Renamed day1 exercise session as session5.

--HG--
rename : day1/exercises.tex => day1/session5.tex

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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%Tutorial slides on Python.
-%
-% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
-% Copyright (c) 2005-2009, Prabhu Ramachandran
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\documentclass[14pt,compress]{beamer}
-%\documentclass[draft]{beamer}
-%\documentclass[compress,handout]{beamer}
-%\usepackage{pgfpages} 
-%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
-
-% Modified from: generic-ornate-15min-45min.de.tex
-\mode<presentation>
-{
-  \usetheme{Warsaw}
-  \useoutertheme{infolines}
-  \setbeamercovered{transparent}
-}
-
-\usepackage[english]{babel}
-\usepackage[latin1]{inputenc}
-%\usepackage{times}
-\usepackage[T1]{fontenc}
-
-% Taken from Fernando's slides.
-\usepackage{ae,aecompl}
-\usepackage{mathpazo,courier,euler}
-\usepackage[scaled=.95]{helvet}
-
-\definecolor{darkgreen}{rgb}{0,0.5,0}
-
-\usepackage{listings}
-\lstset{language=Python,
-    basicstyle=\ttfamily\bfseries,
-    commentstyle=\color{red}\itshape,
-  stringstyle=\color{darkgreen},
-  showstringspaces=false,
-  keywordstyle=\color{blue}\bfseries}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Macros
-\setbeamercolor{emphbar}{bg=blue!20, fg=black}
-\newcommand{\emphbar}[1]
-{\begin{beamercolorbox}[rounded=true]{emphbar} 
-      {#1}
- \end{beamercolorbox}
-}
-\newcounter{time}
-\setcounter{time}{0}
-\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
-
-\newcommand{\typ}[1]{\texttt{#1}}
-
-\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
-
-%%% This is from Fernando's setup.
-% \usepackage{color}
-% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
-% % Use and configure listings package for nicely formatted code
-% \usepackage{listings}
-% \lstset{
-%    language=Python,
-%    basicstyle=\small\ttfamily,
-%    commentstyle=\ttfamily\color{blue},
-%    stringstyle=\ttfamily\color{orange},
-%    showstringspaces=false,
-%    breaklines=true,
-%    postbreak = \space\dots
-% }
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Title page
-\title[Exercises]{Exercises}
-
-\author[FOSSEE] {FOSSEE}
-
-\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {11 January, 2010\\Day 1, Session 5}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
-%\logo{\pgfuseimage{iitmlogo}}
-
-
-%% Delete this, if you do not want the table of contents to pop up at
-%% the beginning of each subsection:
-\AtBeginSubsection[]
-{
-  \begin{frame}<beamer>
-    \frametitle{Outline}
-    \tableofcontents[currentsection,currentsubsection]
-  \end{frame}
-}
-
-
-% If you wish to uncover everything in a step-wise fashion, uncomment
-% the following command: 
-%\beamerdefaultoverlayspecification{<+->}
-
-%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% DOCUMENT STARTS
-\begin{document}
-
-\begin{frame}
-  \titlepage
-\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 cont...}
-  \begin{itemize}
-  \item Label both the axes.
-  \item What kind of motion is this?
-  \item Title the graph accordingly.
-  \item Annotate the position where vertical velocity is zero.
-  \end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{Problem 2}
-  \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}
-\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot2}
-\column{0.35\textwidth}
-\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot4}
-\column{0.35\textwidth}
-\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot6}
-\end{columns}
-\begin{block}{Hint}
-\small
-  \begin{lstlisting}
-savefig('plot'+str(i)+'.png') #i is int variable  
-  \end{lstlisting}  
-\end{block}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{Problem 4}
-  \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}
-
-\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}
-
-\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}
-%%     \column{0.6\textwidth}
-%%     \small{
-%%     \begin{itemize}
-%%       \item[3] Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = kx(1-x)$.  Plot the successive iterates of this process as explained below. 
-%%     \end{itemize}}
-%%     \column{0.35\textwidth}
-%%     \hspace*{-0.5in}
-%%   \includegraphics[height=1.6in, interpolate=true]{data/cobweb}  
-%% \end{columns}
-%% \end{frame}
-
-%% \begin{frame}
-%%   \frametitle{Problem Set 5.3}
-%%   Plot the cobweb plot as follows:
-%%   \begin{enumerate}
-%%     \item Start at $(x_0, 0)$ ($\implies$ i=0)
-%%     \item Draw a line to $(x_i, f(x_i))$
-%%     \item Set $x_{i+1} = f(x_i)$
-%%     \item Draw a line to $(x_{i+1}, x_{i+1})$
-%%     \item $(i\implies i+1)$ 
-%%     \item Repeat from 2 for as long as you want 
-%%   \end{enumerate}
-%% \inctime{20}
-%% \end{frame}