diff options
| -rw-r--r-- | day2/session5.tex | 202 |
1 files changed, 202 insertions, 0 deletions
diff --git a/day2/session5.tex b/day2/session5.tex new file mode 100644 index 0000000..f3b517e --- /dev/null +++ b/day2/session5.tex @@ -0,0 +1,202 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%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} |