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−\documentclass[12pt]{article}
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−\title{Solving Equations \& ODEs}
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−\author{FOSSEE}
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−\begin{document}
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−\date{}
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−\vspace{-1in}
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−\begin{center}
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−\LARGE{Solving Equations \& ODEs}\\
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−\large{FOSSEE}
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−\end{center}
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−\section{Solving linear equations}
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−\begin{verbatim}
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−    In []: A = array([[3,2,-1],
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−                      [2,-2,4],                   
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−                      [-1, 0.5, -1]])
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−    In []: b = array([[1], [-2], [0]])
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−    In []: x = solve(A, b)
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−    In []: Ax = dot(A,x)
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−    In []: allclose(Ax, b)
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−    Out[]: True
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−\end{verbatim}
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−\section{Finding roots}
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−\begin{verbatim}
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−  In []: coeffs = [1, 6, 13]
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−  In []: roots(coeffs)
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−\end{verbatim}
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−Finding the roots of a function
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−\begin{verbatim}
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−In []: fsolve(sin(x)+cos(x)**2, 0)
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−\end{verbatim}
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−\section{ODE}
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−\begin{verbatim}
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−  In []: def epid(y, t):
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−  ....     k, L = 0.00003, 25000
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−  ....     return k*y*(L-y)
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−  ....
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−  
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−  In []: t = arange(0, 12, 0.2)
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−
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−  In []: y = odeint(epid, 250, t)
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−
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−  In []: plot(t, y)
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−\end{verbatim}
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−\end{document}