Experiments on showing how Taylor expansion works.

Probably will be added to the Math chapter once finalized.

experiments/taylor.py

@@ -0,0 +1,56 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Mar 19 08:26:08 2015
+
+@author: rlabbe
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from math import sin, cos, factorial
+def df(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)
+
+
+
+
+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
+
+
+x = 0.1
+a = 0.8
+n = 1
+
+
+
+plt.cla()
+
+xs = np.linspace(-2, 2, 100)
+ts = [taylor(df, i, a, n) for i in xs]
+
+plt.plot(xs, np.sin(xs))
+plt.plot(xs, ts)
+
+