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| -rw-r--r-- | day1/session4.tex | 97 |
1 files changed, 52 insertions, 45 deletions
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} |