ToolPythonAdvanced Perturbation theory with SymPy: the Duffing oscillator's frequency shift return sp.factor(sp.integrate(R * harmonic(tau), (tau, 0, 2 * sp.pi)) / sp.pi)
ToolPythonBeginner SymPy from the ground up: where the pendulum's 1.74 % comes from attempt = sp.integrate(1 / theta_dot_expr, (theta, 0, theta0))phi_integral = sp.integrate(sp.series(integrand, k, 0, 6).removeO(), (phi, 0, sp.pi / 2))