elif else emacs error asymptotic function (erf) message rounding tolerance euler pi euler' method exception handling execute ( program) exit (sys) exp math notation false fast code finite difference method finite precision (of float) flat program float floating point number (float) for loop format png fortran forward difference approximation forward euler scheme fourier series from function asarray assert call definition global handle input parameter local nested output parameter return take parameter garbage collection gauss quadrature gedit graph hardcopy (plot) heat equation heun' method hold (on/off) idle if implement ( program) implementation general specific import math matplotlib pyplot module numpy random (function) indent indexing one based zero based initial conditions input instability instruction int integer division integral analytically approximately exact numerically integration points interactive use (of python) ipython keyboard arrow up/down lambda function language computer programming laplace equation least squares method legend (plot) leibniz pi library function sympy linear algebra linear interpolation linspace list index