Added session 5 day 2(Exercises).

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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{split}
+  \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[] {1, November 2009\\Day 2}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%\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}{Problem 1.1}
+  The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. For example, aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.\\
+  Write a function that returns the aliquot number of a given number. 
+\end{frame}
+
+\begin{frame}{Problem 1.2}
+  A pair of numbers (a, b) is said to be \alert{amicable} if the aliquot number of a is b and the aliquot number of b is a.\\
+  Example: \texttt{220, 284}\\
+  Write a program that prints all four digit amicable pairs.
+  
+\inctime{20}
+\end{frame}
+
+%% \begin{frame}{Problem 2}
+%%   Given an empty chessboard and one Bishop placed in any s%quare, say (r, c), generate the list of all squares the Bi%shop could move to.
+
+%% \end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Problem Set 2}
+  Given a string like, ``1, 3-7, 12, 15, 18-21'', produce the list \\
+  \begin{lstlisting}
+    [1,3,4,5,6,7,12,15,18,19,20,21]
+  \end{lstlisting}
+\inctime{10}
+\end{frame}
+
+\begin{frame} 
+  \frametitle{Problem Set 3}
+  \begin{description}
+    \item[3.1] Count word frequencies in a file.
+\end{description}
+\inctime{5}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Problem set 4}
+  Finite difference
+  \begin{equation*}
+  \frac{sin(x+h)-sin(x)}{h}
+  \end{equation*}
+  \begin{lstlisting}
+  >>> x = linspace(0,2*pi,100)
+  >>> y = sin(x)
+  >>> deltax = x[1] - x[0]
+  \end{lstlisting}
+  \pause
+    \begin{enumerate}
+      \item Given this, get the finite difference of sin in the range 0 to 2*pi
+    \end{enumerate}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Problem Set 5}
+  \begin{itemize}
+      \item[5.1] Write a function that plots any regular n-gon given \typ{n}.
+      \item[5.2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for
+          $k=2.5, 3.5$ and $4$ in the same plot.
+\end{itemize}
+\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}
+
+\end{document}