1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     2 %Tutorial slides on Python.

     3 %

     4 % Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>

     5 % Copyright (c) 2005-2009, Prabhu Ramachandran

     6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     7 

     8 \documentclass[14pt,compress]{beamer}

     9 %\documentclass[draft]{beamer}

    10 %\documentclass[compress,handout]{beamer}

    11 %\usepackage{pgfpages} 

    12 %\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]

    13 

    14 % Modified from: generic-ornate-15min-45min.de.tex

    15 \mode<presentation>

    16 {

    17   \usetheme{Warsaw}

    18   \useoutertheme{infolines}

    19   \setbeamercovered{transparent}

    20 }

    21 

    22 \usepackage[english]{babel}

    23 \usepackage[latin1]{inputenc}

    24 %\usepackage{times}

    25 \usepackage[T1]{fontenc}

    26 

    27 % Taken from Fernando's slides.

    28 \usepackage{ae,aecompl}

    29 \usepackage{mathpazo,courier,euler}

    30 \usepackage[scaled=.95]{helvet}

    31 

    32 \definecolor{darkgreen}{rgb}{0,0.5,0}

    33 

    34 \usepackage{listings}

    35 \lstset{language=Python,

    36     basicstyle=\ttfamily\bfseries,

    37     commentstyle=\color{red}\itshape,

    38   stringstyle=\color{darkgreen},

    39   showstringspaces=false,

    40   keywordstyle=\color{blue}\bfseries}

    41 

    42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    43 % Macros

    44 \setbeamercolor{emphbar}{bg=blue!20, fg=black}

    45 \newcommand{\emphbar}[1]

    46 {\begin{beamercolorbox}[rounded=true]{emphbar} 

    47       {#1}

    48  \end{beamercolorbox}

    49 }

    50 \newcounter{time}

    51 \setcounter{time}{0}

    52 \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}

    53 

    54 \newcommand{\typ}[1]{\texttt{#1}}

    55 

    56 \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }

    57 

    58 %%% This is from Fernando's setup.

    59 % \usepackage{color}

    60 % \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}

    61 % % Use and configure listings package for nicely formatted code

    62 % \usepackage{listings}

    63 % \lstset{

    64 %    language=Python,

    65 %    basicstyle=\small\ttfamily,

    66 %    commentstyle=\ttfamily\color{blue},

    67 %    stringstyle=\ttfamily\color{orange},

    68 %    showstringspaces=false,

    69 %    breaklines=true,

    70 %    postbreak = \space\dots

    71 % }

    72 

    73 

    74 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    75 % Title page

    76 \title[Exercises]{Exercises}

    77 

    78 \author[FOSSEE] {FOSSEE}

    79 

    80 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}

    81 \date[] {7 November, 2009\\Day 1, Session 5}

    82 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    83 

    84 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}

    85 %\logo{\pgfuseimage{iitmlogo}}

    86 

    87 

    88 %% Delete this, if you do not want the table of contents to pop up at

    89 %% the beginning of each subsection:

    90 \AtBeginSubsection[]

    91 {

    92   \begin{frame}<beamer>

    93     \frametitle{Outline}

    94     \tableofcontents[currentsection,currentsubsection]

    95   \end{frame}

    96 }

    97 

    98 

    99 % If you wish to uncover everything in a step-wise fashion, uncomment

   100 % the following command: 

   101 %\beamerdefaultoverlayspecification{<+->}

   102 

   103 %\includeonlyframes{current,current1,current2,current3,current4,current5,current6}

   104 

   105 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   106 % DOCUMENT STARTS

   107 \begin{document}

   108 

   109 \begin{frame}

   110   \titlepage

   111 \end{frame}

   112 

   113 

   114 \begin{frame}

   115   \frametitle{Problem 1}

   116   \begin{itemize}

   117   \item Open file 'pos.txt', it has X and Y Coordinate of a particle under motion

   118   \item Plot X vs Y Graph.

   119   \item Label both the axes.

   120   \item What kind of motion is this?

   121   \item Title the graph accordingly.

   122   \item Annotate the position where vertical velocity is zero.

   123   \end{itemize}

   124 \end{frame}

   125 

   126 \begin{frame}

   127   \frametitle{Problem 2}

   128 Write a Program that plots a regular n-gon(Let n = 5).

   129 \end{frame}

   130 

   131 \begin{frame}[fragile]

   132   \frametitle{Problem 3}

   133 Create a sequence of images in which the damped oscillator($e^{x/10}sin(x)$) slowly evolves over time.

   134 \begin{columns}

   135 \column{0.35\textwidth}

   136 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot2}

   137 \column{0.35\textwidth}

   138 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot4}

   139 \column{0.35\textwidth}

   140 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot6}

   141 \end{columns}

   142 \begin{block}{Hint}

   143 \small

   144   \begin{lstlisting}

   145 savefig('plot'+str(i)+'.png') #i is int variable  

   146   \end{lstlisting}  

   147 \end{block}

   148 \end{frame}

   149 

   150 \begin{frame}

   151   \frametitle{Problem 4}

   152   Legendre polynomials $P_n(x)$ are defined by the following recurrence relation

   153 

   154 \center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\

   155 

   156 with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three 

   157    Legendre polynomials and plot all 6 over the interval [-1,1].

   158 \end{frame}

   159 \end{document}

   160 

   161 %% \begin{frame}[fragile] 

   162 %% \frametitle{Problem Set 5}

   163 %%   \begin{columns}

   164 %%     \column{0.6\textwidth}

   165 %%     \small{

   166 %%     \begin{itemize}

   167 %%       \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. 

   168 %%     \end{itemize}}

   169 %%     \column{0.35\textwidth}

   170 %%     \hspace*{-0.5in}

   171 %%   \includegraphics[height=1.6in, interpolate=true]{data/cobweb}  

   172 %% \end{columns}

   173 %% \end{frame}

   174 

   175 %% \begin{frame}

   176 %%   \frametitle{Problem Set 5.3}

   177 %%   Plot the cobweb plot as follows:

   178 %%   \begin{enumerate}

   179 %%     \item Start at $(x_0, 0)$ ($\implies$ i=0)

   180 %%     \item Draw a line to $(x_i, f(x_i))$

   181 %%     \item Set $x_{i+1} = f(x_i)$

   182 %%     \item Draw a line to $(x_{i+1}, x_{i+1})$

   183 %%     \item $(i\implies i+1)$ 

   184 %%     \item Repeat from 2 for as long as you want 

   185 %%   \end{enumerate}

   186 %% \inctime{20}

   187 %% \end{frame}