From f0b45599547e396ca6a3a229473b7c7ccdc68754 Mon Sep 17 00:00:00 2001
From: Manuel Thalmann <m@nuth.ch>
Date: Thu, 23 Feb 2023 15:27:39 +0100
Subject: [PATCH] Solve HM2 exercise

---
 .../Week 1/Miguel_S1_Aufg1.py                 | 84 +++++++++++++++++++
 Pipfile                                       |  1 +
 Pipfile.lock                                  | 17 +++-
 3 files changed, 101 insertions(+), 1 deletion(-)
 create mode 100644 Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 1/Miguel_S1_Aufg1.py

diff --git a/Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 1/Miguel_S1_Aufg1.py b/Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 1/Miguel_S1_Aufg1.py
new file mode 100644
index 0000000..d1db9f0
--- /dev/null
+++ b/Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 1/Miguel_S1_Aufg1.py	
@@ -0,0 +1,84 @@
+# %%
+from numpy import pi, sin
+import matplotlib.pyplot as plt
+from IPython import get_ipython
+
+def draw3D(x, y, z, title, xlabel, ylabel, zlabel):
+    fig = plt.figure()
+
+    surface = fig.add_subplot(projection="3d")
+    plot = surface.plot_surface(x, y, z, cmap="rainbow")
+    fig.colorbar(plot, shrink=0.5, aspect=5)
+
+    fig = plt.figure()
+    wireframe = fig.add_subplot(projection="3d")
+    wireframe.plot_wireframe(x, y, z)
+    
+    for axes in [surface, wireframe]:
+        axes.set_title(title)
+        axes.set_xlabel(xlabel)
+        axes.set_ylabel(ylabel)
+        axes.set_zlabel(zlabel)
+
+    plt.show()
+
+def drawContour(x, y, z, title, xlabel, ylabel):
+    fig = plt.figure()
+    axes = fig.add_subplot()
+    plot = axes.contour(x, y, z, cmap="rainbow")
+    fig.colorbar(plot, shrink=0.5, aspect=5)
+    axes.set_title(title)
+    axes.set_xlabel(xlabel)
+    axes.set_ylabel(ylabel)
+    plt.show()
+
+def drawPlots(x, y, z, title, xlabel, ylabel, zlabel):
+    draw3D(x, y, z, title, xlabel, ylabel, zlabel)
+    drawContour(x, y, z, title, xlabel, ylabel)
+
+# %%
+g = 9.81
+
+def W(v, a):
+    return ((v ** 2) * sin(a * 2)) / g
+
+import numpy as np
+
+[v, a] = np.meshgrid(np.linspace(0, 100), np.linspace(0, pi / 2))
+z = W(v, a)
+
+get_ipython().run_cell("%matplotlib widget")
+drawPlots(v, a, z, "Wurfdistanz", "v_0", "alpha", "W")
+# %%
+
+R = 3.81
+
+def calcP(V, T):
+    return (R * T) / V
+
+def calcV(p, T):
+    return (R * T) / p
+
+def calcT(p, V):
+    return (p * V) / R
+
+# %%
+
+[V, T] = np.meshgrid(np.linspace(0, 0.2), np.linspace(0, 10 ** 4))
+p = calcP(V, T)
+
+drawPlots(V, T, p, "Druck", "V", "T", "p")
+
+# %%
+
+[p, T] = np.meshgrid(np.linspace(10 ** 4, 10 ** 5), np.linspace(0, 10 ** 4))
+V = calcV(p, T)
+drawPlots(p, T, V, "Volumen", "p", "T", "V")
+
+# %%
+
+[p, V] = np.meshgrid(np.linspace(10 ** 4, 10 ** 6), np.linspace(0, 10))
+T = calcT(p, V)
+drawPlots(p, V, T, "Temperatur in K°", "p", "V", "T")
+
+# %%
diff --git a/Pipfile b/Pipfile
index 9376f77..86fd447 100644
--- a/Pipfile
+++ b/Pipfile
@@ -11,6 +11,7 @@ scipy = "*"
 pexpect = "*"
 pandas = "*"
 ipympl = "*"
+sympy = "*"
 
 [dev-packages]
 
diff --git a/Pipfile.lock b/Pipfile.lock
index 5facda4..70ded2d 100644
--- a/Pipfile.lock
+++ b/Pipfile.lock
@@ -1,7 +1,7 @@
 {
     "_meta": {
         "hash": {
-            "sha256": "feb57859ef42912639d544346f6a70df45acd233855c030f52a04d4069257a88"
+            "sha256": "8c86c6849809fd6594aed0bf17bcfecc16e4e0e68b7949900346649d7b23c60a"
         },
         "pipfile-spec": 6,
         "requires": {
@@ -353,6 +353,13 @@
             "markers": "python_version >= '3.5'",
             "version": "==0.1.6"
         },
+        "mpmath": {
+            "hashes": [
+                "sha256:604bc21bd22d2322a177c73bdb573994ef76e62edd595d17e00aff24b0667e5c",
+                "sha256:79ffb45cf9f4b101a807595bcb3e72e0396202e0b1d25d689134b48c4216a81a"
+            ],
+            "version": "==1.2.1"
+        },
         "nest-asyncio": {
             "hashes": [
                 "sha256:b9a953fb40dceaa587d109609098db21900182b16440652454a146cffb06e8b8",
@@ -747,6 +754,14 @@
             ],
             "version": "==0.6.2"
         },
+        "sympy": {
+            "hashes": [
+                "sha256:938f984ee2b1e8eae8a07b884c8b7a1146010040fccddc6539c54f401c8f6fcf",
+                "sha256:e32380dce63cb7c0108ed525570092fd45168bdae2faa17e528221ef72e88658"
+            ],
+            "index": "pypi",
+            "version": "==1.11.1"
+        },
         "tornado": {
             "hashes": [
                 "sha256:1d54d13ab8414ed44de07efecb97d4ef7c39f7438cf5e976ccd356bebb1b5fca",