--- a/day1/session5.tex Sun Jan 10 22:36:09 2010 +0530
+++ b/day1/session5.tex Sun Jan 10 23:09:00 2010 +0530
@@ -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}