods and iteration methods.
 \item Non-linear system of equation solving.
 \item Numerical integration.
-\item Differential equation eq. solving.
+\item Differential equations solving.
 \item Chaos theorem.
 \end{enumerate}
 
@@ -371,7 +371,7 @@
 
 \begin{frame}\frametitle{Cut-off Errors}
 \begin{small}
-\ARROW This kind of errors erase where the true mathematical problem have some kind of infinite sum.\\
+\ARROW This kind of errors arise where the true mathematical problem have some kind of infinite sum.\\
 \ARROWR Computers are stupid creatures and they don't understand what is $\infty$ so we need to cut of computations at some point. Example:
 \begin{exampleblock}{Maclaurin series:}
 We know that an $e^x$ function can be Taylor expanded:
@@ -457,7 +457,7 @@
 \end{align*}
 \ARROW Using the definition we can write the mantissa and exponent in the following way:
 \begin{align*}
-M=(m_1N^{-1}+m_2N^{-2}+...+m_t N^t)\\
+M=(m_1N^{-1}+m_2N^{-2}+...+m_t N^{-t})\\
 C=\pm(c_1 N^0+ c_2 N^1 + c_3 N^2 + ...+c_d N^{d-1})
 \end{align*}
 \ARROW The most often know base are $2,8,10,16$.
diff --git a/Lectures_my/NumMet/Lecture2/mchrzasz.tex b/Lectures_my/NumMet/Lecture2/mchrzasz.tex
index 1859b4d..f1e8dae 100644
--- a/Lectures_my/NumMet/Lecture2/mchrzasz.tex
+++ b/Lectures_my/NumMet/Lecture2/mchrzasz.tex
@@ -477,7 +477,7 @@
 where:\\
 $\omega_n(x)=(x-x_0)(x-x_1)...(x-x_n)$\\
 $f$ function of class $C^{n+1}$ on $\left [a,b\right]$\\
-$\xi$ rzedna wartosci srednie.
+$\xi$ average values.h
 }
 \end{exampleblock}
 
@@ -602,7 +602,7 @@
 \end{align*}
 where
 \begin{align*}
-x_k(x)=a_{k,0}+a_{k,1}(x-x_k)~~x \in \left[ x_k,  x_{k+1} \right)
+s_k(x)=a_{k,0}+a_{k,1}(x-x_k)~~x \in \left[ x_k,  x_{k+1} \right)
 \end{align*}
 
 \end{small}
@@ -624,7 +624,7 @@
 \end{align*}
 
 \begin{exampleblock}{Advantage:}
-\ARROWR The biggest advantage of this method is it's simplify. If you have a large number of interpolating points that are ''dents'' packed you can get very good and fast aproximation with this function.
+\ARROWR The biggest advantage of this method is it's simplicity. If you have a large number of interpolating points that are ''densely '' packed you can get very good and fast aproximation with this function.
 \end{exampleblock}
 
 \begin{alertblock}{Disadvantage:}
@@ -663,7 +663,7 @@
 
 \begin{frame}\frametitle{Third degree spline function}
 \begin{small}
-\ARROW Now to efficiently solve the system we will define a temporary variables:
+\ARROW Now to efficiently solve the system we will define temporary variables:
 \begin{align*}
 h_k&=x_{k+1}-x_k\\
 d_k&=\frac{y_{k+1}-y_k}{h_k}\\
@@ -745,7 +745,7 @@
 \begin{small}
 
 \ARROW Interpolation playes essential role in almost all numerical methods!\\
-\ARROW Even an very old algorithms like Lagrange are still used(we used it in splines).\\
+\ARROW Even very old algorithms like Lagrange are still used(we used it in splines).\\
 \ARROW There is a lot of algorithms on the market. From simple Lagrange and Newton interpolation algorithms up to modern splines.\\
 \ARROW The most common used today are spline. They require a bit of work but they work very effectively.\\