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| -rw-r--r-- | day1/exercises.tex | 303 | ||||
| -rw-r--r-- | day1/session5.tex | 210 |
2 files changed, 192 insertions, 321 deletions
diff --git a/day1/exercises.tex b/day1/exercises.tex deleted file mode 100644 index 3fe435e..0000000 --- a/day1/exercises.tex +++ /dev/null @@ -1,303 +0,0 @@ -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%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[] {11 January, 2010\\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}[fragile] - \frametitle{Problem 1} - \begin{columns} - \column{0.5\textwidth} - \hspace*{-0.5in} - \includegraphics[height=2in, interpolate=true]{data/L-Tsq.png} - \column{0.45\textwidth} - \begin{block}{Example code} - \tiny - \begin{lstlisting} -l = [] -t = [] -for line in open('pendulum.txt'): - point = line.split() - l.append(float(point[0])) - t.append(float(point[1])) -tsq = [] -for time in t: - tsq.append(time*time) -plot(l, tsq, '.') - \end{lstlisting} - \end{block} - \end{columns} - \begin{block}{Problem Statement} - Tweak above code to plot data in file 'location.txt'. - \end{block} -\end{frame} - -\begin{frame} - \frametitle{Problem 1 cont...} - \begin{itemize} - \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}[fragile] - \frametitle{Problem 2} - \begin{columns} - \column{0.5\textwidth} - \hspace*{-0.5in} - \includegraphics[height=2in, interpolate=true]{data/points} - \column{0.45\textwidth} - \begin{block}{Line between two points} - \tiny - \begin{lstlisting} -In []: x = [1, 5] -In []: y = [1, 4] -In []: plot(x, y) - \end{lstlisting} - \end{block} - \end{columns} - Line can be plotted using arrays of coordinates. - \pause - \begin{block}{Problem statement} - Write a Program that plots a regular n-gon(Let n = 5). - \end{block} -\end{frame} - - -\begin{frame}[fragile] - \frametitle{Problem 3} - \begin{columns} - \column{0.5\textwidth} - \hspace*{-0.5in} - \includegraphics[height=2in, interpolate=true]{data/damp} - \column{0.45\textwidth} - \begin{block}{Damped Oscillation} - \tiny - \begin{lstlisting} -In []: x = linspace(0, 4*pi) -In []: plot(x, exp(x/10)*sin(x)) - \end{lstlisting} - \end{block} - \end{columns} -\end{frame} - -\begin{frame}[fragile] - \frametitle{Problem 3 cont...} -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}[fragile] - \frametitle{Problem 4} - \begin{lstlisting} -In []: x = imread('smoothing.png') -In []: x.shape -Out[]: (256, 256) -In []: imshow(x,cmap=cm.gray) - \end{lstlisting} -\emphbar{Replace each pixel with mean of neighboring pixels} - \begin{center} - \includegraphics[height=1in, interpolate=true]{data/neighbour} - \end{center} -\end{frame} - -\begin{frame} - \begin{center} - \includegraphics[height=3in, interpolate=true]{data/smoothing} - \end{center} -\end{frame} - -\begin{frame}[fragile] - \frametitle{Problem 4: Approach} - For \typ{y} being resultant image: - \begin{lstlisting} -y[1, 1] = x[0, 1]/4 + x[1, 0]/4 - + x[2, 1]/4 + x[1, 2]/4 - \end{lstlisting} - \begin{columns} - \column{0.45\textwidth} - \hspace*{-0.5in} - \includegraphics[height=1.5in, interpolate=true]{data/smoothing} - \column{0.45\textwidth} - \hspace*{-0.5in} - \includegraphics[height=1.5in, interpolate=true]{data/after-filter} - \end{columns} - \begin{block}{Hint:} - Use array Slicing. - \end{block} -\end{frame} - -\begin{frame}[fragile] - \frametitle{Solution} - \begin{lstlisting} -In []: y = zeros_like(x) -In []: y[1:-1,1:-1] = x[:-2,1:-1]/4+ - x[2:,1:-1]/4+ - x[1:-1,2:]/4+ - x[1:-1,:-2]/4 -In []: imshow(y,cmap=cm.gray) - \end{lstlisting} -\end{frame} - - -\end{document} - -%% \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} - -%% \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} diff --git a/day1/session5.tex b/day1/session5.tex index 326e8fe..3fe435e 100644 --- a/day1/session5.tex +++ b/day1/session5.tex @@ -1,8 +1,8 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Tutorial slides on Python. % -% Author: FOSSEE -% Copyright (c) 2009, FOSSEE, IIT Bombay +% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> +% Copyright (c) 2005-2009, Prabhu Ramachandran %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[14pt,compress]{beamer} @@ -23,7 +23,6 @@ \usepackage[latin1]{inputenc} %\usepackage{times} \usepackage[T1]{fontenc} -\usepackage{amsmath} % Taken from Fernando's slides. \usepackage{ae,aecompl} @@ -52,7 +51,7 @@ \setcounter{time}{0} \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} -\newcommand{\typ}[1]{\lstinline{#1}} +\newcommand{\typ}[1]{\texttt{#1}} \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } @@ -74,12 +73,12 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Title page -\title[]{} +\title[Exercises]{Exercises} \author[FOSSEE] {FOSSEE} \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} -\date[] {11, January 2010\\Day 1, Session 5} +\date[] {11 January, 2010\\Day 1, Session 5} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} @@ -96,13 +95,6 @@ \end{frame} } -\AtBeginSection[] -{ - \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: @@ -118,12 +110,194 @@ \titlepage \end{frame} -%% \begin{frame} -%% \frametitle{Outline} -%% \tableofcontents -%% % \pausesections -%% \end{frame} + +\begin{frame}[fragile] + \frametitle{Problem 1} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/L-Tsq.png} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny + \begin{lstlisting} +l = [] +t = [] +for line in open('pendulum.txt'): + point = line.split() + l.append(float(point[0])) + t.append(float(point[1])) +tsq = [] +for time in t: + tsq.append(time*time) +plot(l, tsq, '.') + \end{lstlisting} + \end{block} + \end{columns} + \begin{block}{Problem Statement} + Tweak above code to plot data in file 'location.txt'. + \end{block} +\end{frame} + +\begin{frame} + \frametitle{Problem 1 cont...} + \begin{itemize} + \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}[fragile] + \frametitle{Problem 2} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/points} + \column{0.45\textwidth} + \begin{block}{Line between two points} + \tiny + \begin{lstlisting} +In []: x = [1, 5] +In []: y = [1, 4] +In []: plot(x, y) + \end{lstlisting} + \end{block} + \end{columns} + Line can be plotted using arrays of coordinates. + \pause + \begin{block}{Problem statement} + Write a Program that plots a regular n-gon(Let n = 5). + \end{block} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Problem 3} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/damp} + \column{0.45\textwidth} + \begin{block}{Damped Oscillation} + \tiny + \begin{lstlisting} +In []: x = linspace(0, 4*pi) +In []: plot(x, exp(x/10)*sin(x)) + \end{lstlisting} + \end{block} + \end{columns} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Problem 3 cont...} +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}[fragile] + \frametitle{Problem 4} + \begin{lstlisting} +In []: x = imread('smoothing.png') +In []: x.shape +Out[]: (256, 256) +In []: imshow(x,cmap=cm.gray) + \end{lstlisting} +\emphbar{Replace each pixel with mean of neighboring pixels} + \begin{center} + \includegraphics[height=1in, interpolate=true]{data/neighbour} + \end{center} +\end{frame} + +\begin{frame} + \begin{center} + \includegraphics[height=3in, interpolate=true]{data/smoothing} + \end{center} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Problem 4: Approach} + For \typ{y} being resultant image: + \begin{lstlisting} +y[1, 1] = x[0, 1]/4 + x[1, 0]/4 + + x[2, 1]/4 + x[1, 2]/4 + \end{lstlisting} + \begin{columns} + \column{0.45\textwidth} + \hspace*{-0.5in} + \includegraphics[height=1.5in, interpolate=true]{data/smoothing} + \column{0.45\textwidth} + \hspace*{-0.5in} + \includegraphics[height=1.5in, interpolate=true]{data/after-filter} + \end{columns} + \begin{block}{Hint:} + Use array Slicing. + \end{block} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Solution} + \begin{lstlisting} +In []: y = zeros_like(x) +In []: y[1:-1,1:-1] = x[:-2,1:-1]/4+ + x[2:,1:-1]/4+ + x[1:-1,2:]/4+ + x[1:-1,:-2]/4 +In []: imshow(y,cmap=cm.gray) + \end{lstlisting} +\end{frame} \end{document} +%% \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} + +%% \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} |