1 \documentclass[12pt]{article}

     2 \title{Solving Equations \& ODEs}

     3 \author{FOSSEE}

     4 \begin{document}

     5 \date{}

     6 \vspace{-1in}

     7 \begin{center}

     8 \LARGE{Solving Equations \& ODEs}\\

     9 \large{FOSSEE}

    10 \end{center}

    11 \section{Solving linear equations}

    12 \begin{verbatim}

    13     In []: A = array([[3,2,-1],

    14                       [2,-2,4],                   

    15                       [-1, 0.5, -1]])

    16     In []: b = array([[1], [-2], [0]])

    17     In []: x = solve(A, b)

    18     In []: Ax = dot(A,x)

    19     In []: allclose(Ax, b)

    20     Out[]: True

    21 \end{verbatim}

    22 \section{Finding roots}

    23 \begin{verbatim}

    24   In []: coeffs = [1, 6, 13]

    25   In []: roots(coeffs)

    26 \end{verbatim}

    27 Finding the roots of a function

    28 \begin{verbatim}

    29 In []: fsolve(sin(x)+cos(x)**2, 0)

    30 \end{verbatim}

    31 \section{ODE}

    32 \begin{verbatim}

    33   In []: def epid(y, t):

    34   ....     k, L = 0.00003, 25000

    35   ....     return k*y*(L-y)

    36   ....

    37   

    38   In []: t = arange(0, 12, 0.2)

    39 

    40   In []: y = odeint(epid, 250, t)

    41 

    42   In []: plot(t, y)

    43 \end{verbatim}

    44 \end{document}