Merged branches.

11 files changed, 286 insertions, 687 deletions

diff --git a/day1/cheatsheet1.tex b/day1/cheatsheet1.tex
index 583e098..4a71028 100644
--- a/day1/cheatsheet1.tex
+++ b/day1/cheatsheet1.tex
@@ -2,54 +2,43 @@
 \title{Interactive Plotting}
 \author{FOSSEE}
 \begin{document}
-\maketitle
-
+\date{}
+\vspace{-1in}
+\begin{center}
+\LARGE{Interactive Plotting}\\
+\large{FOSSEE}
+\end{center}
 \section{Starting up...}
+
 \begin{verbatim}
   $ ipython -pylab  
 \end{verbatim}
-Exiting Ipython
+Exiting 
 \begin{verbatim}     
-  In [1]: print "Hello, World!"
-  In [2]: ^D
-  Do you really want to exit ([y]/n)? y
+In [2]: (Ctrl-D)^D
+Do you really want to exit ([y]/n)? y
 \end{verbatim}
 Breaking out of loops
 \begin{verbatim}     
-  In [1]: while True:
-    ...:     print "Hello, World!"
-    ...:     
-  Hello, World!
-  Hello, World!^C
-\end{verbatim}
-
-\section{First Plot}
-\begin{verbatim}
-  In [2]: x=linspace(0, 2*pi, 50)
-
-  In [3]: plot(x,sin(x))
-  Out[3]: [<matplotlib.lines.Line2D object at 0xb6e5874c>]
+In [1]: while True:
+   ...:     print "Hello, World!"
+   ...:     
+Hello, World!
+Hello, World!(Ctrl-C)^C
 \end{verbatim}
 
-\section{Labeling}
+\section{Plotting}
 \begin{verbatim}
-  In [4]: xlabel('x')
-
-  In [5]: ylabel('sin(x)')
+In [1]: x = linspace(0, 2*pi, 50)
+In [2]: plot(x,sin(x))
+In [3]: xlabel('x')
+In [4]: ylabel('sin(x)')
+In [5]: legend(['x', '-x', 'sin(x)', 'xsin(x)'])
+In [6]: annotate('origin', xy=(0, 0), xytext=(0, -7),
+                 arrowprops=dict(shrink=0.05))
+In [7]: xlim(5*pi, 5*pi)
+In [8]: ylim(5*pi, 5*pi)
+In [9]: clf() #Clears the Plot area
 \end{verbatim}
-
-\section{Another example}
-\begin{verbatim}
-In [6]: clf()
-
-In [7]: y = linspace(0,10,101)
-
-In [8]: plot(y, exp(-y))
-
-In [9]: xlabel('y')
-
-In [10]: ylabel(r'$e^{-y}$')
-\end{verbatim}
-
 \end{document}
 
diff --git a/day1/data/annotate.png b/day1/data/annotate.png
index a9f9a04..368e1ef 100644
--- a/day1/data/annotate.png
+++ b/day1/data/annotate.png
diff --git a/day1/data/interpolate.png b/day1/data/interpolate.png
new file mode 100755
index 0000000..dd91788
--- /dev/null
+++ b/day1/data/interpolate.png
diff --git a/day1/data/missing_points.png b/day1/data/missing_points.png
new file mode 100755
index 0000000..ff74050
--- /dev/null
+++ b/day1/data/missing_points.png
diff --git a/day1/data/pos_vel_accel.png b/day1/data/pos_vel_accel.png
new file mode 100755
index 0000000..b495123
--- /dev/null
+++ b/day1/data/pos_vel_accel.png
diff --git a/day1/links.tex b/day1/links.tex
index 7734d47..c820d22 100644
--- a/day1/links.tex
+++ b/day1/links.tex
@@ -1,6 +1,7 @@
 \documentclass[12pt]{article}
 \title{Links and References}
-\author{Asokan Pichai\\Prabhu Ramachandran}
+\author{FOSSEE}
+\date{}
 \begin{document}
 \maketitle
 \begin{itemize}
@@ -8,7 +9,9 @@
   \item ``may be one of the thinnest programming language books on my shelf, but it's also one of the best.'' -- \emph{Slashdot, AccordianGuy, September 8, 2004}- available at \url{http://diveintopython.org/}
   \item How to Think Like a Computer Scientist: Learning with Python available at \url{http://www.openbookproject.net/thinkcs/python/english/}\\``The concepts covered here apply to all programming languages and to problem solving in general.'' -- \emph{Guido van Rossum, creator of Python}
   \item Some assorted articles related to Python \url{http://effbot.org/zone/index.htm}
+  \item Reference manual to describe the standard libraries  that are distributed with Python is available at \url{http://docs.python.org/library/} 
   \item To read more on strings refer to: \\ \url{http://docs.python.org/library/stdtypes.html#string-methods}
+  \item Some coding conventions for using Python language are available at \\ \url{http://www.python.org/dev/peps/pep-0008/}
   \item For documentation on IPython refer: \\ \url{http://ipython.scipy.org/moin/Documentation}
   \item Documentation for Numpy and Scipy is available at: \url{http://docs.scipy.org/doc/}
   \item For "recipes" or worked examples of commonly-done tasks in SciPy explore: \url{http://www.scipy.org/Cookbook/}
diff --git a/day1/session1.tex b/day1/session1.tex
index 85a8f48..fbaadc3 100644
--- a/day1/session1.tex
+++ b/day1/session1.tex
@@ -49,7 +49,7 @@
 }
 \newcounter{time}
 \setcounter{time}{0}
-\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
+\newcommand{%\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
 
 \newcommand{\typ}[1]{\lstinline{#1}}
 
@@ -77,7 +77,7 @@
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {31, October 2009\\Day 1, Session 1}
+\date[] {31 October, 2009\\Day 1, Session 1}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
@@ -106,7 +106,7 @@
 % the following command: 
 %\beamerdefaultoverlayspecification{<+->}
 
-%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
+%%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % DOCUMENT STARTS
@@ -129,10 +129,10 @@
 	\item[Session 2] Sat 10:05--11:05
 	\item[Session 3] Sat 11:20--12:20
 	\item[Session 4] Sat 12:25--13:25
-        \item[Quiz -1]   Sat 14:25--14:40
+        \item[Quiz 1] Sat 14:25--14:40
         \item[Session 5] Sat 14:40--15:40
         \item[Session 6] Sat 15:55--16:55
-        \item[Quiz -2]   Sat 17:00--17:15
+        \item[Quiz 2] Sat 17:00--17:15
   \end{description}
 \end{frame}
 
@@ -143,10 +143,10 @@
 	\item[Session 2] Sun 10:05--11:05
 	\item[Session 3] Sun 11:20--12:20
 	\item[Session 4] Sun 12:25--13:25
-        \item[Quiz -1]   Sun 14:25--14:40
+        \item[Quiz 1] Sun 14:25--14:40
         \item[Session 5] Sun 14:40--15:40
         \item[Session 6] Sun 15:55--16:55
-        \item[Quiz -2]   Sun 17:00--17:15
+        \item[Quiz 2] Sun 17:00--17:15
   \end{description}
 \end{frame}
 
@@ -161,9 +161,9 @@
 
   \begin{block}{Goal: Successful participants will be able to}
     \begin{itemize}
-      \item Use Python as plotting, computational toolkit
-      \item Understand how Python can be used as scripting and problem solving language.
-      \item Train the students to use Python for the same
+      \item Use Python as plotting, computational tool
+      \item Understand how Python can be used as a scripting and problem solving language.
+      \item Train students for the same
     \end{itemize}
   \end{block}
 \end{frame}
@@ -172,14 +172,25 @@
 \begin{frame}
 \frametitle{Checklist}
   \begin{enumerate}
-    \item IPython: Type ipython at the command line. Is it available?
+    \item IPython
     \item Editor: We recommend scite.
-    \item Data files: Make sure you have all data files.
+    \item Data files: 
+      \begin{itemize}
+      \item \typ{sslc1.txt}
+      \item \typ{pendulum.txt}
+      \item \typ{points.txt}
+      \item \typ{pos.txt}
+      \end{itemize}
+    \item Python scripts: 
+      \begin{itemize}
+      \item \typ{sslc_allreg.py}
+      \item \typ{sslc_science.py}
+      \end{itemize}
   \end{enumerate}
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Starting up...}
+\frametitle{Starting up \ldots}
 \begin{block}{}
 \begin{verbatim}
   $ ipython -pylab  
@@ -196,20 +207,20 @@ Exiting
 \end{lstlisting}
 \end{frame}
 
-\begin{frame}[fragile]
-\frametitle{Loops}
-Breaking out of loops
-\begin{lstlisting}     
-  In []: while True:
-    ...:     print "Hello, World!"
-    ...:     
-  Hello, World!
-  Hello, World!^C(Ctrl-C)
-  ------------------------------------
-  KeyboardInterrupt                   
-
-\end{lstlisting}
-\end{frame}
+%% \begin{frame}[fragile]
+%% \frametitle{Loops}
+%% Breaking out of loops
+%% \begin{lstlisting}     
+%%   In []: while True:
+%%     ...:     print "Hello, World!"
+%%     ...:     
+%%   Hello, World!
+%%   Hello, World!^C(Ctrl-C)
+%%   ------------------------------------
+%%   KeyboardInterrupt                   
+
+%% \end{lstlisting}
+%% \end{frame}
 
 \section{Plotting}
 
@@ -224,7 +235,7 @@ Breaking out of loops
     \begin{block}{}
     \begin{small}
 \begin{lstlisting}
-In []: x = linspace(0, 2*pi, 51)
+In []: x = linspace(0, 2*pi, 50)
 In []: plot(x, sin(x))
 \end{lstlisting}
     \end{small}
@@ -246,6 +257,7 @@ x[num - 1] = end
 \begin{block}{\typ{plot(x, y)}}
 plots \typ{x} and \typ{y} using default line style and color
 \end{block}
+%\inctime{10}
 \end{frame}
 
 \subsection{Decoration}
@@ -279,12 +291,11 @@ In []: ylabel('sin(x)')
   \begin{lstlisting}
 In []: clf()
 #Clears the plot area.
-In []: y = linspace(0, 2*pi, 51)
+In []: y = linspace(0, 2*pi, 50)
 In []: plot(y, sin(2*y))
 In []: xlabel('y')
 In []: ylabel('sin(2y)')
   \end{lstlisting}
-\emphbar{By default plots would be overlaid!}
 \end{frame}
 
 \subsection{More decoration}
@@ -308,11 +319,10 @@ In []: legend(['sin(2y)'])
 
 \begin{frame}[fragile]
 \frametitle{Legend Placement}
-
 \begin{block}{}
     \small
 \begin{lstlisting}
-In []: legend(['sin(2y)'], loc='center')
+In []: legend(['sin(2y)'], loc = 'center')
 \end{lstlisting}
 \end{block}
 
@@ -348,6 +358,7 @@ In []: legend(['sin(2y)'], loc=(.8,.1))
 \begin{center}
   \includegraphics[height=2in, interpolate=true]{data/loc}  
 \end{center}
+%\inctime{10}
 \end{frame}
 
 \begin{frame}[fragile]
@@ -361,8 +372,22 @@ In []: close()
 
 \section{Multiple plots}
 \begin{frame}[fragile]
+\frametitle{Overlaid Plots}
+\begin{lstlisting}
+In []: clf()
+In []: plot(y, sin(y))
+In []: plot(y, cos(y))
+In []: xlabel('y')
+In []: ylabel('f(y)')
+In []: legend(['sin(y)', 'cos(y)']) 
+\end{lstlisting}
+\emphbar{By default plots would be overlaid!}
+\end{frame}
+
+\begin{frame}[fragile]
 \frametitle{Plotting separate figures}
 \begin{lstlisting}
+In []: clf()
 In []: figure(1)
 In []: plot(y, sin(y))
 In []: figure(2)
@@ -381,23 +406,20 @@ In []: close()
 In []: plot(y, sin(y), 'g')
 
 In []: clf()
-In []: plot(y, sin(y), linewidth=2)
+In []: plot(y, sin(y), 'g', linewidth=2)
 \end{lstlisting}
 \vspace*{-0.2in}
 \begin{center}
   \includegraphics[height=2.2in, interpolate=true]{data/green}  
 \end{center}
+%\inctime{10}
 \end{frame}
 
 \begin{frame}[fragile]
 \frametitle{Annotating}
 \vspace*{-0.15in}
 \begin{lstlisting}
-In []: annotate('local max', 
-       xy=(1.5, 1), 
-       xytext=(2.5, .8),
-       arrowprops=dict(
-       shrink=0.05),)
+In []: annotate('local max', xy=(1.5, 1))
 \end{lstlisting}
 \vspace*{-0.2in}
 \begin{center}
@@ -415,7 +437,7 @@ In []: ymin, ymax = ylim()
 In []: xmax = 2*pi
 #Set the axes limits
 In []: xlim(xmin, xmax) 
-In []: ylim(ymin, ymax) 
+In []: ylim(ymin-0.2, ymax+0.2) 
   \end{lstlisting}
 \end{frame}
 
@@ -428,34 +450,29 @@ In []: ylim(ymin, ymax)
 \item Set axis limits to the range of x
 \end{enumerate}
 \begin{lstlisting}
-In []: x=linspace(-5*pi, 5*pi, 501)
+In []: x=linspace(-5*pi, 5*pi, 500)
 In []: plot(x, x, 'b')
 In []: plot(x, -x, 'b')
 \end{lstlisting}
 $\vdots$
 \end{frame}
 
-\section{Exercises}
 \begin{frame}[fragile]
 \frametitle{Review Problem \ldots}
-\small{
 \begin{lstlisting}
 In []: plot(x, sin(x), 'g', linewidth=2)
-In []: plot(x, x*sin(x), 'r', linewidth=3)
+In []: plot(x, x*sin(x), 'r', 
+            linewidth=3)
 \end{lstlisting}
-
 \begin{lstlisting}
-In []: legend(['x', '-x', 'sin(x)', 'xsin(x)'])
-In []: annotate('origin', 
-                 xy=(0, 0), 
-                 xytext=(0, -7),
-                 arrowprops=dict(
-                 shrink=0.05))
-In []: xlim(5*pi, 5*pi)
-In []: ylim(5*pi, 5*pi)
+In []: legend(['x', '-x', 'sin(x)', 
+               'xsin(x)'])
+In []: annotate('origin', xy = (0, 0))
+In []: xlim(-5*pi, 5*pi)
+In []: ylim(-5*pi, 5*pi)
 \end{lstlisting}
-}
 \end{frame}
+
 \begin{frame}
   \frametitle{What did we learn?}
   \begin{itemize}
@@ -467,6 +484,7 @@ In []: ylim(5*pi, 5*pi)
   \begin{block}{Note}
     \centerline{\alert{Don't Close \typ{IPython}}}
   \end{block}
+%%\inctime{10}
 \end{frame}
 
 \end{document}
diff --git a/day1/session2.tex b/day1/session2.tex
index 6ebd58a..41e71d7 100644
--- a/day1/session2.tex
+++ b/day1/session2.tex
@@ -265,6 +265,7 @@ Out[]: [2, 3, 4]
 \alert{\typ{list[initial:final]}}
 \end{frame}
 
+%% more on list slicing
 \begin{frame}[fragile]
 \frametitle{List operations}
 \begin{lstlisting}
diff --git a/day1/session3.tex b/day1/session3.tex
index 7019a7c..a6ed0fd 100644
--- a/day1/session3.tex
+++ b/day1/session3.tex
@@ -527,115 +527,4 @@ In []: TSq = T*T
 \end{lstlisting}
 \end{frame}
 
-\begin{frame}[fragile]
-\frametitle{Least Squares Fit}
-\vspace{-0.15in}
-\begin{figure}
-\includegraphics[width=4in]{data/L-Tsq-Line.png}
-\end{figure}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Least Squares Fit}
-\vspace{-0.15in}
-\begin{figure}
-\includegraphics[width=4in]{data/L-Tsq-points.png}
-\end{figure}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Least Squares Fit}
-\vspace{-0.15in}
-\begin{figure}
-\includegraphics[width=4in]{data/least-sq-fit.png}
-\end{figure}
-\end{frame}
-
-\begin{frame}
-\frametitle{Least Square Fit Curve}
-\begin{itemize}
-\item $T^2$ and $L$ have a linear relationship
-\item Hence, Least Square Fit Curve is a line
-\item we shall use the \typ{lstsq} function
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{\typ{lstsq}}
-\begin{itemize}
-\item We need to fit a line through points for the equation $T^2 = m \cdot L+c$
-\item The equation can be re-written as $T^2 = A \cdot p$
-\item where A is   
-  $\begin{bmatrix}
-  L_1 & 1 \\
-  L_2 & 1 \\
-  \vdots & \vdots\\
-  L_N & 1 \\
-  \end{bmatrix}$
-  and p is 
-  $\begin{bmatrix}
-  m\\
-  c\\
-  \end{bmatrix}$
-\item We need to find $p$ to plot the line
-\end{itemize}
-\end{frame}
-
-\subsection{Van der Monde matrix generation}
-\begin{frame}[fragile]
-\frametitle{Van der Monde Matrix}
-\begin{itemize}
-\item A is also called a Van der Monde matrix
-\item It can be generated using \typ{vander}
-\end{itemize}
-\begin{lstlisting}
-In []: A = vander(L, 2)
-\end{lstlisting}
-Gives the required Van der Monde matrix
-\begin{equation*}
-  \begin{bmatrix}
-    l_1 & 1 \\
-    l_2 & 1 \\
-    \vdots & \vdots\\
-    l_N & 1 \\
-  \end{bmatrix}
-\end{equation*}
-
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{\typ{lstsq} \ldots}
-\begin{itemize}
-\item Now use the \typ{lstsq} function
-\item Along with a lot of things, it returns the least squares solution
-\end{itemize}
-\begin{lstlisting}
-In []: coef, res, r, s = lstsq(A,TSq)
-\end{lstlisting}
-\end{frame}
-
-\subsection{Plotting}
-\begin{frame}[fragile]
-\frametitle{Least Square Fit Line \ldots}
-We get the points of the line from \typ{coef}
-\begin{lstlisting}
-In []: Tline = coef[0]*L + coef[1]
-\end{lstlisting}
-\begin{itemize}
-\item Now plot Tline vs. L, to get the Least squares fit line. 
-\end{itemize}
-\begin{lstlisting}
-In []: plot(L, Tline)
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{What did we learn?}
-  \begin{itemize}
-   \item Least square fit
-   \item Van der Monde matrix generation
-   \item Plotting the least square fit curve
-  \end{itemize}
-\end{frame}
-
 \end{document}
diff --git a/day1/session5.tex b/day1/session5.tex
index ac1d8b6..22a274d 100644
--- a/day1/session5.tex
+++ b/day1/session5.tex
@@ -74,7 +74,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Title page
-\title[Calculus]{Python for Science and Engg: Interpolation, Differentiation and Integration}
+\title[]{}
 
 \author[FOSSEE] {FOSSEE}
 
@@ -125,306 +125,5 @@
 %% \end{frame}
 
 
-\section{\typ{loadtxt}}
-
-\begin{frame}[fragile]
-  \frametitle{\typ{loadtxt}}
-  \begin{itemize}
-  \item Load data from a text file.
-  \item Each row must have same number of values.
-  \end{itemize}
-\begin{lstlisting}
-In []: data = loadtxt('pendulum.txt')
-In []: L = data[:,0]
-In []: T = data[:,1]
-\end{lstlisting}
-\end{frame}
-
-%% \begin{frame}[fragile]
-%%   \frametitle{\typ{loadtxt}}
-%% \end{frame}
-
-\section{Interpolation}
-\begin{frame}[fragile]
-\frametitle{Interpolation}
-\begin{itemize}
-  \item Given data file \typ{points.txt}.
-  \item It contains x,y position of particle.
-  \item Plot the given points.
-%%  \item Interpolate the missing region.
-\end{itemize}
-\emphbar{Loading data (revisited)}
-\begin{lstlisting}
-In []: data = loadtxt('points.txt')
-In []: data.shape
-Out[]: (40, 2)
-In []: x = data[:,0]
-In []: y = data[:,1]
-In []: plot(x, y, '.')
-\end{lstlisting}
-\end{frame}
-
-%% \begin{frame}[fragile]
-%% \frametitle{Interpolation \ldots}
-%% \begin{small}
-%%   \typ{In []: from scipy.interpolate import interp1d}
-%% \end{small}
-%% \begin{itemize}
-%% \item The \typ{interp1d} function returns a function
-%% \begin{lstlisting}
-%%   In []: f = interp1d(L, T)
-%% \end{lstlisting}
-%% \item Functions can be assigned to variables 
-%% \item This function interpolates between known data values to obtain unknown
-%% \end{itemize}
-%% \end{frame}
-
-%% \begin{frame}[fragile]
-%% \frametitle{Interpolation \ldots}
-%% \begin{lstlisting}
-%% In []: Ln = arange(0.1,0.99,0.005)
-%% # Interpolating! 
-%% # The new values in range of old data
-%% In []: plot(L, T, 'o', Ln, f(Ln), '-')
-%% In []: f = interp1d(L, T, kind='cubic')
-%% # When kind not specified, it's linear
-%% # Others are ...
-%% # 'nearest', 'zero', 
-%% # 'slinear', 'quadratic'
-%% \end{lstlisting}
-%% \end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Spline Interpolation}
-\begin{small}
-\begin{lstlisting}
-In []: from scipy.interpolate import splrep
-In []: from scipy.interpolate import splev
-\end{lstlisting}
-\end{small}
-\begin{itemize}
-\item Involves two steps
-  \begin{enumerate}
-  \item Find out the spline curve, coefficients
-  \item Evaluate the spline at new points
-  \end{enumerate}
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{\typ{splrep}}
-To find the spline curve
-\begin{lstlisting}
-In []: tck = splrep(x, y)
-\end{lstlisting}
-\typ{tck} contains parameters required for representing the spline curve!
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{\typ{splev}}
-To Evaluate a B-spline and it's derivatives
-\begin{lstlisting}
-In []: Xnew = arange(0.01,3,0.02)
-In []: Ynew = splev(Xnew, tck)
-
-In []: y.shape
-Out[]: (40,)
-
-In []: Ynew.shape
-Out[]: (150,)
- 
-In []: plot(Xnew, Ynew)
-\end{lstlisting}
-
-\end{frame}
-
-%% \begin{frame}[fragile]
-%% \frametitle{Interpolation \ldots}
-%% \begin{itemize}
-%% \item 
-%% \end{itemize}
-%% \end{frame}
-
-\section{Differentiation}
-
-\begin{frame}[fragile]
-\frametitle{Numerical Differentiation}
-\begin{itemize}
-\item Given function $f(x)$ or data points $y=f(x)$
-\item We wish to calculate $f^{'}(x)$ at points $x$
-\item Taylor series - finite difference approximations
-\end{itemize}
-\begin{center}
-\begin{tabular}{l l}
-$f(x+h)=f(x)+h.f^{'}(x)$ &Forward \\
-$f(x-h)=f(x)-h.f^{'}(x)$ &Backward
-\end{tabular}
-\end{center}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Forward Difference}
-\begin{lstlisting}
-In []: x = linspace(0, 2*pi, 100)
-In []: y = sin(x)
-In []: deltax = x[1] - x[0]
-\end{lstlisting}
-Obtain the finite forward difference of y
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Forward Difference \ldots}
-\begin{lstlisting}
-In []: fD = (y[1:] - y[:-1]) / deltax
-In []: plot(x, y, x[:-1], fD)
-\end{lstlisting}
-\begin{center}
-  \includegraphics[height=2in, interpolate=true]{data/fwdDiff}
-\end{center}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Example}
-\begin{itemize}
-\item Given x, y positions of a particle in \typ{pos.txt}
-\item Find velocity \& acceleration in x, y directions
-\end{itemize}
-\small{
-\begin{center}
-\begin{tabular}{| c | c | c |}
-\hline
-$X$ & $Y$ \\ \hline
-0.     &  0.\\ \hline
-0.25   &  0.47775\\ \hline
-0.5    &  0.931\\ \hline
-0.75   &  1.35975\\ \hline
-1.     &  1.764\\ \hline
-1.25   &  2.14375\\ \hline
-\vdots & \vdots\\ \hline
-\end{tabular}
-\end{center}}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Example \ldots}
-\begin{itemize}
-\item Read the file
-\item Obtain an array of x, y
-\item Obtain velocity and acceleration
-\item use \typ{deltaT = 0.05}
-\end{itemize}
-\begin{lstlisting}
-In []: X = []
-In []: Y = []
-In []: for line in open('location.txt'):
-  ....     points = line.split()
-  ....     X.append(float(points[0]))
-  ....     Y.append(float(points[1]))
-In []: S = array([X, Y])
-\end{lstlisting}
-\end{frame}
-
-
-\begin{frame}[fragile]
-\frametitle{Example \ldots}
-\begin{itemize}
-\item use \typ{deltaT = 0.05}
-\end{itemize}
-\begin{lstlisting}
-In []: deltaT = 0.05
-
-In []: v = (S[:,1:]-S[:,:-1])/deltaT
-
-In []: a = (v[:,1:]-v[:,:-1])/deltaT
-\end{lstlisting}
-Try Plotting the position, velocity \& acceleration.
-\end{frame}
-
-\section{Quadrature}
-
-\begin{frame}[fragile]
-\frametitle{Quadrature}
-\begin{itemize}
-\item We wish to find area under a curve
-\item Area under $(sin(x) + x^2)$ in $(0,1)$
-\item scipy has functions to do that
-\end{itemize}
-\begin{small}
-  \typ{In []: from scipy.integrate import quad}
-\end{small}
-\begin{itemize}
-\item Inputs - function to integrate, limits
-\end{itemize}
-\begin{lstlisting}
-In []: x = 0
-In []: quad(sin(x)+x**2, 0, 1)
-\end{lstlisting}
-\begin{small}
-\alert{\typ{error:}}
-\typ{First argument must be a callable function.}
-\end{small}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Functions - Definition}
-We have been using them all along. Now let's see how to define them.
-\begin{lstlisting}
-In []: def f(x):
-           return sin(x)+x**2
-In []: quad(f, 0, 1)
-\end{lstlisting}
-\begin{itemize}
-\item \typ{def}
-\item name
-\item arguments
-\item \typ{return}
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Functions - Calling them}
-\begin{lstlisting}
-In [15]: f()
----------------------------------------
-\end{lstlisting}
-\alert{\typ{TypeError:}}\typ{f() takes exactly 1 argument}
-\typ{(0 given)}
-\begin{lstlisting}
-In []: f(0)
-Out[]: 0.0
-In []: f(1)
-Out[]: 1.8414709848078965
-\end{lstlisting}
-More on Functions later \ldots
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Quadrature \ldots}
-\begin{lstlisting}
-In []: quad(f, 0, 1)
-\end{lstlisting}
-Returns the integral and an estimate of the absolute error in the result.
-\begin{itemize}
-\item Look at \typ{dblquad} for Double integrals
-\item Use \typ{tplquad} for Triple integrals
-\end{itemize}
-\end{frame}
-
-\begin{frame}
-  \frametitle{Things we have learned}
-  \begin{itemize}
-  \item Interpolation
-  \item Differentiation
-  \item Functions
-    \begin{itemize}
-    \item Definition
-    \item Calling
-    \item Default Arguments
-    \item Keyword Arguments
-    \end{itemize}
-  \item Quadrature
-  \end{itemize}
-\end{frame}
-
 \end{document}
 
diff --git a/day1/session6.tex b/day1/session6.tex
index 0b5f681..01b0fc9 100644..100755
--- a/day1/session6.tex
+++ b/day1/session6.tex
@@ -73,7 +73,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Title page
-\title[ODEs \& Root Finding]{Python for Science and Engg:\\ODEs \& Finding Roots}
+\title[Solving Equations \& ODEs]{Python for Science and Engg:\\Solving Equations \& ODEs}
 
 \author[FOSSEE] {FOSSEE}
 
@@ -123,219 +123,166 @@
 %%   % You might wish to add the option [pausesections]
 %% \end{frame}
 
-\section{ODEs}
+\section{Solving linear equations}
 
 \begin{frame}[fragile]
-\frametitle{ODE Integration}
-We shall use the simple ODE of a simple pendulum. 
-\begin{equation*}
-\ddot{\theta} = -\frac{g}{L}sin(\theta)
-\end{equation*}
-\begin{itemize}
-\item This equation can be written as a system of two first order ODEs
-\end{itemize}
-\begin{align}
-\dot{\theta} &= \omega \\
-\dot{\omega} &= -\frac{g}{L}sin(\theta) \\
- \text{At}\ t &= 0 : \nonumber \\
- \theta = \theta_0\quad & \&\quad  \omega = 0 \nonumber
-\end{align}
+\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 ODEs using SciPy}
-\begin{itemize}
-\item We use the \typ{odeint} function from scipy to do the integration
-\item Define a function as below
-\end{itemize}
-\begin{lstlisting}
-In []: def pend_int(unknown, t, p):
-  ....     theta, omega = unknown
-  ....     g, L = p
-  ....     f=[omega, -(g/L)*sin(theta)]
-  ....     return f
-  ....
-\end{lstlisting}
+\frametitle{Solving using Matrices}
+Let us now look at how to solve this using \kwrd{matrices}
+  \begin{lstlisting}
+    In []: A = array([[3,2,-1],
+                      [2,-2,4],                   
+                      [-1, 0.5, -1]])
+    In []: b = array([[1], [-2], [0]])
+    In []: x = solve(A, b)
+    In []: Ax = dot(A,x)
+  \end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Solving ODEs using SciPy \ldots}
-\begin{itemize}
-\item \typ{t} is the time variable \\ 
-\item \typ{p} has the constants \\
-\item \typ{initial} has the initial values
-\end{itemize}
+\frametitle{Solution:}
 \begin{lstlisting}
-In []: t = linspace(0, 10, 101)
-In []: p=(-9.81, 0.2)
-In []: initial = [10*2*pi/360, 0]
+In []: x
+Out[]: 
+array([[ 1.],
+       [-2.],
+       [-2.]])
 \end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Solving ODEs using SciPy \ldots}
-\begin{small}
-  \typ{In []: from scipy.integrate import odeint}
-\end{small}
+\frametitle{Let's check!}
 \begin{lstlisting}
-In []: pend_sol = odeint(pend_int, 
-                         initial,t, 
-                         args=(p,))
+In []: Ax
+Out[]: 
+array([[  1.00000000e+00],
+       [ -2.00000000e+00],
+       [  2.22044605e-16]])
+\end{lstlisting}
+\begin{block}{}
+The last term in the matrix is actually \alert{0}!\\
+We can use \kwrd{allclose()} to check.
+\end{block}
+\begin{lstlisting}
+In []: allclose(Ax, b)
+Out[]: True
 \end{lstlisting}
+\inctime{15}
 \end{frame}
 
-\section{Finding Roots}
+\subsection{Exercises}
 
 \begin{frame}[fragile]
-\frametitle{Roots of $f(x)=0$}
+\frametitle{Problem 1}
+Given the matrix:\\
+\begin{center}
+$\begin{bmatrix}
+-2 & 2 & 3\\
+ 2 & 1 & 6\\
+-1 &-2 & 0\\
+\end{bmatrix}$
+\end{center}
+Find:
 \begin{itemize}
-\item Roots --- values of $x$ satisfying $f(x)=0$
-\item $f(x)=0$ may have real or complex roots
-\item Presently, let's look at real roots
+  \item[i] Transpose
+  \item[ii]Inverse
+  \item[iii]Determinant
+  \item[iv] Eigenvalues and Eigen vectors
+  \item[v] Singular Value decomposition
 \end{itemize}
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Roots of $f(x)=0$}
+\frametitle{Problem 2}
+Given 
+\begin{center}
+A = 
+$\begin{bmatrix}
+-3 & 1 & 5 \\
+1 & 0 & -2 \\
+5 & -2 & 4 \\
+\end{bmatrix}$
+, B = 
+$\begin{bmatrix}
+0 & 9 & -12 \\
+-9 & 0 & 20 \\
+12 & -20 & 0 \\
+\end{bmatrix}$
+\end{center}
+Find:
 \begin{itemize}
-\item Given function $cosx-x^2$ 
-\item First we find \alert{a} root in $(-\pi/2, \pi/2)$
-\item Then we find \alert{all} roots in $(-\pi/2, \pi/2)$
+  \item[i] Sum of A and B
+  \item[ii]Elementwise Product of A and B
+  \item[iii] Matrix product of A and B
 \end{itemize}
 \end{frame}
 
-%% \begin{frame}[fragile]
-%% \frametitle{Fixed Point Method}
-%% \begin{enumerate}
-%% \item Convert $f(x)=0$ to the form $x=g(x)$
-%% \item Start with an initial value of $x$ and iterate successively
-%% \item $x_{n+1}=g(x_n)$ and $x_0$ is our initial guess
-%% \item Iterate until $x_{n+1}-x_n \le tolerance$
-%% \end{enumerate}
-%% \end{frame}
-
-%% \begin{frame}[fragile]
-%% \frametitle{Fixed Point \dots}
-%% \begin{lstlisting}
-%% In []: def our_g(x):
-%%  ....:     return sqrt(cos(x))
-%%  ....: 
-%% In []: tolerance = 1e-5
-%% In []: while abs(x1-x0)>tolerance:
-%%  ....:     x0 = x1
-%%  ....:     x1 = our_g(x1)
-%%  ....:   
-%% In []: x0
-%% \end{lstlisting}
-%% \end{frame}
-
 \begin{frame}[fragile]
-\frametitle{Bisection Method}
-\begin{enumerate}
-\item Start with the given interval $(-\pi/2, \pi/2)$ ($(a, b)$)
-\item $f(a)\cdot f(b) < 0$
-\item Bisect the interval. $c = \frac{a+b}{2}$
-\item Change the interval to $(a, c)$ if $f(a)\cdot f(c) < 0$
-\item Else, change the interval to $(c, b)$
-\item Go back to 3 until $(b-a) \le$ tolerance
-\end{enumerate}
-\alert{\typ{tolerance = 1e-5}}
+\frametitle{Solution}
+Sum: 
+$\begin{bmatrix}
+-3 & 10 & 7 \\
+-8 & 0 & 18 \\
+17 & -22 & 4 \\
+\end{bmatrix}$
+,\\ Elementwise Product:
+$\begin{bmatrix}
+0 & 9 & -60 \\
+-9 & 0 & -40 \\
+60 & 40 & 0 \\
+\end{bmatrix}$
+,\\ Matrix product:
+$\begin{bmatrix}
+51 & -127 & 56 \\
+-24 & 49 & -12 \\
+66 & -35 & -100 \\
+\end{bmatrix}$
 \end{frame}
 
-%% \begin{frame}[fragile]
-%% \frametitle{Bisection \dots}
-%% \begin{lstlisting}
-%% In []: tolerance = 1e-5
-%% In []: a = -pi/2
-%% In []: b = 0
-%% In []: while b-a > tolerance:
-%%  ....:     c = (a+b)/2
-%%  ....:     if our_f(a)*our_f(c) < 0:
-%%  ....:         b = c
-%%  ....:     else:
-%%  ....:         a = c
-%%  ....:         
-%% \end{lstlisting}
-%% \end{frame}
-
 \begin{frame}[fragile]
-\frametitle{Newton-Raphson Method}
-\begin{enumerate}
-\item Start with an initial guess of x for the root
-\item $\Delta x = -f(x)/f^{'}(x)$
-\item $ x \leftarrow x + \Delta x$
-\item Go back to 2 until $|\Delta x| \le$ tolerance
-\end{enumerate}
+\frametitle{Problem 3}
+Solve the set of equations:
+\begin{align*}
+  x + y + 2z -w & = 3\\
+  2x + 5y - z - 9w & = -3\\
+  2x + y -z + 3w & = -11 \\
+  x - 3y + 2z + 7w & = -5\\
+\end{align*}
+\inctime{10}
 \end{frame}
 
-%% \begin{frame}[fragile]
-%% \frametitle{Newton-Raphson \dots}
-%% \begin{lstlisting}
-%% In []: def our_df(x):
-%%  ....:     return -sin(x)-2*x
-%%  ....: 
-%% In []: delx = 10*tolerance
-%% In []: while delx > tolerance:
-%%  ....:     delx = -our_f(x)/our_df(x)
-%%  ....:     x = x + delx
-%%  ....:     
-%%  ....:     
-%% \end{lstlisting}
-%% \end{frame}
-
-%% \begin{frame}[fragile]
-%% \frametitle{Newton-Raphson \ldots}
-%% \begin{itemize}
-%% \item What if $f^{'}(x) = 0$?
-%% \item Can you write a better version of the Newton-Raphson?
-%% \item What if the differential is not easy to calculate?
-%% \item Look at Secant Method
-%% \end{itemize}
-%% \end{frame}
-
 \begin{frame}[fragile]
-\frametitle{Initial Estimates}
-\begin{itemize}
-\item Given an interval
-\item How to find \alert{all} the roots?
-\end{itemize}
-\begin{enumerate}
-\item Check for change of signs of $f(x)$ in the given interval
-\item A root lies in the interval where the sign change occurs
-\end{enumerate}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Initial Estimates \ldots}
-\begin{lstlisting}
-  In []: def our_f(x):
-   ....:     return cos(x)-x**2
-   ....: 
-  In []: x = linspace(-pi/2, pi/2, 11)
-\end{lstlisting}
-\begin{itemize}
-\item Get the intervals of x, where sign changes occur
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Initial Estimates \ldots}
-\begin{lstlisting}
-In []: pos = y[:-1]*y[1:] < 0
-In []: rpos = zeros(x.shape, dtype=bool)
-In []: rpos[:-1] = pos
-In []: rpos[1:] += pos
-In []: rts = x[rpos]
-\end{lstlisting}
-Now use Newton-Raphson?
+\frametitle{Solution}
+Use \kwrd{solve()}
+\begin{align*}
+  x & = -5\\
+  y & = 2\\
+  z & = 3\\
+  w & = 0\\
+\end{align*}
 \end{frame}
 
+\section{Finding Roots}
 
 \begin{frame}[fragile]
 \frametitle{Scipy Methods - \typ{roots}}
 \begin{itemize}
 \item Calculates the roots of polynomials
-\item Array of coefficients is the only parameter
 \end{itemize}
 \begin{lstlisting}
   In []: coeffs = [1, 6, 13]
@@ -360,29 +307,82 @@ Now use Newton-Raphson?
 \end{lstlisting}
 \end{frame}
 
+%% \begin{frame}[fragile]
+%% \frametitle{Scipy Methods \dots}
+%% \begin{small}
+%% \begin{lstlisting}
+%% In []: from scipy.optimize import fixed_point
+
+%% In []: from scipy.optimize import bisect
+
+%% In []: from scipy.optimize import newton
+%% \end{lstlisting}
+%% \end{small}
+%% \end{frame}
+
+\section{ODEs}
 \begin{frame}[fragile]
-\frametitle{Scipy Methods \dots}
-\begin{small}
+\frametitle{ODE Integration}
+We shall use the simple ODE of a simple pendulum. 
+\begin{equation*}
+\ddot{\theta} = -\frac{g}{L}sin(\theta)
+\end{equation*}
+\begin{itemize}
+\item This equation can be written as a system of two first order ODEs
+\end{itemize}
+\begin{align}
+\dot{\theta} &= \omega \\
+\dot{\omega} &= -\frac{g}{L}sin(\theta) \\
+ \text{At}\ t &= 0 : \nonumber \\
+ \theta = \theta_0(10^o)\quad & \&\quad  \omega = 0\ (Initial\ values)\nonumber 
+\end{align}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solving ODEs using SciPy}
+\begin{itemize}
+\item We use the \typ{odeint} function from scipy to do the integration
+\item Define a function as below
+\end{itemize}
 \begin{lstlisting}
-In []: from scipy.optimize import fixed_point
+In []: def pend_int(initial, t):
+  ....     theta, omega = initial
+  ....     g, L = -9.81, 0.2
+  ....     f=[omega, -(g/L)*sin(theta)]
+  ....     return f
+  ....
+\end{lstlisting}
+\end{frame}
 
-In []: from scipy.optimize import bisect
+\begin{frame}[fragile]
+\frametitle{Solving ODEs using SciPy \ldots}
+\begin{itemize}
+\item \typ{t} is the time variable \\ 
+\item \typ{initial} has the initial values
+\end{itemize}
+\begin{lstlisting}
+In []: t = linspace(0, 10, 101)
+In []: initial = [10*2*pi/360, 0]
+\end{lstlisting} 
+\end{frame}
 
-In []: from scipy.optimize import newton
+\begin{frame}[fragile]
+\frametitle{Solving ODEs using SciPy \ldots}
+%%\begin{small}
+\typ{In []: from scipy.integrate import odeint}
+%%\end{small}
+\begin{lstlisting}
+In []: pend_sol = odeint(pend_int, 
+                         initial,t)
 \end{lstlisting}
-\end{small}
 \end{frame}
 
+
 \begin{frame}
   \frametitle{Things we have learned}
   \begin{itemize}
   \item Solving ODEs
   \item Finding Roots
-    \begin{itemize}
-    \item Estimating Interval
-    \item Newton-Raphson
-    \item Scipy methods
-    \end{itemize}
   \end{itemize}
 \end{frame}