Added another ODE example to session6.

4 files changed, 73 insertions, 117 deletions

diff --git a/day1/session1.tex b/day1/session1.tex
index c4d33e5..125f823 100644
--- a/day1/session1.tex
+++ b/day1/session1.tex
@@ -488,6 +488,14 @@ Save commands of review problem into file
 \end{frame}
 
 \begin{frame}
+\frametitle{Python Scripts\ldots}
+ This is called a Python Script.
+ \begin{itemize}
+ \item run the script in IPython using \typ{\%run -i sine_plot.py}\\
+ \end{itemize}
+\end{frame}
+
+\begin{frame}
   \frametitle{What did we learn?}
   \begin{itemize}
     \item Creating simple plots.
diff --git a/day1/session2.tex b/day1/session2.tex
index 361b9b3..6df6649 100644
--- a/day1/session2.tex
+++ b/day1/session2.tex
@@ -123,28 +123,7 @@
   % You might wish to add the option [pausesections]
 \end{frame}
 
-%\begin{frame}
-%\frametitle{Python Scripts\ldots}
-%  \begin{itemize}
-%    \item Open a new file in an \alert{editor}
-%    \item Copy and paste from the output of \typ{\%hist -n}
-%    \item Save the file as \typ{sine_plot.py}
-%  \end{itemize}
-%  \begin{itemize}
-%  \item run the file in IPython using \typ{\%run -i sine_plot.py}\\
-%  \end{itemize}
-%\end{frame}
-
-\section{Scripts}
-
-\begin{frame}[fragile]
-\frametitle{Python Scripts}
-  \begin{itemize}
-  \item four\_plot.py is called a Python Script
-  \item run the file in IPython using \typ{\%run -i four_plot.py}
-  \end{itemize}
-\end{frame}
-
+\section{Plotting Points}
 \begin{frame}[fragile]
 \frametitle{Why would I plot f(x)?}
 How often do we plot analytical functions?\\We plot experimental data more.
@@ -483,8 +462,6 @@ plot(l, tsq, '.')
 \begin{frame}[fragile]
 \frametitle{What did we learn?}
 \begin{itemize}
-  \item Python scripts
-  \item \kwrd{\%run -i}
   \item Plotting points
   \item Plot attributes
   \item Lists
diff --git a/day1/session4.tex b/day1/session4.tex
index fd8a088..79da193 100644
--- a/day1/session4.tex
+++ b/day1/session4.tex
@@ -148,6 +148,29 @@ array([[ 1,  1,  2, -1],
 \end{frame}
 
 \begin{frame}[fragile]
+\frametitle{Initializing some special matrices}
+\begin{small}
+  \begin{lstlisting}
+In []: ones((3,5))
+Out[]: 
+array([[ 1.,  1.,  1.,  1.,  1.],
+       [ 1.,  1.,  1.,  1.,  1.],
+       [ 1.,  1.,  1.,  1.,  1.]])
+
+In []: ones_like([1, 2, 3, 4, 5]) 
+Out[]: array([1, 1, 1, 1, 1])   
+
+In []: identity(2)
+Out[]: 
+array([[ 1.,  0.],
+       [ 0.,  1.]])
+  \end{lstlisting}
+Also available \alert{\typ{zeros, zeros_like, empty, empty_like}}
+\end{small}
+\end{frame}
+
+
+\begin{frame}[fragile]
   \frametitle{Accessing elements}
   \begin{lstlisting}
 In []: C = array([[1,1,2],
@@ -426,7 +449,7 @@ Out[]: array([-1.,  8., -1.])
 
 \section{Least Squares Fit}
 \begin{frame}[fragile]
-\frametitle{$L$ vs. $T^2$}
+\frametitle{$L$ vs. $T^2$ - Scatter}
 \vspace{-0.15in}
 \begin{figure}
 \includegraphics[width=4in]{data/L-Tsq-points}
@@ -434,7 +457,7 @@ Out[]: array([-1.,  8., -1.])
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{$L$ vs. $T^2$}
+\frametitle{$L$ vs. $T^2$ - Line}
 \vspace{-0.15in}
 \begin{figure}
 \includegraphics[width=4in]{data/L-Tsq-Line}
@@ -442,7 +465,8 @@ Out[]: array([-1.,  8., -1.])
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Least Squares Fit}
+\frametitle{$L$ vs. $T^2$ }
+\frametitle{$L$ vs. $T^2$ - Least Square Fit}
 \vspace{-0.15in}
 \begin{figure}
 \includegraphics[width=4in]{data/least-sq-fit}
@@ -484,22 +508,6 @@ Out[]: array([-1.,  8., -1.])
 In []: A = array([L, ones_like(L)])
 In []: A = A.T
 \end{lstlisting}
-\begin{small}
-\begin{block}{}
-  \begin{lstlisting}
-In []: ones((3,5))
-Out[]: 
-array([[ 1.,  1.,  1.,  1.,  1.],
-       [ 1.,  1.,  1.,  1.,  1.],
-       [ 1.,  1.,  1.,  1.,  1.]])
-
-In []: ones_like([1, 2, 3, 4, 5]) 
-Out[]: array([1, 1, 1, 1, 1])   
-  \end{lstlisting}
-Also available \alert{\typ{zeros, zeros_like, empty, empty_like}}
-\end{block}
-\end{small}
-
 %% \begin{itemize}
 %% \item A is also called a Van der Monde matrix
 %% \item It can also be generated using \typ{vander}
@@ -549,6 +557,7 @@ In []: plot(L, Tline)
   \begin{itemize}
   \item Matrices
     \begin{itemize}
+      \item Initializing
       \item Accessing elements
       \item Slicing and Striding
       \item Transpose
diff --git a/day1/session6.tex b/day1/session6.tex
index a647eb1..acfc687 100755
--- a/day1/session6.tex
+++ b/day1/session6.tex
@@ -188,74 +188,7 @@ Out[]: True
 \subsection{Exercises}
 
 \begin{frame}[fragile]
-\frametitle{Problem 1}
-Given the matrix:\\
-\begin{center}
-$\begin{bmatrix}
--2 & 2 & 3\\
- 2 & 1 & 6\\
--1 &-2 & 0\\
-\end{bmatrix}$
-\end{center}
-Find:
-\begin{itemize}
-  \item[i] Transpose
-  \item[ii]Inverse
-  \item[iii]Determinant
-  \item[iv] Eigenvalues and Eigen vectors
-  \item[v] Singular Value decomposition
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Problem 2}
-Given 
-\begin{center}
-A = 
-$\begin{bmatrix}
--3 & 1 & 5 \\
-1 & 0 & -2 \\
-5 & -2 & 4 \\
-\end{bmatrix}$
-, B = 
-$\begin{bmatrix}
-0 & 9 & -12 \\
--9 & 0 & 20 \\
-12 & -20 & 0 \\
-\end{bmatrix}$
-\end{center}
-Find:
-\begin{itemize}
-  \item[i] Sum of A and B
-  \item[ii]Elementwise Product of A and B
-  \item[iii] Matrix product of A and B
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Solution}
-Sum: 
-$\begin{bmatrix}
--3 & 10 & 7 \\
--8 & 0 & 18 \\
-17 & -22 & 4 \\
-\end{bmatrix}$
-,\\ Elementwise Product:
-$\begin{bmatrix}
-0 & 9 & -60 \\
--9 & 0 & -40 \\
-60 & 40 & 0 \\
-\end{bmatrix}$
-,\\ Matrix product:
-$\begin{bmatrix}
-51 & -127 & 56 \\
--24 & 49 & -12 \\
-66 & -35 & -100 \\
-\end{bmatrix}$
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Problem 3}
+\frametitle{Problem}
 Solve the set of equations:
 \begin{align*}
   x + y + 2z -w & = 3\\
@@ -374,8 +307,38 @@ Out[]: -0.66623943249251527
 %% \end{frame}
 
 \section{ODEs}
+
 \begin{frame}[fragile]
-\frametitle{ODE Integration}
+\frametitle{Solving ODEs using SciPy}
+\begin{itemize}
+\item Let's consider the spread of an epidemic in a population
+\item $\frac{dy}{dt} = ky(L-y)$ gives the spread of the disease
+\item L is the total population.
+\item Use L = 25000, k = 0.00003, y(0) = 250
+\item Define a function as below
+\end{itemize}
+\begin{lstlisting}
+In []: def epid(y, t):
+  ....     k, L = 0.00003, 25000
+  ....     return k*y*(L-y)
+  ....
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solving ODEs using SciPy \ldots}
+\begin{lstlisting}
+In []: t = arange(0, 12, 0.2)
+
+In []: y = odeint(epid, 250, t)
+
+In []: plot(t, y)
+\end{lstlisting}
+%Insert Plot
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{ODEs - Simple Pendulum}
 We shall use the simple ODE of a simple pendulum. 
 \begin{equation*}
 \ddot{\theta} = -\frac{g}{L}sin(\theta)
@@ -392,10 +355,9 @@ We shall use the simple ODE of a simple pendulum.
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Solving ODEs using SciPy}
+\frametitle{ODEs - Simple Pendulum \ldots}
 \begin{itemize}
-\item We use the \typ{odeint} function from scipy to do the integration
-\item Define a function as below
+\item Use \typ{odeint} to do the integration
 \end{itemize}
 \begin{lstlisting}
 In []: def pend_int(initial, t):
@@ -408,7 +370,7 @@ In []: def pend_int(initial, t):
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Solving ODEs using SciPy \ldots}
+\frametitle{ODEs - Simple Pendulum \ldots}
 \begin{itemize}
 \item \typ{t} is the time variable \\ 
 \item \typ{initial} has the initial values
@@ -420,7 +382,7 @@ In []: initial = [10*2*pi/360, 0]
 \end{frame}
 
 \begin{frame}[fragile]
-\frametitle{Solving ODEs using SciPy \ldots}
+\frametitle{ODEs - Simple Pendulum \ldots}
 %%\begin{small}
 \typ{In []: from scipy.integrate import odeint}
 %%\end{small}