From fe8866f1df56215391c8daeb0eaacbb7bb73f2f8 Mon Sep 17 00:00:00 2001
From: git-sandro <sandro.zimmermann@szdn.ch>
Date: Thu, 26 Feb 2026 22:42:18 +0100
Subject: [PATCH] feat: aufgabe 4 abgeschlossen

---
 introduction/serie_2.py | 35 +++++++++++++++++++++++++++++++++++
 1 file changed, 35 insertions(+)
 create mode 100644 introduction/serie_2.py

diff --git a/introduction/serie_2.py b/introduction/serie_2.py
new file mode 100644
index 0000000..e6811ae
--- /dev/null
+++ b/introduction/serie_2.py
@@ -0,0 +1,35 @@
+#%%
+import numpy as np
+
+# %%
+print("Aufgabe 4")
+
+def fixpunkt_iteration(f, x, tol=1e-7):
+    x_new = f(x)
+    i = 0
+
+    while(np.abs(x_new-x) > tol):
+        x = x_new
+        x_new = f(x)
+        i += 1
+    return [x_new, i]
+
+x0 = 1.0
+
+f = lambda x: 1-(1/5)*x
+fixpunkt_a, iterationen_a = fixpunkt_iteration(f, x0)
+
+f = np.cos
+fixpunkt_b, iterationen_b = fixpunkt_iteration(f, x0)
+
+f = lambda x: np.e**-x
+fixpunkt_c, iterationen_c = fixpunkt_iteration(f, x0)
+
+# Ausgabe
+print("----------------------------------------------------------------------")
+print(__file__)
+print("----------------------------------------------------------------------")
+print(f"a) f(x) = 1-(1/5)*x\nFixpunkt: {fixpunkt_a}\nIterationen: {iterationen_a}\n")
+print(f"b) f(x) = cos(x)\nFixpunkt: {fixpunkt_b}\nIterationen: {iterationen_b}\n")
+print(f"c) f(x) = e⁻x\nFixpunkt: {fixpunkt_c}\nIterationen: {iterationen_c}\n")
+print("----------------------------------------------------------------------")