Merged Madhu and Mainline branches.
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}
+