Merged Madhu and Mainline branches.
authorMadhusudan.C.S <madhusudancs@gmail.com>
Tue, 27 Oct 2009 19:25:54 +0530
changeset 205 bba40c856f68
parent 204 87f914f38ba1 (current diff)
parent 203 5c0332b97ed6 (diff)
child 207 545c7bb07e68
child 208 c663c8daa109
Merged Madhu and Mainline branches.
day1/session3.tex
Binary file day1/data/L-TSq-limited.png has changed
Binary file day1/data/stline_dots.png has changed
Binary file day1/data/stline_points.png has changed
Binary file day1/data/straightline.png has changed
--- a/day1/session2.tex	Tue Oct 27 19:25:25 2009 +0530
+++ b/day1/session2.tex	Tue Oct 27 19:25:54 2009 +0530
@@ -207,6 +207,13 @@
 \end{frame}
 
 \begin{frame}[fragile]
+\begin{figure}
+\includegraphics[width=2in]{data/stline_dots.png}
+\includegraphics[width=2in]{data/stline_points.png}
+\end{figure}
+\end{frame}
+
+\begin{frame}[fragile]
 \frametitle{Additional Plotting Attributes}
 \begin{itemize}
   \item \kwrd{'o'} - Dots
@@ -328,6 +335,12 @@
 \end{frame}
 
 \begin{frame}[fragile]
+\begin{figure}
+\includegraphics[width=3.5in]{data/L-TSq-limited.png}
+\end{figure}
+\end{frame}
+
+\begin{frame}[fragile]
 \frametitle{More of \texttt{for}}
 \begin{itemize}
 \item Used to iterate over lists
@@ -348,11 +361,11 @@
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Whats unusual about the previous example??}
+\frametitle{What about larger data sets??}
 \alert{Data is usually present in a file!} \\
 Lets look at the pendulum.txt file.
 \begin{lstlisting}
-cat data/pendulum.txt
+$cat data/pendulum.txt
 1.0000e-01 6.9004e-01
 1.1000e-01 6.9497e-01
 1.2000e-01 7.4252e-01
@@ -403,6 +416,12 @@
 \end{frame}
 
 \begin{frame}[fragile]
+\begin{figure}
+\includegraphics[width=3.5in]{data/L-Tsq.png}
+\end{figure}
+\end{frame}
+
+\begin{frame}[fragile]
   \frametitle{Reading files \ldots}
 \typ{In []: for line in open('pendulum.txt'):}
 \begin{itemize}
@@ -456,14 +475,6 @@
   \end{lstlisting}
 \end{frame}
 
-\begin{frame}[fragile]
-\begin{figure}
-\includegraphics[width=3.5in]{data/L-Tsq.png}
-\end{figure}
-\vspace{-0.2in}
-Coming up - \alert{Least Square Fit \ldots}
-\end{frame}
-
 \section {Summary}
 \begin{frame}
 \frametitle{Summary}
--- a/day1/session3.tex	Tue Oct 27 19:25:25 2009 +0530
+++ b/day1/session3.tex	Tue Oct 27 19:25:54 2009 +0530
@@ -397,6 +397,15 @@
   \includegraphics[height=3in, interpolate=true]{data/all_regions}
 \end{frame}
 
+\begin{frame}
+\frametitle{L vs $T^2$ \ldots}
+Let's go back to the L vs $T^2$ plot
+\begin{itemize}
+\item We first look at obtaining $T^2$ from T
+\item Then, we look at plotting a Least Squares fit
+\end{itemize}
+\end{frame}
+
 \begin{frame}[fragile]
   \frametitle{Obtaining statistics}
   \begin{lstlisting}
--- a/day1/session4.tex	Tue Oct 27 19:25:25 2009 +0530
+++ b/day1/session4.tex	Tue Oct 27 19:25:54 2009 +0530
@@ -74,7 +74,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Title page
-\title[Basic Python]{Matrices, Solution of equations and Integration\\}
+\title[Basic Python]{Matrices, Solution of equations}
 
 \author[FOSSEE] {FOSSEE}
 
@@ -124,54 +124,14 @@
 %  \pausesections
 \end{frame}
 
-\section{Solving linear equations}
-\begin{frame}[fragile]
-\frametitle{Solution of equations}
-Consider,
-  \begin{align*}
-    3x + 2y - z  & = 1 \\
-    2x - 2y + 4z  & = -2 \\
-    -x + \frac{1}{2}y -z & = 0
-  \end{align*}
-Solution:
-  \begin{align*}
-    x & = 1 \\
-    y & = -2 \\
-    z & = -2
-  \end{align*}
+\section{Matrices}
+
+\begin{frame}
+\frametitle{Matrices: Introduction}
+We looked at the Van der Monde matrix in the previous session,\\ 
+let us now look at matrices in a little more detail.
 \end{frame}
 
-\begin{frame}[fragile]
-\frametitle{Solving using Matrices}
-Let us now look at how to solve this using \kwrd{matrices}
-  \begin{lstlisting}
-    In []: A = matrix([[3,2,-1],[2,-2,4],[-1, 0.5, -1]])
-    In []: b = matrix([[1], [-2], [0]])
-    In []: x = linalg.solve(A, b)
-    In []: Ax = dot(A, x)
-    In []: allclose(Ax, b)
-    Out[]: True
-  \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Solution:}
-\begin{lstlisting}
-In []: x
-Out[]: 
-array([[ 1.],
-       [-2.],
-       [-2.]])
-
-In []: Ax
-Out[]: 
-matrix([[  1.00000000e+00],
-        [ -2.00000000e+00],
-        [  2.22044605e-16]])
-\end{lstlisting}
-\end{frame}
-
-\section{Matrices}
 \subsection{Initializing}
 \begin{frame}[fragile]
 \frametitle{Matrices: Initializing}
@@ -237,173 +197,51 @@
 \end{small}
 \end{frame}
 
-
-\section{Integration}
-
-\subsection{Quadrature}
-
-\begin{frame}[fragile]
-\frametitle{Quadrature}
-\begin{itemize}
-\item We wish to find area under a curve
-\item Area under $(sin(x) + x^2)$ in $(0,1)$
-\item scipy has functions to do that
-\end{itemize}
-\small{\typ{In []: from scipy.integrate import quad}}
-\begin{itemize}
-\item Inputs - function to integrate, limits
-\end{itemize}
-\begin{lstlisting}
-In []: x = 0
-In []: quad(sin(x)+x**2, 0, 1)
-\end{lstlisting}
-\alert{\typ{error:}}
-\typ{First argument must be a callable function.}
-\end{frame}
+\section{Solving linear equations}
 
 \begin{frame}[fragile]
-\frametitle{Functions - Definition}
-\begin{lstlisting}
-In []: def f(x):
-           return sin(x)+x**2
-In []: quad(f, 0, 1)
-\end{lstlisting}
-\begin{itemize}
-\item \typ{def}
-\item arguments
-\item \typ{return}
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Functions - Calling them}
-\begin{lstlisting}
-In [15]: f()
----------------------------------------
-\end{lstlisting}
-\alert{\typ{TypeError:}}\typ{f() takes exactly 1 argument}
-\typ{(0 given)}
-\begin{lstlisting}
-In []: f(0)
-Out[]: 0.0
-In []: f(1)
-Out[]: 1.8414709848078965
-\end{lstlisting}
-\end{frame}
-
-
-\begin{frame}[fragile]
-\frametitle{Functions - Default Arguments}
-\begin{lstlisting}
-In []: def f(x=1):
-           return sin(x)+x**2
-In []: f(10)
-Out[]: 99.455978889110625
-In []: f(1)
-Out[]: 1.8414709848078965
-In []: f()
-Out[]: 1.8414709848078965
-\end{lstlisting}
+\frametitle{Solution of equations}
+Consider,
+  \begin{align*}
+    3x + 2y - z  & = 1 \\
+    2x - 2y + 4z  & = -2 \\
+    -x + \frac{1}{2}y -z & = 0
+  \end{align*}
+Solution:
+  \begin{align*}
+    x & = 1 \\
+    y & = -2 \\
+    z & = -2
+  \end{align*}
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Functions - Keyword Arguments}
-\begin{lstlisting}
-In []: def f(x=1, y=pi):
-           return sin(y)+x**2
-In []: f()
-Out[]: 1.0000000000000002
-In []: f(2)
-Out[]: 4.0
-In []: f(y=2)
-Out[]: 1.9092974268256817
-In []: f(y=pi/2,x=0)
-Out[]: 1.0
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{More on functions}
-  \begin{itemize}
-  \item Scope of variables in the function is local
-  \item Mutable items are \alert{passed by reference}
-  \item First line after definition may be a documentation string
-    (\alert{recommended!})
-  \item Function definition and execution defines a name bound to the
-    function
-  \item You \emph{can} assign a variable to a function!
-  \end{itemize}
+\frametitle{Solving using Matrices}
+Let us now look at how to solve this using \kwrd{matrices}
+  \begin{lstlisting}
+    In []: A = matrix([[3,2,-1],[2,-2,4],[-1, 0.5, -1]])
+    In []: b = matrix([[1], [-2], [0]])
+    In []: x = linalg.solve(A, b)
+    In []: Ax = dot(A, x)
+    In []: allclose(Ax, b)
+    Out[]: True
+  \end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Quadrature \ldots}
+\frametitle{Solution:}
 \begin{lstlisting}
-In []: quad(f, 0, 1)
-\end{lstlisting}
-Returns the integral and an estimate of the absolute error in the result.
-\begin{itemize}
-\item Use \typ{dblquad} for Double integrals
-\item Use \typ{tplquad} for Triple integrals
-\end{itemize}
-\end{frame}
-
-\subsection{ODEs}
-
-\begin{frame}[fragile]
-\frametitle{ODE Integration}
-We shall use the simple ODE of a simple pendulum. 
-\begin{equation*}
-\ddot{\theta} = -\frac{g}{L}sin(\theta)
-\end{equation*}
-\begin{itemize}
-\item This equation can be written as a system of two first order ODEs
-\end{itemize}
-\begin{align}
-\dot{\theta} &= \omega \\
-\dot{\omega} &= -\frac{g}{L}sin(\theta) \\
- \text{At}\ t &= 0 : \nonumber \\
- \theta = \theta_0\quad & \&\quad  \omega = 0 \nonumber
-\end{align}
-\end{frame}
+In []: x
+Out[]: 
+array([[ 1.],
+       [-2.],
+       [-2.]])
 
-\begin{frame}[fragile]
-\frametitle{Solving ODEs using SciPy}
-\begin{itemize}
-\item We use the \typ{odeint} function from scipy to do the integration
-\item Define a function as below
-\end{itemize}
-\begin{lstlisting}
-In []: def pend_int(unknown, t, p):
-  ....     theta, omega = unknown
-  ....     g, L = p
-  ....     f=[omega, -(g/L)*sin(theta)]
-  ....     return f
-  ....
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Solving ODEs using SciPy \ldots}
-\begin{itemize}
-\item \typ{t} is the time variable \\ 
-\item \typ{p} has the constants \\
-\item \typ{initial} has the initial values
-\end{itemize}
-\begin{lstlisting}
-In []: t = linspace(0, 10, 101)
-In []: p=(-9.81, 0.2)
-In []: initial = [10*2*pi/360, 0]
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Solving ODEs using SciPy \ldots}
-
-\small{\typ{In []: from scipy.integrate import odeint}}
-\begin{lstlisting}
-In []: pend_sol = odeint(pend_int, 
-                         initial,t, 
-                         args=(p,))
+In []: Ax
+Out[]: 
+matrix([[  1.00000000e+00],
+        [ -2.00000000e+00],
+        [  2.22044605e-16]])
 \end{lstlisting}
 \end{frame}
 
@@ -412,18 +250,6 @@
   \begin{itemize}
   \item
   \item
-  \item Functions
-    \begin{itemize}
-    \item Definition
-    \item Calling
-    \item Default Arguments
-    \item Keyword Arguments
-    \end{itemize}
-    \item Integration
-    \begin{itemize}
-      \item Quadrature
-      \item ODEs
-    \end{itemize}
   \end{itemize}
 \end{frame}
 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/day1/session5.tex	Tue Oct 27 19:25:54 2009 +0530
@@ -0,0 +1,311 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%Tutorial slides on Python.
+%
+% Author: FOSSEE 
+% Copyright (c) 2009, FOSSEE, IIT Bombay
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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}
+\usepackage{amsmath}
+
+% 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]{\lstinline{#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[Basic Python]{Interpolation, Differentiation and Integration}
+
+\author[FOSSEE] {FOSSEE}
+
+\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
+\date[] {31, October 2009\\Day 1, Session 4}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%\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}
+}
+
+%%\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: 
+%\beamerdefaultoverlayspecification{<+->}
+
+%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% DOCUMENT STARTS
+\begin{document}
+
+\begin{frame}
+  \titlepage
+\end{frame}
+
+\begin{frame}
+  \frametitle{Outline}
+  \tableofcontents
+%  \pausesections
+\end{frame}
+
+\section{Integration}
+
+\subsection{Quadrature}
+
+\begin{frame}[fragile]
+\frametitle{Quadrature}
+\begin{itemize}
+\item We wish to find area under a curve
+\item Area under $(sin(x) + x^2)$ in $(0,1)$
+\item scipy has functions to do that
+\end{itemize}
+\small{\typ{In []: from scipy.integrate import quad}}
+\begin{itemize}
+\item Inputs - function to integrate, limits
+\end{itemize}
+\begin{lstlisting}
+In []: x = 0
+In []: quad(sin(x)+x**2, 0, 1)
+\end{lstlisting}
+\alert{\typ{error:}}
+\typ{First argument must be a callable function.}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Functions - Definition}
+\begin{lstlisting}
+In []: def f(x):
+           return sin(x)+x**2
+In []: quad(f, 0, 1)
+\end{lstlisting}
+\begin{itemize}
+\item \typ{def}
+\item arguments
+\item \typ{return}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Functions - Calling them}
+\begin{lstlisting}
+In [15]: f()
+---------------------------------------
+\end{lstlisting}
+\alert{\typ{TypeError:}}\typ{f() takes exactly 1 argument}
+\typ{(0 given)}
+\begin{lstlisting}
+In []: f(0)
+Out[]: 0.0
+In []: f(1)
+Out[]: 1.8414709848078965
+\end{lstlisting}
+\end{frame}
+
+
+\begin{frame}[fragile]
+\frametitle{Functions - Default Arguments}
+\begin{lstlisting}
+In []: def f(x=1):
+           return sin(x)+x**2
+In []: f(10)
+Out[]: 99.455978889110625
+In []: f(1)
+Out[]: 1.8414709848078965
+In []: f()
+Out[]: 1.8414709848078965
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Functions - Keyword Arguments}
+\begin{lstlisting}
+In []: def f(x=1, y=pi):
+           return sin(y)+x**2
+In []: f()
+Out[]: 1.0000000000000002
+In []: f(2)
+Out[]: 4.0
+In []: f(y=2)
+Out[]: 1.9092974268256817
+In []: f(y=pi/2,x=0)
+Out[]: 1.0
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{More on functions}
+  \begin{itemize}
+  \item Scope of variables in the function is local
+  \item Mutable items are \alert{passed by reference}
+  \item First line after definition may be a documentation string
+    (\alert{recommended!})
+  \item Function definition and execution defines a name bound to the
+    function
+  \item You \emph{can} assign a variable to a function!
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Quadrature \ldots}
+\begin{lstlisting}
+In []: quad(f, 0, 1)
+\end{lstlisting}
+Returns the integral and an estimate of the absolute error in the result.
+\begin{itemize}
+\item Use \typ{dblquad} for Double integrals
+\item Use \typ{tplquad} for Triple integrals
+\end{itemize}
+\end{frame}
+
+\subsection{ODEs}
+
+\begin{frame}[fragile]
+\frametitle{ODE Integration}
+We shall use the simple ODE of a simple pendulum. 
+\begin{equation*}
+\ddot{\theta} = -\frac{g}{L}sin(\theta)
+\end{equation*}
+\begin{itemize}
+\item This equation can be written as a system of two first order ODEs
+\end{itemize}
+\begin{align}
+\dot{\theta} &= \omega \\
+\dot{\omega} &= -\frac{g}{L}sin(\theta) \\
+ \text{At}\ t &= 0 : \nonumber \\
+ \theta = \theta_0\quad & \&\quad  \omega = 0 \nonumber
+\end{align}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solving ODEs using SciPy}
+\begin{itemize}
+\item We use the \typ{odeint} function from scipy to do the integration
+\item Define a function as below
+\end{itemize}
+\begin{lstlisting}
+In []: def pend_int(unknown, t, p):
+  ....     theta, omega = unknown
+  ....     g, L = p
+  ....     f=[omega, -(g/L)*sin(theta)]
+  ....     return f
+  ....
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solving ODEs using SciPy \ldots}
+\begin{itemize}
+\item \typ{t} is the time variable \\ 
+\item \typ{p} has the constants \\
+\item \typ{initial} has the initial values
+\end{itemize}
+\begin{lstlisting}
+In []: t = linspace(0, 10, 101)
+In []: p=(-9.81, 0.2)
+In []: initial = [10*2*pi/360, 0]
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solving ODEs using SciPy \ldots}
+
+\small{\typ{In []: from scipy.integrate import odeint}}
+\begin{lstlisting}
+In []: pend_sol = odeint(pend_int, 
+                         initial,t, 
+                         args=(p,))
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Things we have learned}
+  \begin{itemize}
+  \item Functions
+    \begin{itemize}
+    \item Definition
+    \item Calling
+    \item Default Arguments
+    \item Keyword Arguments
+    \end{itemize}
+  \item Quadrature
+  \end{itemize}
+\end{frame}
+
+\end{document}
+