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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−%Tutorial slides on Python.
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−%
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−% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
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−% Copyright (c) 2005-2009, Prabhu Ramachandran
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−
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−\documentclass[14pt,compress]{beamer}
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−%\documentclass[draft]{beamer}
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−%\documentclass[compress,handout]{beamer}
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−%\usepackage{pgfpages} 
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−%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
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−
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−% Modified from: generic-ornate-15min-45min.de.tex
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−\mode<presentation>
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−{
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−  \usetheme{Warsaw}
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−  \useoutertheme{infolines}
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−  \setbeamercovered{transparent}
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−}
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−
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−\usepackage[english]{babel}
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−\usepackage[latin1]{inputenc}
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−%\usepackage{times}
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−\usepackage[T1]{fontenc}
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−
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−% Taken from Fernando's slides.
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−\usepackage{ae,aecompl}
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−\usepackage{mathpazo,courier,euler}
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−\usepackage[scaled=.95]{helvet}
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−
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−\definecolor{darkgreen}{rgb}{0,0.5,0}
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−
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−\usepackage{listings}
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−\lstset{language=Python,
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−    basicstyle=\ttfamily\bfseries,
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−    commentstyle=\color{red}\itshape,
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−  stringstyle=\color{darkgreen},
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−  showstringspaces=false,
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−  keywordstyle=\color{blue}\bfseries}
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−
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−% Macros
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−\setbeamercolor{emphbar}{bg=blue!20, fg=black}
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−\newcommand{\emphbar}[1]
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−{\begin{beamercolorbox}[rounded=true]{emphbar} 
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−      {#1}
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− \end{beamercolorbox}
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−}
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−\newcounter{time}
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−\setcounter{time}{0}
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−\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
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−
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−\newcommand{\typ}[1]{\texttt{#1}}
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−
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−\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
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−
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−%%% This is from Fernando's setup.
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−% \usepackage{color}
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−% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
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−% % Use and configure listings package for nicely formatted code
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−% \usepackage{listings}
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−% \lstset{
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−%    language=Python,
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−%    basicstyle=\small\ttfamily,
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−%    commentstyle=\ttfamily\color{blue},
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−%    stringstyle=\ttfamily\color{orange},
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−%    showstringspaces=false,
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−%    breaklines=true,
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−%    postbreak = \space\dots
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−% }
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−
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−
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−% Title page
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−\title[Exercises]{Exercises}
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−
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−\author[FOSSEE] {FOSSEE}
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−
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−\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
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−\date[] {30 April, 2010\\Day 1, Session 5}
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−
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−%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
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−%\logo{\pgfuseimage{iitmlogo}}
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−
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−
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−%% Delete this, if you do not want the table of contents to pop up at
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−%% the beginning of each subsection:
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−\AtBeginSubsection[]
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−{
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−  \begin{frame}<beamer>
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−    \frametitle{Outline}
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−    \tableofcontents[currentsection,currentsubsection]
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−  \end{frame}
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−}
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−
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−
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−% If you wish to uncover everything in a step-wise fashion, uncomment
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−% the following command: 
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−%\beamerdefaultoverlayspecification{<+->}
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−
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−%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
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−
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−% DOCUMENT STARTS
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−\begin{document}
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−
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−\begin{frame}
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−  \titlepage
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−\end{frame}
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−
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−
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−\begin{frame}[fragile]
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−  \frametitle{Problem 1}
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−  \begin{columns}
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−    \column{0.5\textwidth}
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−    \hspace*{-0.5in}
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−    \includegraphics[height=2in, interpolate=true]{data/L-Tsq.png}
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−    \column{0.45\textwidth}
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−    \begin{block}{Example code}
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−    \tiny
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−    \begin{lstlisting}
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−l = []
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−t = []
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−for line in open('pendulum.txt'):
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−    point = line.split()
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−    l.append(float(point[0]))
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−    t.append(float(point[1]))
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−plot(l, t, '.')
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−    \end{lstlisting}
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−    \end{block}
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−  \end{columns}
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−  \begin{block}{Problem Statement}
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−    Tweak above code to plot data in file `pos.txt'.
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−  \end{block}
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−\end{frame}
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−
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−\begin{frame}
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−  \frametitle{Problem 1 cont...}
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−  \begin{itemize}
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−  \item Label both the axes.
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−  \item What kind of motion is this?
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−  \item Title the graph accordingly.
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−  \item Annotate the position where vertical velocity is zero.
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−  \end{itemize}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−  \frametitle{Problem 2}
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−  \begin{columns}
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−    \column{0.5\textwidth}
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−    \hspace*{-0.5in}
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−    \includegraphics[height=2in, interpolate=true]{data/triangle}
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−    \column{0.45\textwidth}
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−    \begin{block}{Plot points given x and y coordinates}
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−    \tiny
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−    \begin{lstlisting}
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−In []: x = [3, 2, -2, 3]
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−In []: y = [1, -3, 4, 1]
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−In []: plot(x, y)
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−    \end{lstlisting}
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−    \end{block}
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−  \end{columns}
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−  Line can be plotted using arrays of coordinates.
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−  \pause
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−  \begin{block}{Problem statement}
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−    Write a Program that plots a regular n-gon(Let n = 5).
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−  \end{block}  
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−\end{frame}
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−
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−
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−\begin{frame}[fragile]
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−  \frametitle{Problem 3}
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−  \begin{columns}
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−    \column{0.5\textwidth}
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−    \hspace*{-0.5in}
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−    \includegraphics[height=2in, interpolate=true]{data/damp}
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−    \column{0.45\textwidth}
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−    \begin{block}{Damped Oscillation}
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−    \tiny
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−    \begin{lstlisting}
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−In []: x = linspace(0, 4*pi)
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−In []: plot(x, exp(x/10)*sin(x))
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−    \end{lstlisting}
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−    \end{block}
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−  \end{columns}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−  \frametitle{Problem 3 cont...}
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−Create a sequence of images in which the damped oscillator($e^{-x/10}sin(x)$) slowly evolves over time.
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−\begin{columns}
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−\column{0.35\textwidth}
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−\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot2}
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−\column{0.35\textwidth}
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−\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot4}
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−\column{0.35\textwidth}
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−\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot6}
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−\end{columns}
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−\begin{block}{Hint}
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−\small
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−  \begin{lstlisting}
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−savefig('plot'+str(i)+'.png') #i is int variable  
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−  \end{lstlisting}  
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−\end{block}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−  \frametitle{Problem 4}
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−  \begin{lstlisting}
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−In []: x = imread('smoothing.png')
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−In []: x.shape
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−Out[]: (256, 256)
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−In []: imshow(x,cmap=cm.gray)
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−  \end{lstlisting}
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−\emphbar{Replace each pixel with mean of neighboring pixels}
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−  \begin{center}
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−  \includegraphics[height=1in, interpolate=true]{data/neighbour}
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−  \end{center}
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−\end{frame}
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−
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−\begin{frame}
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−  \begin{center}
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−    \includegraphics[height=3in, interpolate=true]{data/smoothing}    
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−  \end{center}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−  \frametitle{Problem 4: Approach}
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−  For \typ{y} being resultant image:
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−  \begin{lstlisting}
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−y[1, 1] = x[0, 1]/4 + x[1, 0]/4 
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−          + x[2, 1]/4 + x[1, 2]/4    
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−  \end{lstlisting}
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−   \begin{columns}
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−    \column{0.45\textwidth}
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−    \hspace*{-0.5in}
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−    \includegraphics[height=1.5in, interpolate=true]{data/smoothing}
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−    \column{0.45\textwidth}
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−    \hspace*{-0.5in}
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−    \includegraphics[height=1.5in, interpolate=true]{data/after-filter}
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−  \end{columns}
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−   \begin{block}{Hint:}
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−     Use array Slicing.
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−   \end{block}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−  \frametitle{Solution}
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−  \begin{lstlisting}
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−In []: y = zeros_like(x)
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−In []: y[1:-1,1:-1] = x[:-2,1:-1]/4+
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−                      x[2:,1:-1]/4+
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−                      x[1:-1,2:]/4+
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−                      x[1:-1,:-2]/4
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−In []: imshow(y,cmap=cm.gray)
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−  \end{lstlisting}
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−\end{frame}
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−
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−
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−\end{document}
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−
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−%% \begin{frame}
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−%%   \frametitle{Problem 4}
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−%%   Legendre polynomials $P_n(x)$ are defined by the following recurrence relation
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−
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−%% \center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\
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−
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−%% with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three 
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−%%    Legendre polynomials and plot all 6 over the interval [-1,1].
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−%% \end{frame}
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−
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−%% \begin{frame}[fragile] 
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−%% \frametitle{Problem Set 5}
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−%%   \begin{columns}
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−%%     \column{0.6\textwidth}
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−%%     \small{
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−%%     \begin{itemize}
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−%%       \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. 
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−%%     \end{itemize}}
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−%%     \column{0.35\textwidth}
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−%%     \hspace*{-0.5in}
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−%%   \includegraphics[height=1.6in, interpolate=true]{data/cobweb}  
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−%% \end{columns}
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−%% \end{frame}
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−
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−%% \begin{frame}
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−%%   \frametitle{Problem Set 5.3}
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−%%   Plot the cobweb plot as follows:
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−%%   \begin{enumerate}
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−%%     \item Start at $(x_0, 0)$ ($\implies$ i=0)
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−%%     \item Draw a line to $(x_i, f(x_i))$
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−%%     \item Set $x_{i+1} = f(x_i)$
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−%%     \item Draw a line to $(x_{i+1}, x_{i+1})$
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−%%     \item $(i\implies i+1)$ 
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−%%     \item Repeat from 2 for as long as you want 
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−%%   \end{enumerate}
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−%% \inctime{20}
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−%% \end{frame}