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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−%Tutorial slides on Python.
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−%
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−% Author: FOSSEE 
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−% Copyright (c) 2009, FOSSEE, IIT Bombay
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−
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−\documentclass[14pt,compress]{beamer}
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−%\documentclass[draft]{beamer}
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−%\documentclass[compress,handout]{beamer}
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−%\usepackage{pgfpages} 
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−%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
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−
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−% Modified from: generic-ornate-15min-45min.de.tex
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−\mode<presentation>
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−{
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−}
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−\usepackage[english]{babel}
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−\usepackage[latin1]{inputenc}
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−%\usepackage{times}
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−\usepackage[T1]{fontenc}
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−\usepackage{amsmath}
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−
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−% Taken from Fernando's slides.
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−\usepackage{ae,aecompl}
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−\usepackage{mathpazo,courier,euler}
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−\usepackage[scaled=.95]{helvet}
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−
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−\definecolor{darkgreen}{rgb}{0,0.5,0}
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−
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−\usepackage{listings}
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−\lstset{language=Python,
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−    basicstyle=\ttfamily\bfseries,
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−
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−% Macros
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−}
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−\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
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−
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−\newcommand{\typ}[1]{\lstinline{#1}}
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−
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−\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
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−
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−%%% This is from Fernando's setup.
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−% \usepackage{color}
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−% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
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−% % Use and configure listings package for nicely formatted code
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−% \usepackage{listings}
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−% \lstset{
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−%    language=Python,
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−%    basicstyle=\small\ttfamily,
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−%    commentstyle=\ttfamily\color{blue},
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−%    stringstyle=\ttfamily\color{orange},
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−%    showstringspaces=false,
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−%    breaklines=true,
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−%    postbreak = \space\dots
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−% }
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−
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−
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−% Title page
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−\title[Basic Python]{Matrices, Solution of equations and Integration\\}
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−
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−\author[FOSSEE] {FOSSEE}
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−
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−\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
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−\date[] {31, October 2009\\Day 1, Session 4}
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−
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−%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
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−%\logo{\pgfuseimage{iitmlogo}}
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−
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−
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−%% Delete this, if you do not want the table of contents to pop up at
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−%% the beginning of each subsection:
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−\AtBeginSubsection[]
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−{
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−  \begin{frame}<beamer>
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−    \frametitle{Outline}
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−    \tableofcontents[currentsection,currentsubsection]
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−  \end{frame}
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−}
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−
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−%%\AtBeginSection[]
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−%%{
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−  %%\begin{frame}<beamer>
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−%%    \frametitle{Outline}
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−  %%  \tableofcontents[currentsection,currentsubsection]
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−  %%\end{frame}
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−%%}
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−
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−% If you wish to uncover everything in a step-wise fashion, uncomment
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−% the following command: 
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−%\beamerdefaultoverlayspecification{<+->}
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−
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−%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
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−
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−% DOCUMENT STARTS
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−\begin{document}
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−
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−\begin{frame}
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−  \titlepage
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−\end{frame}
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−
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−\begin{frame}
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−  \frametitle{Outline}
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−  \tableofcontents
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−%  \pausesections
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−\end{frame}
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−
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−\section{Matrices}
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−\subsection{Initializing}
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−\begin{frame}[fragile]
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−\frametitle{Matrices: Initializing}
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−\begin{lstlisting}
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−  In []: a = matrix([[1,2,3],
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−                     [4,5,6],
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−                     [7,8,9]])
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−
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−  In []: a
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−  Out[]: 
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−  matrix([[1, 2, 3],
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−         [4, 5, 6],
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−         [7, 8, 9]])
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−\end{lstlisting}
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−\end{frame}
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−
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−\subsection{Basic Operations}
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−\begin{frame}[fragile]
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−\frametitle{Inverse of a Matrix}
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−\begin{small}
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−\begin{lstlisting}
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−  In []: linalg.inv(a)
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−  Out[]: 
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−  matrix([[  3.15221191e+15,  -6.30442381e+15,   3.15221191e+15],
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−          [ -6.30442381e+15,   1.26088476e+16,  -6.30442381e+15],
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−          [  3.15221191e+15,  -6.30442381e+15,   3.15221191e+15]])
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−\end{lstlisting}
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−\end{small}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−\frametitle{Determinant}
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−\begin{lstlisting}
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−  In []: linalg.det(a)
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−  Out[]: -9.5171266700777579e-16
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−\end{lstlisting}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−\frametitle{Computing Norms}
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−\begin{lstlisting}
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−  In []: linalg.norm(a)
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−  Out[]: 16.881943016134134
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−\end{lstlisting}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−\frametitle{Eigen Values and Eigen Matrix}
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−\begin{small}
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−\begin{lstlisting}
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−  In []: linalg.eigvals(a)
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−  Out[]: array([  1.61168440e+01,  -1.11684397e+00,  -1.22196337e-15])
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−
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−  In []: linalg.eig(a)
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−  Out[]: 
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−  (array([  1.61168440e+01,  -1.11684397e+00,  -1.22196337e-15]),
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−   matrix([[-0.23197069, -0.78583024,  0.40824829],
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−          [-0.52532209, -0.08675134, -0.81649658],
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−          [-0.8186735 ,  0.61232756,  0.40824829]]))
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−\end{lstlisting}
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−\end{small}
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−\end{frame}
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−
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−\section{Solving linear equations}
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−\begin{frame}[fragile]
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−\frametitle{Solution of equations}
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−Example problem: Consider the set of equations
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−\vspace{-0.1in}
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−  \begin{align*}
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−    3x + 2y - z  & = 1 \\
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−    2x - 2y + 4z  & = -2 \\
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−    -x + \frac{1}{2}y -z & = 0
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−  \end{align*}
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−\vspace{-0.08in}
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−  To Solve this, 
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−  \begin{lstlisting}
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−    In []: A = array([[3,2,-1],[2,-2,4],[-1, 0.5, -1]])
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−    In []: b = array([1, -2, 0])
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−    In []: x = linalg.solve(A, b)
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−    In []: Ax = dot(A, x)
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−    In []: allclose(Ax, b)
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−    Out[]: True
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−  \end{lstlisting}
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−\end{frame}
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−
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−\section{Integration}
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−
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−\subsection{ODEs}
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−
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−\begin{frame}[fragile]
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−\frametitle{ODE Integration}
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−We shall use the simple ODE of a simple pendulum. 
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−\begin{equation*}
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−\ddot{\theta} = -\frac{g}{L}sin(\theta)
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−\end{equation*}
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−\begin{itemize}
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−\item This equation can be written as a system of two first order ODEs
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−\end{itemize}
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−\begin{align}
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−\dot{\theta} &= \omega \\
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−\dot{\omega} &= -\frac{g}{L}sin(\theta) \\
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− \text{At}\ t &= 0 : \nonumber \\
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− \theta = \theta_0\quad & \&\quad  \omega = 0 \nonumber
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−\end{align}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−\frametitle{Solving ODEs using SciPy}
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−\begin{itemize}
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−\item We use the \typ{odeint} function from scipy to do the integration
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−\item Define a function as below
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−\end{itemize}
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−\begin{lstlisting}
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−In []: def pend_int(unknown, t, p):
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−  ....     theta, omega = unknown
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−  ....     g, L = p
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−  ....     f=[omega, -(g/L)*sin(theta)]
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−  ....     return f
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−  ....
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−\end{lstlisting}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−\frametitle{Solving ODEs using SciPy \ldots}
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−\begin{itemize}
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−\item \typ{t} is the time variable \\ 
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−\item \typ{p} has the constants \\
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−\item \typ{initial} has the initial values
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−\end{itemize}
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−\begin{lstlisting}
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−In []: t = linspace(0, 10, 101)
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−In []: p=(-9.81, 0.2)
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−In []: initial = [10*2*pi/360, 0]
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−\end{lstlisting}
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−\end{frame}
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−
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−\begin{frame}[fragile]
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−\frametitle{Solving ODEs using SciPy \ldots}
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−
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−\small{\typ{In []: from scipy.integrate import odeint}}
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−\begin{lstlisting}
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−In []: pend_sol = odeint(pend_int, 
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−                         initial,t, 
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−                         args=(p,))
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−\end{lstlisting}
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−\end{frame}
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−
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−\subsection{Quadrature}
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−
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−\begin{frame}[fragile]
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−\frametitle{Quadrature}
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−Calculate the area under $(sin(x) + x^2)$ in the range $(0,1)$
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−\small{\typ{In []: from scipy.integrate import quad}}
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−  \begin{lstlisting}
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−In []: f(x):
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−        return sin(x)+x**2
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−In []: integrate.quad(f, 0, 1)
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−  \end{lstlisting}
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−\end{frame}
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−
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−\end{document}
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−