From 8db7d15742085fc03549be61489f74fe687dd7d6 Mon Sep 17 00:00:00 2001
From: Santosh G. Vattam
Date: Tue, 27 Oct 2009 17:11:52 +0530
Subject: Updated session 4 slides based on review.

---
 day1/session4.tex | 97 +++++++++++++++++++++++++++++--------------------------
 1 file changed, 52 insertions(+), 45 deletions(-)

(limited to 'day1/session4.tex')

diff --git a/day1/session4.tex b/day1/session4.tex
index 4f1eb7d..b466ca1 100644
--- a/day1/session4.tex
+++ b/day1/session4.tex
@@ -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*}
-\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.]])
+\section{Matrices}
 
-In []: Ax
-Out[]: 
-matrix([[  1.00000000e+00],
-        [ -2.00000000e+00],
-        [  2.22044605e-16]])
-\end{lstlisting}
+\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}
 
-\section{Matrices}
 \subsection{Initializing}
 \begin{frame}[fragile]
 \frametitle{Matrices: Initializing}
@@ -237,6 +197,53 @@ matrix([[ 0.07734807,  0.01657459,  0.32044199],
 \end{small}
 \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*}
+\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{Integration}
 
-- 
cgit 


From aca4e4c3cf4824edf6c3a1af2714a9a646dea682 Mon Sep 17 00:00:00 2001
From: Puneeth Chaganti
Date: Tue, 27 Oct 2009 18:31:03 +0530
Subject: Removed Integration etc from session4.

---
 day1/session4.tex | 183 +-----------------------------------------------------
 1 file changed, 1 insertion(+), 182 deletions(-)

(limited to 'day1/session4.tex')

diff --git a/day1/session4.tex b/day1/session4.tex
index b466ca1..68fe51b 100644
--- a/day1/session4.tex
+++ b/day1/session4.tex
@@ -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}
 
@@ -245,192 +245,11 @@ matrix([[  1.00000000e+00],
 \end{lstlisting}
 \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
   \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}
 
-- 
cgit 

