Binary file day1/data/after-filter.png has changed

Binary file day1/data/damp.png has changed

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/day1/data/location.txt	Mon Jan 04 19:02:28 2010 +0530
@@ -0,0 +1,41 @@
+0.  0.
+0.25     0.47775
+0.5    0.931
+0.75     1.35975
+1.     1.764
+1.25     2.14375
+1.5    2.499
+1.75     2.82975
+2.     3.136
+2.25     3.41775
+2.5    3.675
+2.75     3.90775
+3.     4.116
+3.25     4.29975
+3.5    4.459
+3.75     4.59375
+4.     4.704
+4.25     4.78975
+4.5    4.851
+4.75     4.88775
+5.   4.9
+5.25     4.88775
+5.5    4.851
+5.75     4.78975
+6.     4.704
+6.25     4.59375
+6.5    4.459
+6.75     4.29975
+7.     4.116
+7.25     3.90775
+7.5    3.675
+7.75     3.41775
+8.     3.136
+8.25     2.82975
+8.5    2.499
+8.75     2.14375
+9.     1.764
+9.25     1.35975
+9.5    0.931
+9.75     0.47775
+10.   0.

Binary file day1/data/neighbour.png has changed

Binary file day1/data/points.png has changed

--- a/day1/data/pos.txt	Tue Dec 29 19:26:13 2009 +0530
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,41 +0,0 @@
-0.  0.
-0.25     0.47775
-0.5    0.931
-0.75     1.35975
-1.     1.764
-1.25     2.14375
-1.5    2.499
-1.75     2.82975
-2.     3.136
-2.25     3.41775
-2.5    3.675
-2.75     3.90775
-3.     4.116
-3.25     4.29975
-3.5    4.459
-3.75     4.59375
-4.     4.704
-4.25     4.78975
-4.5    4.851
-4.75     4.88775
-5.   4.9
-5.25     4.88775
-5.5    4.851
-5.75     4.78975
-6.     4.704
-6.25     4.59375
-6.5    4.459
-6.75     4.29975
-7.     4.116
-7.25     3.90775
-7.5    3.675
-7.75     3.41775
-8.     3.136
-8.25     2.82975
-8.5    2.499
-8.75     2.14375
-9.     1.764
-9.25     1.35975
-9.5    0.931
-9.75     0.47775
-10.   0.

Binary file day1/data/smoothing.png has changed

--- a/day1/exercises.tex	Tue Dec 29 19:26:13 2009 +0530
+++ b/day1/exercises.tex	Mon Jan 04 19:02:28 2010 +0530
@@ -78,7 +78,7 @@
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {14 December, 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}[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}
+  \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}
+  \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 @@
 \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}
+
+\begin{frame}
+  \begin{center}
+    \includegraphics[height=3in, interpolate=true]{data/smoothing}    
+  \end{center}
+\end{frame}
 
-\center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\
+\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}