serie 01 and 02

.gitignore

@@ -174,3 +174,5 @@ cython_debug/
 # PyPI configuration file
 .pypirc
 
+/.idea/misc.xml
+/.idea/

Kuengjoe_S01/Kuengjoe_S2_Aufg1.py

@@ -0,0 +1,162 @@
+
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib import cm
+from mpl_toolkits.mplot3d import Axes3D
+
+
+#a): Die Reichweite W erreicht ihr Maximum bei einem Winkel alpha = 45 Grad.
+
+g = 9.81
+
+v0_values = np.linspace(0, 100)
+alpha_deg_values = np.linspace(0, 90)
+
+[v0_grid, alpha_deg_grid] = np.meshgrid(v0_values, alpha_deg_values)
+alpha_rad_grid = np.deg2rad(alpha_deg_grid)
+
+W = (v0_grid**2) * np.sin(2 * alpha_rad_grid) / g
+
+
+fig = plt.figure(0)
+cont = plt.contour(v0_grid, alpha_deg_grid, W, cmap=cm.coolwarm)
+fig.colorbar(cont, shrink=0.5, aspect=5)
+plt.title('Wurfweite W(v0, α) – Höhenlinien')
+plt.xlabel('v0 [m/s]')
+plt.ylabel('α [deg]')
+plt.show()
+
+
+fig = plt.figure(1)
+ax = fig.add_subplot(111, projection='3d')
+surf = ax.plot_surface(v0_grid, alpha_deg_grid, W, cmap=cm.coolwarm, linewidth=0, antialiased=False)
+fig.colorbar(surf, shrink=0.5, aspect=5)
+plt.title('Wurfweite W(v0, α) – Oberfläche')
+ax.set_xlabel('v0 [m/s]')
+ax.set_ylabel('α [deg]')
+ax.set_zlabel('W [m]')
+plt.show()
+
+
+fig = plt.figure(2)
+ax = fig.add_subplot(111, projection='3d')
+ax.plot_wireframe(v0_grid, alpha_deg_grid, W, rstride=5, cstride=5)
+plt.title('Wurfweite W(v0, α) – Gitter')
+ax.set_xlabel('v0 [m/s]')
+ax.set_ylabel('α [deg]')
+ax.set_zlabel('W [m]')
+plt.show()
+
+
+
+R = 8.31
+
+
+V_values = np.linspace(1e-6, 0.2)
+T_values = np.linspace(0, 1e4)
+
+[V_grid, T_grid] = np.meshgrid(V_values, T_values)
+p = R * T_grid / V_grid
+
+fig = plt.figure(3)
+cont = plt.contour(V_grid, T_grid, p, cmap=cm.coolwarm)
+fig.colorbar(cont, shrink=0.5, aspect=5)
+plt.title('p(V, T) = R T / V – Höhenlinien')
+plt.xlabel('V [m^3]')
+plt.ylabel('T [K]')
+plt.show()
+
+
+fig = plt.figure(4)
+ax = fig.add_subplot(111, projection='3d')
+surf = ax.plot_surface(V_grid, T_grid, p, cmap=cm.coolwarm, linewidth=0, antialiased=False)
+fig.colorbar(surf, shrink=0.5, aspect=5)
+plt.title('p(V, T) = R T / V – Oberfläche')
+ax.set_xlabel('V [m^3]')
+ax.set_ylabel('T [K]')
+ax.set_zlabel('p [N/m^2]')
+plt.show()
+
+fig = plt.figure(5)
+ax = fig.add_subplot(111, projection='3d')
+ax.plot_wireframe(V_grid, T_grid, p, rstride=5, cstride=5)
+plt.title('p(V, T) = R T / V – Gitter')
+ax.set_xlabel('V [m^3]')
+ax.set_ylabel('T [K]')
+ax.set_zlabel('p [N/m^2]')
+plt.show()
+
+
+# 2)
+p_values = np.linspace(1e4, 1e5)
+T_values = np.linspace(0, 1e4)
+
+[p_grid, T_grid] = np.meshgrid(p_values, T_values)
+V = R * T_grid / p_grid
+
+
+fig = plt.figure(6)
+cont = plt.contour(p_grid, T_grid, V, cmap=cm.coolwarm)
+fig.colorbar(cont, shrink=0.5, aspect=5)
+plt.title('V(p, T) = R T / p – Höhenlinien')
+plt.xlabel('p [N/m^2]')
+plt.ylabel('T [K]')
+plt.show()
+
+
+fig = plt.figure(7)
+ax = fig.add_subplot(111, projection='3d')
+surf = ax.plot_surface(p_grid, T_grid, V, cmap=cm.coolwarm, linewidth=0, antialiased=False)
+fig.colorbar(surf, shrink=0.5, aspect=5)
+plt.title('V(p, T) = R T / p – Oberfläche')
+ax.set_xlabel('p [N/m^2]')
+ax.set_ylabel('T [K]')
+ax.set_zlabel('V [m^3]')
+plt.show()
+
+
+fig = plt.figure(8)
+ax = fig.add_subplot(111, projection='3d')
+ax.plot_wireframe(p_grid, T_grid, V, rstride=5, cstride=5)
+plt.title('V(p, T) = R T / p – Gitter')
+ax.set_xlabel('p [N/m^2]')
+ax.set_ylabel('T [K]')
+ax.set_zlabel('V [m^3]')
+plt.show()
+
+
+# 3)
+p_values = np.linspace(1e4, 1e6)
+V_values = np.linspace(0, 10)
+
+[p_grid, V_grid] = np.meshgrid(p_values, V_values)
+T = (p_grid * V_grid) / R
+
+
+fig = plt.figure(9)
+cont = plt.contour(p_grid, V_grid, T, cmap=cm.coolwarm)
+fig.colorbar(cont, shrink=0.5, aspect=5)
+plt.title('T(p, V) = p V / R – Höhenlinien')
+plt.xlabel('p [N/m^2]')
+plt.ylabel('V [m^3]')
+plt.show()
+
+fig = plt.figure(10)
+ax = fig.add_subplot(111, projection='3d')
+surf = ax.plot_surface(p_grid, V_grid, T, cmap=cm.coolwarm, linewidth=0, antialiased=False)
+fig.colorbar(surf, shrink=0.5, aspect=5)
+plt.title('T(p, V) = p V / R – Oberfläche')
+ax.set_xlabel('p [N/m^2]')
+ax.set_ylabel('V [m^3]')
+ax.set_zlabel('T [K]')
+plt.show()
+
+
+fig = plt.figure(11)
+ax = fig.add_subplot(111, projection='3d')
+ax.plot_wireframe(p_grid, V_grid, T, rstride=5, cstride=5)
+plt.title('T(p, V) = p V / R – Gitter')
+ax.set_xlabel('p [N/m^2]')
+ax.set_ylabel('V [m^3]')
+ax.set_zlabel('T [K]')
+plt.show()

Kuengjoe_S02/Kuengjoe_S2_Aufg2.py

@@ -0,0 +1,36 @@
+import sympy as sp
+
+x1, x2, x3 = sp.symbols("x1 x2 x3", real=True)
+
+
+f_a = sp.Matrix([
+    5 * x1 * x2,
+    x1**2 * x2**2 + x1 + 2 * x2
+])
+
+D_f_a = f_a.jacobian(sp.Matrix([x1, x2]))
+D_f_a_at_point = D_f_a.subs({x1: 1, x2: 2})
+
+print("D_f_a(x) =")
+sp.pprint(D_f_a)
+
+
+print("Aufgabe 2a:")
+
+sp.pprint(D_f_a_at_point)
+
+
+f_b = sp.Matrix([
+    sp.log(x1**2 + x2**2) + x3**2,
+    sp.exp(x2**2 + x3**2) + x1**2,
+    1 / (x3**2 + x1**2) + x2**2
+])
+
+D_f_b = f_b.jacobian(sp.Matrix([x1, x2, x3]))
+D_f_b_at_point = D_f_b.subs({x1: 1, x2: 2, x3: 3})
+
+print("\nD_f_b(x) =")
+sp.pprint(D_f_b)
+
+print("\nAufgabe 2b:")
+sp.pprint(sp.simplify(D_f_b_at_point))

Kuengjoe_S02/Kuengjoe_S2_Aufg3.py

@@ -0,0 +1,43 @@
+import sympy as sp
+
+x1, x2, x3 = sp.symbols("x1 x2 x3", real=True)
+
+x = sp.Matrix([x1, x2, x3])
+
+f = sp.Matrix([
+    x1 + x2**2 - x3**2 - 13,
+    sp.log(x2 / 4) + sp.exp(sp.Rational(1, 2) * x3 - 1) - 1,
+    (x2 - 3)**2 - x3**3 + 7
+])
+
+x0 = sp.Matrix([
+    sp.Rational(3, 2),
+    3,
+    sp.Rational(5, 2)
+])
+
+substitution_dictionary = {
+    x1: x0[0],
+    x2: x0[1],
+    x3: x0[2]
+}
+
+function_value_at_x0 = f.subs(substitution_dictionary)
+jacobian_matrix = f.jacobian(x)
+jacobian_matrix_at_x0 = jacobian_matrix.subs(substitution_dictionary)
+
+linearized_function = sp.simplify(
+    function_value_at_x0 + jacobian_matrix_at_x0 * (x - x0)
+)
+
+print("f(x0) =")
+sp.pprint(function_value_at_x0)
+
+print("\nDf(x) =")
+sp.pprint(jacobian_matrix)
+
+print("\nDf(x0) =")
+sp.pprint(jacobian_matrix_at_x0)
+
+print("\nL(x) =")
+sp.pprint(linearized_function)

main.py

@@ -0,0 +1,16 @@
+# This is a sample Python script.
+
+# Press ⌃R to execute it or replace it with your code.
+# Press Double ⇧ to search everywhere for classes, files, tool windows, actions, and settings.
+
+
+def print_hi(name):
+    # Use a breakpoint in the code line below to debug your script.
+    print(f'Hi, {name}')  # Press ⌘F8 to toggle the breakpoint.
+
+
+# Press the green button in the gutter to run the script.
+if __name__ == '__main__':
+    print_hi('PyCharm')
+
+# See PyCharm help at https://www.jetbrains.com/help/pycharm/