%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt

from scipy import integrate

def f(x):
    return np.exp(-x ** 2)

integrate.quad(f, 0, 5)

def f(x, A, B):
    return A * np.exp(-B * x ** 2)

integrate.quad(f, 0, 5, args=(1.0, 1.0))

def f(y, t):
    return -y

y0 = 1.0

t = np.linspace(0, 3)

sol = integrate.odeint(f, y0, t)

plt.plot(t, sol)

def f(y, t):
    return np.array([y[1], -y[0]])

t = np.linspace(0, 10)

y0 = np.array([1.0, 0.0])

sol = integrate.odeint(f, y0, t)

plt.plot(t, sol[:, 0], label='$y$')
plt.plot(t, sol[:, 1], '--k', label='$\dot{y}$')
plt.legend()

from scipy import optimize

def F(E, e, M):
    return E - e * np.sin(E) - M

sol = optimize.root(F, 0.1, args=(0.016, 0.1))
sol.x