added 6th week

ex_21.py

@@ -0,0 +1,16 @@
+from scipy.special import zeta
+
+class ZetaApprox(object):
+	def __init__(self, N):
+		self._N = N
+	def __call__(self, s):
+		result = 1
+		for n in range(1, self._N + 1):
+			result += 1 / n**s
+		return result
+
+if( __name__ == "__main__"):
+	zeta_approx= ZetaApprox(10000000)
+	print(zeta_approx(1.15))
+	print(zeta(1.15))
+	

ex_22.py

@@ -0,0 +1,34 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+def sin_approx_factory(n):
+	def factorial(k):
+		result = 1
+		for i in range(1, k + 1):
+			result *= i
+		return result
+
+
+	def sin(x):
+		result = 0
+		for i in range(0, n + 1):
+			#print("+ (-1)**{} * x**{} / {} ".format(i, 2*i + 1, factorial(2*i + 1)), end = "")
+			result += (-1)**(i) * x**(2*i + 1) / factorial(2*i + 1)
+		#print()
+		return result 
+	return sin
+
+
+X = np.arange(-4, 4, 0.01)
+plots = list()
+
+p0, = plt.plot(X, np.sin(X), label="sin(x)")
+plots.append(p0)
+
+for i in range(5):
+	p, = plt.plot(X, sin_approx_factory(i)(X), label="approx({})".format(i))
+	plots.append(p)
+
+plt.legend(handles=plots)
+plt.show()
+

ex_23.py

@@ -0,0 +1,23 @@
+import matplotlib.pyplot as plt
+from matplotlib.ticker import FixedLocator, FuncFormatter
+import numpy as np
+
+
+X1 = np.arange(0, 8*np.pi, 0.01)
+Y1 = np.cos(X1)
+
+plt.plot(X1, Y1)
+
+X2 = np.array([i*np.pi for i in range(9)])
+X3 = np.array([i*np.pi/2 for i in range(1, 16, 2)])
+Y2 = np.cos(X2)
+Y3 = np.cos(X3)
+
+plt.scatter(X2, Y2, color="green")
+plt.scatter(X3, Y3, color="red")
+
+plt.gca().xaxis.set_major_locator(FixedLocator(X2))
+plt.gca().xaxis.set_major_formatter(FuncFormatter(lambda x,_: "${}\\pi$".format(x // np.pi)))
+
+plt.show()
+

ex_24.py

@@ -0,0 +1,23 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+X = np.arange(0, 10, 0.01)
+K = 100
+alpha = 0.15
+
+real_Y = K*np.exp(-alpha * X)
+
+def approx_function_generator(delta, alpha, K):
+
+	def f(x):
+		if(x <= 0):
+			return K
+		return (1 - delta*alpha)*f(x - delta)
+
+	return f
+
+plt.plot(X, real_Y)
+plt.plot(X, [approx_function_generator(2, alpha, K)(x) for x in X])
+plt.plot(X, [approx_function_generator(1, alpha, K)(x) for x in X])
+plt.plot(X, [approx_function_generator(0.1, alpha, K)(x) for x in X])
+plt.show()