Branches merged.

21 files changed, 229 insertions, 69 deletions

diff --git a/day1/cheatsheet2.tex b/day1/cheatsheet2.tex
index 58076f6..acffa20 100755
--- a/day1/cheatsheet2.tex
+++ b/day1/cheatsheet2.tex
@@ -29,7 +29,7 @@
 \section{Plotting Points with Lists}
 
 \begin{lstlisting}
-In []: x = [0, 1, 2, 3]
+In []: x = [0, 1, 2, 3] # Creating a list
 In []: y = [7, 11, 15, 19]
 In []: plot(x, y)
 In []: clf()
diff --git a/day1/cheatsheet3.tex b/day1/cheatsheet3.tex
index db50de3..244cb86 100755
--- a/day1/cheatsheet3.tex
+++ b/day1/cheatsheet3.tex
@@ -69,7 +69,7 @@ Drawing Pie Charts
 \begin{lstlisting}
 In []: pie(science.values(), labels=science.keys())
 \end{lstlisting}
-Numpy Arrays
+Arrays
 \begin{lstlisting}
 In []: a = array([1, 2, 3]) #Creating
 In []: b = array([4, 5, 6])
@@ -77,7 +77,7 @@ In []: a + b #Sum; Element-wise
 \end{lstlisting}
 Numpy statistical operations 
 \begin{lstlisting}
-In []: mean(math_scores)
+In []: mean(math_scores) 
 In []: median(math_scores)
 In []: std(math_scores)
 \end{lstlisting}
diff --git a/day1/cheatsheet4.tex b/day1/cheatsheet4.tex
index 68257a8..7410368 100755
--- a/day1/cheatsheet4.tex
+++ b/day1/cheatsheet4.tex
@@ -38,7 +38,7 @@ Out[]: (3, 2)
 \typ{In []: B = ones_like(C)} \\
 B would be array of ones with the same shape and type as C.\\
 \typ{In []: A = ones((3,2))} \\
-A would be new array of given shape(arguments), filled with ones.\\ 
+A would be new matrix of given shape(arguments), filled with ones.\\ 
 \typ{In []: I = identity(3)}\\
 I would be identity matrix of shape 3x3
 
diff --git a/day1/data/after-filter.png b/day1/data/after-filter.png
new file mode 100644
index 0000000..ac4d953
--- /dev/null
+++ b/day1/data/after-filter.png
diff --git a/day1/data/damp.png b/day1/data/damp.png
new file mode 100644
index 0000000..5307a5d
--- /dev/null
+++ b/day1/data/damp.png
diff --git a/day1/data/four_plot.png b/day1/data/four_plot.png
new file mode 100644
index 0000000..00a3a7a
--- /dev/null
+++ b/day1/data/four_plot.png
diff --git a/day1/data/fsolve.png b/day1/data/fsolve.png
new file mode 100644
index 0000000..0108215
--- /dev/null
+++ b/day1/data/fsolve.png
diff --git a/day1/data/image.png b/day1/data/image.png
new file mode 100644
index 0000000..e1c7e08
--- /dev/null
+++ b/day1/data/image.png
diff --git a/day1/data/pos.txt b/day1/data/location.txt
index adf92c8..adf92c8 100644
--- a/day1/data/pos.txt
+++ b/day1/data/location.txt
diff --git a/day1/data/neighbour.png b/day1/data/neighbour.png
new file mode 100755
index 0000000..1bb69a1
--- /dev/null
+++ b/day1/data/neighbour.png
diff --git a/day1/data/ode.png b/day1/data/ode.png
new file mode 100644
index 0000000..c76a483
--- /dev/null
+++ b/day1/data/ode.png
diff --git a/day1/data/points.png b/day1/data/points.png
new file mode 100644
index 0000000..210286e
--- /dev/null
+++ b/day1/data/points.png
diff --git a/day1/data/roots.png b/day1/data/roots.png
new file mode 100644
index 0000000..c13a1a4
--- /dev/null
+++ b/day1/data/roots.png
diff --git a/day1/data/smoothing.png b/day1/data/smoothing.png
new file mode 100644
index 0000000..8456e77
--- /dev/null
+++ b/day1/data/smoothing.png
diff --git a/day1/exercises.tex b/day1/exercises.tex
index da88e05..3fe435e 100644
--- a/day1/exercises.tex
+++ b/day1/exercises.tex
@@ -78,7 +78,7 @@
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {7 November, 2009\\Day 1, Session 5}
+\date[] {11 January, 2010\\Day 1, Session 5}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
@@ -111,11 +111,37 @@
 \end{frame}
 
 
-\begin{frame}
+\begin{frame}[fragile]
   \frametitle{Problem 1}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+    \includegraphics[height=2in, interpolate=true]{data/L-Tsq.png}
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+    \begin{lstlisting}
+l = []
+t = []
+for line in open('pendulum.txt'):
+    point = line.split()
+    l.append(float(point[0]))
+    t.append(float(point[1]))
+tsq = []
+for time in t:
+    tsq.append(time*time)
+plot(l, tsq, '.')
+    \end{lstlisting}
+    \end{block}
+  \end{columns}
+  \begin{block}{Problem Statement}
+    Tweak above code to plot data in file 'location.txt'.
+  \end{block}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Problem 1 cont...}
   \begin{itemize}
-  \item Open file 'pos.txt', it has X and Y Coordinate of a particle under motion
-  \item Plot X vs Y Graph.
   \item Label both the axes.
   \item What kind of motion is this?
   \item Title the graph accordingly.
@@ -123,13 +149,49 @@
   \end{itemize}
 \end{frame}
 
-\begin{frame}
+\begin{frame}[fragile]
   \frametitle{Problem 2}
-Write a Program that plots a regular n-gon(Let n = 5).
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+    \includegraphics[height=2in, interpolate=true]{data/points}
+    \column{0.45\textwidth}
+    \begin{block}{Line between two points}
+    \tiny
+    \begin{lstlisting}
+In []: x = [1, 5]
+In []: y = [1, 4]
+In []: plot(x, y)
+    \end{lstlisting}
+    \end{block}
+  \end{columns}
+  Line can be plotted using arrays of coordinates.
+  \pause
+  \begin{block}{Problem statement}
+    Write a Program that plots a regular n-gon(Let n = 5).
+  \end{block}  
 \end{frame}
 
+
 \begin{frame}[fragile]
   \frametitle{Problem 3}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+    \includegraphics[height=2in, interpolate=true]{data/damp}
+    \column{0.45\textwidth}
+    \begin{block}{Damped Oscillation}
+    \tiny
+    \begin{lstlisting}
+In []: x = linspace(0, 4*pi)
+In []: plot(x, exp(x/10)*sin(x))
+    \end{lstlisting}
+    \end{block}
+  \end{columns}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Problem 3 cont...}
 Create a sequence of images in which the damped oscillator($e^{x/10}sin(x)$) slowly evolves over time.
 \begin{columns}
 \column{0.35\textwidth}
@@ -147,17 +209,71 @@ savefig('plot'+str(i)+'.png') #i is int variable
 \end{block}
 \end{frame}
 
-\begin{frame}
+\begin{frame}[fragile]
   \frametitle{Problem 4}
-  Legendre polynomials $P_n(x)$ are defined by the following recurrence relation
+  \begin{lstlisting}
+In []: x = imread('smoothing.png')
+In []: x.shape
+Out[]: (256, 256)
+In []: imshow(x,cmap=cm.gray)
+  \end{lstlisting}
+\emphbar{Replace each pixel with mean of neighboring pixels}
+  \begin{center}
+  \includegraphics[height=1in, interpolate=true]{data/neighbour}
+  \end{center}
+\end{frame}
 
-\center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\
+\begin{frame}
+  \begin{center}
+    \includegraphics[height=3in, interpolate=true]{data/smoothing}    
+  \end{center}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Problem 4: Approach}
+  For \typ{y} being resultant image:
+  \begin{lstlisting}
+y[1, 1] = x[0, 1]/4 + x[1, 0]/4 
+          + x[2, 1]/4 + x[1, 2]/4    
+  \end{lstlisting}
+   \begin{columns}
+    \column{0.45\textwidth}
+    \hspace*{-0.5in}
+    \includegraphics[height=1.5in, interpolate=true]{data/smoothing}
+    \column{0.45\textwidth}
+    \hspace*{-0.5in}
+    \includegraphics[height=1.5in, interpolate=true]{data/after-filter}
+  \end{columns}
+   \begin{block}{Hint:}
+     Use array Slicing.
+   \end{block}
+\end{frame}
 
-with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three 
-   Legendre polynomials and plot all 6 over the interval [-1,1].
+\begin{frame}[fragile]
+  \frametitle{Solution}
+  \begin{lstlisting}
+In []: y = zeros_like(x)
+In []: y[1:-1,1:-1] = x[:-2,1:-1]/4+
+                      x[2:,1:-1]/4+
+                      x[1:-1,2:]/4+
+                      x[1:-1,:-2]/4
+In []: imshow(y,cmap=cm.gray)
+  \end{lstlisting}
 \end{frame}
+
+
 \end{document}
 
+%% \begin{frame}
+%%   \frametitle{Problem 4}
+%%   Legendre polynomials $P_n(x)$ are defined by the following recurrence relation
+
+%% \center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\
+
+%% with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three 
+%%    Legendre polynomials and plot all 6 over the interval [-1,1].
+%% \end{frame}
+
 %% \begin{frame}[fragile] 
 %% \frametitle{Problem Set 5}
 %%   \begin{columns}
diff --git a/day1/session1.tex b/day1/session1.tex
index 47051cc..48cd878 100644
--- a/day1/session1.tex
+++ b/day1/session1.tex
@@ -77,7 +77,7 @@
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {7 November, 2009\\Day 1, Session 1}
+\date[] {11 January, 2010\\Day 1, Session 1}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
@@ -125,28 +125,28 @@
 \begin{frame}
   \frametitle{Workshop Schedule: Day 1}
   \begin{description}
-	\item[Session 1] Sat 09:00--10:00
-	\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[Session 5] Sat 14:40--15:25
-        \item[Session 6] Sat 15:40--16:40
-        \item[Quiz 2] Sat 16:45--17:00
+	\item[Session 1] Mon 09:00--10:00
+	\item[Session 2] Mon 10:05--11:05
+	\item[Session 3] Mon 11:20--12:20
+	\item[Session 4] Mon 12:25--13:25
+        \item[Quiz 1] Mon 14:25--14:40
+        \item[Exercises] Mon 14:40--15:25
+        \item[Session 5] Mon 15:40--16:40
+        \item[Quiz 2] Mon 16:45--17:00
   \end{description}
 \end{frame}
 
 \begin{frame}
   \frametitle{Workshop Schedule: Day 2}
   \begin{description}
-	\item[Session 1] Sun 09:00--10:00
-	\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[Session 5] Sun 14:40--15:25
-        \item[Session 6] Sun 15:40--16:40
-        \item[Quiz 2] Sun 16:45--17:00
+	\item[Session 1] Tue 09:00--10:00
+	\item[Session 2] Tue 10:05--11:05
+	\item[Session 3] Tue 11:20--12:20
+	\item[Session 4] Tue 12:25--13:25
+        \item[Quiz 1]  Tue 14:25--14:40
+        \item[Exercises] Tue 14:40--15:25
+        \item[Session 5] Tue 15:40--16:40
+        \item[Quiz 2]  Tue 16:45--17:00
   \end{description}
 \end{frame}
 
@@ -189,7 +189,6 @@
     \item Images
       \begin{itemize}
       \item \typ{lena.png}
-      \item \typ{smoothing.gif}
       \end{itemize}
   \end{enumerate}
 \end{frame}
@@ -197,9 +196,9 @@
 \begin{frame}[fragile]
 \frametitle{Starting up \ldots}
 \begin{block}{}
-\begin{verbatim}
+\begin{lstlisting}
   $ ipython -pylab  
-\end{verbatim}
+\end{lstlisting} %$
 \end{block}
 \begin{lstlisting}     
   In []: print "Hello, World!"
@@ -448,25 +447,36 @@ In []: ylim(ymin-0.2, ymax+0.2)
 \item Annotate the origin
 \item Set axes limits to the range of x
 \end{enumerate}
+\vspace*{-0.1in}
+\begin{center}
+  \includegraphics[height=2.1in, interpolate=true]{data/four_plot}  
+\end{center}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Review Problem \ldots}
+\alert{Plotting \ldots}
 \begin{lstlisting}
 In []: x=linspace(-5*pi, 5*pi, 500)
 In []: plot(x, x, 'b')
 In []: plot(x, -x, 'b')
+In []: plot(x, sin(x), 'g', linewidth=2)
+In []: plot(x, x*sin(x), 'r', 
+            linewidth=3)
 \end{lstlisting}
 $\vdots$
 \end{frame}
 
 \begin{frame}[fragile]
 \frametitle{Review Problem \ldots}
-\begin{lstlisting}
-In []: plot(x, sin(x), 'g', linewidth=2)
-In []: plot(x, x*sin(x), 'r', 
-            linewidth=3)
-\end{lstlisting}
+\alert{Legend \& Annotation\ldots}
 \begin{lstlisting}
 In []: legend(['x', '-x', 'sin(x)', 
                'xsin(x)'])
 In []: annotate('origin', xy = (0, 0))
+\end{lstlisting}
+\alert{Setting Axes limits\ldots}
+\begin{lstlisting}
 In []: xlim(-5*pi, 5*pi)
 In []: ylim(-5*pi, 5*pi)
 \end{lstlisting}
diff --git a/day1/session2.tex b/day1/session2.tex
index 73637c9..12dbb58 100644
--- a/day1/session2.tex
+++ b/day1/session2.tex
@@ -78,7 +78,7 @@
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {7 November, 2009\\Day 1, Session 2}
+\date[] {11 January, 2010\\Day 1, Session 2}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
@@ -418,12 +418,12 @@ Out[]: ['hello', 'world']
   \end{lstlisting}
 This is what happens with \typ{line}
   \begin{lstlisting}
-In []: line = '1.2000e-01 7.4252e-01'
+In []: line = '1.20 7.42'
 
 In []: point = line.split()
 
 In []: point
-Out[]: ['1.2000e-01', '7.4252e-01']
+Out[]: ['1.20', '7.42']
   \end{lstlisting}
 \end{frame}
 
diff --git a/day1/session3.tex b/day1/session3.tex
index 3db46b3..c769fe5 100644
--- a/day1/session3.tex
+++ b/day1/session3.tex
@@ -79,7 +79,7 @@
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
 
-\date[] {7 November, 2009\\Day 1, Session 3}
+\date[] {11 January, 2010\\Day 1, Session 3}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
@@ -147,7 +147,7 @@ In []: for line in open('pendulum.txt'):
   ....     point = line.split()
   ....     l = float(point[0])
   ....     t = float(point[1])
-  ....     g = 4 * pi * pi * l / t * t
+  ....     g = 4 * pi * pi * l / (t * t)
   ....     G.append(g)
   \end{lstlisting}
 \end{frame}
@@ -166,8 +166,8 @@ total = 0
 for g in G:
     total += g
 
-g_mean = total / len(g)
-print "Mean: ", g_mean
+g_mean = total / len(G)
+print 'Mean: ', g_mean
   \end{lstlisting}
 \end{frame}
 
@@ -175,7 +175,7 @@ print "Mean: ", g_mean
   \frametitle{Mean ``g''}
   \begin{lstlisting}
 g_mean = sum(G) / len(G)
-print "Mean: ", g_mean
+print 'Mean: ', g_mean
   \end{lstlisting}
 \end{frame}
 
@@ -183,7 +183,7 @@ print "Mean: ", g_mean
   \frametitle{Mean ``g''}
   \begin{lstlisting}
 g_mean = mean(G)
-print "Mean: ", g_mean
+print 'Mean: ', g_mean
   \end{lstlisting}
   \inctime{10}
 \end{frame}
@@ -277,11 +277,11 @@ for record in open('sslc1.txt'):
 \begin{frame}[fragile]
   \frametitle{Dictionaries \ldots}
   \begin{lstlisting}
-In []: d = {"jpg" : "image file",
-      "txt" : "text file", 
-      "py" : "python code"}
+In []: d = {'jpg' : 'image file',
+      'txt' : 'text file', 
+      'py' : 'python code'}
 
-In []: d["txt"]
+In []: d['txt']
 Out[]: 'text file'
   \end{lstlisting}
 \end{frame}
@@ -289,10 +289,10 @@ Out[]: 'text file'
 \begin{frame}[fragile]
   \frametitle{Dictionaries \ldots}
   \begin{lstlisting}
-In []: "py" in d
+In []: 'py' in d
 Out[]: True
 
-In []: "cpp" in d
+In []: 'cpp' in d
 Out[]: False
   \end{lstlisting}
 \end{frame}
@@ -417,11 +417,11 @@ for record in open('sslc1.txt'):
 \begin{frame}[fragile]
   \frametitle{Obtaining statistics}
   \begin{lstlisting}
-print "Mean: ", mean(math_scores)
+print 'Mean: ', mean(math_scores)
 
-print "Median: ", median(math_scores)
+print 'Median: ', median(math_scores)
 
-print "Standard Deviation: ",
+print 'Standard Deviation: ',
               std(math_scores)
   \end{lstlisting}
   \inctime{10}
@@ -432,11 +432,11 @@ print "Standard Deviation: ",
   \begin{lstlisting}
 math_array = array(math_scores)
 
-print "Mean: ", mean(math_array)
+print 'Mean: ', mean(math_array)
 
-print "Median: ", median(math_array)
+print 'Median: ', median(math_array)
 
-print "Standard Deviation: ",
+print 'Standard Deviation: ',
               std(math_array)
   \end{lstlisting}
   \inctime{5}
diff --git a/day1/session4.tex b/day1/session4.tex
index 3cff99c..bfff165 100644
--- a/day1/session4.tex
+++ b/day1/session4.tex
@@ -79,7 +79,7 @@
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {7 November, 2009\\Day 1, Session 4}
+\date[] {11 January, 2010\\Day 1, Session 4}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
@@ -287,8 +287,6 @@ In []: a = imread('lena.png')
 In []: imshow(a)
 Out[]: <matplotlib.image.AxesImage object at 0xa0384cc>
 
-In []: a.shape 
-Out[]: (512, 512, 4)
   \end{lstlisting}
 \end{small}
   \begin{itemize}
@@ -317,6 +315,11 @@ Out[]: <matplotlib.image.AxesImage object at 0xb765c8c>
 \begin{frame}[fragile]
 \frametitle{Transpose of a Matrix}
 \begin{lstlisting}
+In []: a = array([[ 1,  1,  2, -1],
+  ...:            [ 2,  5, -1, -9],
+  ...:            [ 2,  1, -1,  3],
+  ...:            [ 1, -3,  2,  7]])
+
 In []: a.T
 Out[]:
 array([[ 1,  2,  2,  1],
@@ -485,7 +488,14 @@ Out[]: array([-1.,  8., -1.])
 \frametitle{\typ{lstsq}}
 \begin{itemize}
 \item We need to fit a line through points for the equation $T^2 = m \cdot L+c$
-\item In matrix form, the equation can be represented as $T^2 = A \cdot p$, where A is   
+\item In matrix form, the equation can be represented as $T_{sq} = A \cdot p$, where $T_{sq}$ is
+  $\begin{bmatrix}
+  T^2_1 \\
+  T^2_2 \\
+  \vdots\\
+  T^2_N \\
+  \end{bmatrix}$
+, A is   
   $\begin{bmatrix}
   L_1 & 1 \\
   L_2 & 1 \\
diff --git a/day1/session5.tex b/day1/session5.tex
index 22a274d..326e8fe 100644
--- a/day1/session5.tex
+++ b/day1/session5.tex
@@ -79,7 +79,7 @@
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {31, October 2009\\Day 1, Session 5}
+\date[] {11, January 2010\\Day 1, Session 5}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
diff --git a/day1/session6.tex b/day1/session6.tex
index 0f1523e..0f2120f 100755
--- a/day1/session6.tex
+++ b/day1/session6.tex
@@ -78,7 +78,7 @@
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {7 November, 2009\\Day 1, Session 6}
+\date[] {11 January, 2010\\Day 1, Session 6}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
@@ -150,7 +150,6 @@ Let us now look at how to solve this using \kwrd{matrices}
                       [-1, 0.5, -1]])
     In []: b = array([[1], [-2], [0]])
     In []: x = solve(A, b)
-    In []: Ax = dot(A,x)
   \end{lstlisting}
 \end{frame}
 
@@ -168,6 +167,7 @@ array([[ 1.],
 \begin{frame}[fragile]
 \frametitle{Let's check!}
 \begin{lstlisting}
+In []: Ax = dot(A,x)
 In []: Ax
 Out[]: 
 array([[  1.00000000e+00],
@@ -216,11 +216,17 @@ Use \kwrd{solve()}
 \frametitle{Scipy Methods - \typ{roots}}
 \begin{itemize}
 \item Calculates the roots of polynomials
+\item To calculate the roots of $x^2-5x+6$ 
 \end{itemize}
 \begin{lstlisting}
-  In []: coeffs = [1, 6, 13]
+  In []: coeffs = [1, -5, 6]
   In []: roots(coeffs)
+  Out[]: array([3., 2.])
 \end{lstlisting}
+\vspace*{-.2in}
+\begin{center}
+\includegraphics[height=1.6in, interpolate=true]{data/roots}    
+\end{center}
 \end{frame}
 
 \begin{frame}[fragile]
@@ -291,6 +297,9 @@ Find the root of $sin(x)+cos^2(x)$ nearest to $0$
 In []: fsolve(f, 0)
 Out[]: -0.66623943249251527
 \end{lstlisting}
+\begin{center}
+\includegraphics[height=2in, interpolate=true]{data/fsolve}    
+\end{center}
 \end{frame}
 
 %% \begin{frame}[fragile]
@@ -318,6 +327,7 @@ Out[]: -0.66623943249251527
 \item Define a function as below
 \end{itemize}
 \begin{lstlisting}
+In []: from scipy.integrate import odeint
 In []: def epid(y, t):
   ....     k, L = 0.00003, 25000
   ....     return k*y*(L-y)
@@ -338,6 +348,14 @@ In []: plot(t, y)
 \end{frame}
 
 \begin{frame}[fragile]
+\frametitle{Result}
+\begin{center}
+\includegraphics[height=2in, interpolate=true]{data/image}  
+\end{center}
+\end{frame}
+
+
+\begin{frame}[fragile]
 \frametitle{ODEs - Simple Pendulum}
 We shall use the simple ODE of a simple pendulum. 
 \begin{equation*}
@@ -392,6 +410,12 @@ In []: pend_sol = odeint(pend_int,
 \end{lstlisting}
 \end{frame}
 
+\begin{frame}[fragile]
+\frametitle{Result}
+\begin{center}
+\includegraphics[height=2in, interpolate=true]{data/ode}  
+\end{center}
+\end{frame}
 
 \begin{frame}
   \frametitle{Things we have learned}