In [3]:
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from math import sin, cos, factorial
def f_sin(x, p):
if p == 0:
return sin(x)
return x
if p % 4 == 1:
return cos(x)
if p % 4 == 2:
return -sin(x)
if p % 4 == 3:
return -cos(x)
return sin(x)
In [4]:
def taylor(df, x, a, n):
f = 0.0
for i in range(n+1):
term = df(a, i) * (x - a)**i / factorial(i)
f += term
return f
In [23]:
from IPython.html.widgets import interact, interactive, fixed
from IPython.html.widgets import FloatSliderWidget as fWidget
from IPython.html.widgets import IntSliderWidget as iWidget
x = 0.1
a = 0.8
n = 1
def plot_data(a, n):
xs = np.linspace(-2, 2, 50)
ts = [taylor(f_sin, i, a, n) for i in xs]
plt.plot(xs, np.sin(xs))
plt.plot(xs, ts)
plt.xlim(-2,2)
plt.ylim(-2,2)
plt.axvline(a)
plt.show()
interact(plot_data,
a = fWidget(value=0.8, min=-1.9, max=1.9),
n = iWidget(value=2, min=1, max=8))
