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