From 2dda88569c62feb3522611d435a28787bc8ef566 Mon Sep 17 00:00:00 2001
From: Jackie <jacklyn.videira@uconn.edu>
Date: Tue, 12 Sep 2017 11:01:44 -0400
Subject: [PATCH] Taylor Series

---
 TaylorSeries.py | 50 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100644 TaylorSeries.py

diff --git a/TaylorSeries.py b/TaylorSeries.py
new file mode 100644
index 0000000..1fe5818
--- /dev/null
+++ b/TaylorSeries.py
@@ -0,0 +1,50 @@
+import sympy as sy
+import numpy as np
+from sympy.functions import sin,cos
+import matplotlib.pyplot as plt
+
+plt.style.use("ggplot")
+
+# Define the variable and the function to approximate
+x = sy.Symbol('x')
+f = sin(x)
+
+# Factorial function
+def factorial(n):
+	if n <= 0:
+		return 1
+	else:
+		return n*factorial(n-1)
+
+# Taylor approximation at x0 of the function 'function'
+def taylor(function,x0,n):
+	i = 0
+	p = 0
+	while i <= n:
+		p = p + (function.diff(x,i).subs(x,x0))/(factorial(i))*(x-x0)**i
+		i += 1
+	return p
+def plot():
+	x_lims = [-5,5]
+	x1 = np.linspace(x_lims[0],x_lims[1],800)
+	y1 = []
+    # Approximate up until 10 starting from 1 and using steps of 2
+	for j in range(1,10,2):
+		func = taylor(f,0,j)
+		print('Taylor expansion at n='+str(j),func)
+		for k in x1:
+			y1.append(func.subs(x,k))	
+		plt.plot(x1,y1,label='order '+str(j))
+		y1 = []
+	# Plot the function to approximate (sine, in this case)
+	plt.plot(x1,np.sin(x1),label='sin of x')
+	plt.xlim(x_lims)
+	plt.ylim([-5,5])
+	plt.xlabel('x')
+	plt.ylabel('y')
+	plt.legend()
+	plt.grid(True)
+	plt.title('Taylor series approximation')
+	plt.show()
+
+plot()