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+++ b/day1/exercises.tex Tue Nov 10 12:21:29 2009 +0530
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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[] {7 November, 2009\\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}
+ \frametitle{Problem 1}
+ \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.
+ \item Annotate the position where vertical velocity is zero.
+ \end{itemize}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Problem 2}
+Write a Program that plots a regular n-gon(Let n = 5).
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Problem 3}
+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}
+ \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}
+\end{document}
+
+%% \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}