--- a/day1/session2.tex	Tue Oct 27 11:58:55 2009 +0530
+++ b/day1/session2.tex	Tue Oct 27 12:01:11 2009 +0530
@@ -123,6 +123,26 @@
   % You might wish to add the option [pausesections]
 \end{frame}
 
+\begin{frame}
+\frametitle{Why we didn't close the IPython??}
+\begin{itemize}
+  \item Because all the command history is lost
+  \item We can go back, edit, and re-execute our commands
+\end{itemize}
+\end{frame}
+
+\begin{frame}
+\frametitle{But its impractical..}
+\begin{itemize}
+  \item Because we can't always keep running the IPython shell for days
+  \item And lets admit it, its a pain to go back and edit
+\end{itemize}
+And the solution is..\\
+\begin{center}
+\alert {\typ{Scripts!!}}
+\end{center}
+\end{frame}
+
 \section{Creating and running scripts}
 \begin{frame}[fragile]
 \frametitle{Python Scripts}
@@ -141,29 +161,107 @@
   \begin{itemize}
     \item Open a new file in an \alert{editor}
     \item Copy and paste required lines from the output of \typ{\%hist -n}
-    \item Save the file as \typ{first_plot.py}
+    \item Save the file as \typ{sine_plot.py}
   \end{itemize}
   \begin{itemize}
-  \item run the file in IPython using \typ{\%run first_plot.py}\\
+  \item run the file in IPython using \typ{\%run sine_plot.py}\\
   \end{itemize}
 \end{frame}
 
-\section{Plotting Points}
+\begin{frame}[fragile]
+\frametitle{How often do we plot analytical functions?}
+Let us look at a small example:
+\begin{lstlisting}
+In []: x = [0, 1, 2, 3]
+
+In []: y = [7, 11, 15, 19]
+
+In []: plot(x, y)
+Out[]: [<matplotlib.lines.Line2D object at 0xa73aa8c>]
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Plotting points}
+\begin{itemize}
+\item What if we want to plot points!
+\end{itemize}
+\begin{lstlisting}
+  In []: clf()
+
+  In []: plot(L, TSq, 'o')
+  Out[]: [<matplotlib.lines.Line2D object at 0xac17e0c>]
+
+  In []: clf()
+  In []: plot(L, TSq, '.')
+  Out[]: [<matplotlib.lines.Line2D object at 0xac17e0c>]
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Additional Plotting Attributes}
+\begin{itemize}
+  \item \kwrd{'o'} - Dots
+  \item \kwrd{'.'} - Smaller Dots
+  \item \kwrd{'-'} - Lines
+  \item \kwrd{'- -'} - Dashed lines
+\end{itemize}
+\end{frame}
+
+\section{Lists}
+\begin{frame}[fragile]
+  \frametitle{How to create?}
+What are \typ{x} and \typ{y} here??\\
+\begin{center}
+\alert{\typ{lists!!}}
+\end{center}
+\begin{lstlisting}
+In []: mtlist = [] #Empty List
+
+In []: lst = [1,2,3,4,5] 
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Accessing elements of a list}
+\begin{lstlisting}
+In []: lst[0]+lst[1]+lst[-1]
+Out[]: 7
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{List: Slicing}
+\alert{\typ{list[initial:final:step]}}
+\begin{lstlisting}
+In []: lst[1:3]  # A slice.
+Out[]: [2, 3]
+
+In []: lst[1:-1]
+Out[]: [2, 3]
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{List concatenation and list methods}
+\begin{lstlisting}
+In []: anthrlst = [6,7,8,9]
+In []: lnglst = lst + anthrlst
+
+In []: lnglst
+Out[]: [1, 2, 3, 4, 5, 6, 7, 8, 9]
+
+In []: lst.append(6)
+In []: lst
+Out[]: [1, 2, 3, 4, 5, 6]
+\end{lstlisting}
+%\inctime{10}
+\end{frame}
+
+\section{Simple Pendulum}
 \begin{frame}[fragile]
 \frametitle{Simple Pendulum - L and T}
-  \begin{itemize}
-    \item Given data of Length and Time-period of a Simple pendulum 
-    \item $T^2 = \frac{4\pi^2}{g}L$\\ \alert{{$L$} and {$T^2$} vary linearly}
-    \item We wish to plot L vs. \alert{$T^2$}
-  \end{itemize}    
-\begin{lstlisting}
-In []: L = [0.1,  0.2,  0.3,  
-            0.4,  0.5,  0.6,  
-            0.7,  0.8,  0.9]
-In []: T = [0.6529, 0.8485, 1.0590, 
-            1.2390, 1.4124, 1.5061, 
-            1.6441, 1.7949, 1.8758]
-\end{lstlisting}
+Let us look at a more realistic example of the Simple Pendulum experiment.
 \end{frame}
 
 \begin{frame}[fragile]
@@ -188,33 +286,6 @@
 \end{lstlisting}
 \end{frame}
 
-\begin{frame}[fragile]
-\frametitle{Plotting points}
-\begin{itemize}
-\item But we want to plot points!
-\end{itemize}
-\begin{lstlisting}
-  In []: clf()
-
-  In []: plot(L, TSq, 'o')
-  Out[]: [<matplotlib.lines.Line2D object at 0xac17e0c>]
-
-  In []: clf()
-  In []: plot(L, TSq, '.')
-  Out[]: [<matplotlib.lines.Line2D object at 0xac17e0c>]
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Additional Plotting Attributes}
-\begin{itemize}
-  \item \kwrd{'o'} - Dots
-  \item \kwrd{'.'} - Smaller Dots
-  \item \kwrd{'-'} - Lines
-  \item \kwrd{'- -'} - Dashed lines
-\end{itemize}
-\end{frame}
-
 \begin{frame}{New Concepts}
   \begin{itemize}
     \item lists
@@ -222,41 +293,6 @@
   \end{itemize}
 \end{frame}
 
-\section{Lists}
-\begin{frame}[fragile]
-  \frametitle{How to create and use lists?}
-\begin{lstlisting}
-In []: mtlist = [] #Empty List
-
-In []: lst = [1,2,3,4] 
-
-In []: lst[0]+lst[1]+lst[-1]
-Out[]: 7
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{List: Slicing}
-list[initial:final:step]
-\begin{lstlisting}
-In []: lst[1:3]  # A slice.
-Out[]: [2, 3]
-
-In []: lst[1:-1]
-Out[]: [2, 3]
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{List methods}
-\begin{lstlisting}
-In []: lst.append(6)
-In []: lst
-Out[]: [1, 2, 3, 4, 5, 6]
-\end{lstlisting}
-%\inctime{10}
-\end{frame}
-
 \begin{frame}[fragile]
 \frametitle{\texttt{for}}
 Used to iterate over lists\\ Let us look at another example.

--- a/day1/session4.tex	Tue Oct 27 11:58:55 2009 +0530
+++ b/day1/session4.tex	Tue Oct 27 12:01:11 2009 +0530
@@ -124,6 +124,53 @@
 %  \pausesections
 \end{frame}
 
+\section{Solving linear equations}
+\begin{frame}[fragile]
+\frametitle{Solution of equations}
+Consider,
+  \begin{align*}
+    3x + 2y - z  & = 1 \\
+    2x - 2y + 4z  & = -2 \\
+    -x + \frac{1}{2}y -z & = 0
+  \end{align*}
+Solution:
+  \begin{align*}
+    x & = 1 \\
+    y & = -2 \\
+    z & = -2
+  \end{align*}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solving using Matrices}
+Let us now look at how to solve this using \kwrd{matrices}
+  \begin{lstlisting}
+    In []: A = matrix([[3,2,-1],[2,-2,4],[-1, 0.5, -1]])
+    In []: b = matrix([[1], [-2], [0]])
+    In []: x = linalg.solve(A, b)
+    In []: Ax = dot(A, x)
+    In []: allclose(Ax, b)
+    Out[]: True
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solution:}
+\begin{lstlisting}
+In []: x
+Out[]: 
+array([[ 1.],
+       [-2.],
+       [-2.]])
+
+In []: Ax
+Out[]: 
+matrix([[  1.00000000e+00],
+        [ -2.00000000e+00],
+        [  2.22044605e-16]])
+\end{lstlisting}
+\end{frame}
+
 \section{Matrices}
 \subsection{Initializing}
 \begin{frame}[fragile]
@@ -144,13 +191,15 @@
 \subsection{Basic Operations}
 \begin{frame}[fragile]
 \frametitle{Inverse of a Matrix}
+
 \begin{small}
 \begin{lstlisting}
-  In []: linalg.inv(a)
-  Out[]: 
-  matrix([[  3.15221191e+15,  -6.30442381e+15,   3.15221191e+15],
-          [ -6.30442381e+15,   1.26088476e+16,  -6.30442381e+15],
-          [  3.15221191e+15,  -6.30442381e+15,   3.15221191e+15]])
+In []: linalg.inv(A)
+Out[]: 
+matrix([[ 0.07734807,  0.01657459,  0.32044199],
+        [ 0.09944751, -0.12154696, -0.01657459],
+        [-0.02762431, -0.07734807,  0.17127072]])
+
 \end{lstlisting}
 \end{small}
 \end{frame}
@@ -176,11 +225,11 @@
 \begin{small}
 \begin{lstlisting}
   In []: linalg.eigvals(a)
-  Out[]: array([  1.61168440e+01,  -1.11684397e+00,  -1.22196337e-15])
+  Out[]: array([1.61168440e+01, -1.11684397e+00, -1.22196337e-15])
 
   In []: linalg.eig(a)
   Out[]: 
-  (array([  1.61168440e+01,  -1.11684397e+00,  -1.22196337e-15]),
+  (array([ 1.61168440e+01, -1.11684397e+00, -1.22196337e-15]),
    matrix([[-0.23197069, -0.78583024,  0.40824829],
           [-0.52532209, -0.08675134, -0.81649658],
           [-0.8186735 ,  0.61232756,  0.40824829]]))
@@ -188,28 +237,6 @@
 \end{small}
 \end{frame}
 
-\section{Solving linear equations}
-\begin{frame}[fragile]
-\frametitle{Solution of equations}
-Example problem: Consider the set of equations
-\vspace{-0.1in}
-  \begin{align*}
-    3x + 2y - z  & = 1 \\
-    2x - 2y + 4z  & = -2 \\
-    -x + \frac{1}{2}y -z & = 0
-  \end{align*}
-\vspace{-0.08in}
-  To Solve this, 
-  \begin{lstlisting}
-    In []: A = array([[3,2,-1],[2,-2,4],[-1, 0.5, -1]])
-    In []: b = array([1, -2, 0])
-    In []: x = linalg.solve(A, b)
-    In []: Ax = dot(A, x)
-    In []: allclose(Ax, b)
-    Out[]: True
-  \end{lstlisting}
-\end{frame}
-
 
 \section{Integration}