Re-structure of Module 3 to make each file a seperate lecture

1 files changed, 35 insertions, 0 deletions

diff --git a/tutorials/module_3/newton-raphson_nonlinear_systemspy b/tutorials/module_3/newton-raphson_nonlinear_systemspy
new file mode 100644
index 0000000..55a6cf1
--- /dev/null
+++ b/tutorials/module_3/newton-raphson_nonlinear_systemspy
@@ -0,0 +1,35 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Sep 27 15:31:11 2025
+
+@author: christian
+"""
+
+u = lambda x, y: x**2 + x*y - 10
+v = lambda x, y: y + 3*x*y**2 - 57
+
+# Initial guesses
+x_0 = 1.5
+y_0 = 3.5
+
+# Evaluate partial derivatives at initial guesses
+dudx = 2*x_0+y_0
+dudy = x_0
+
+dvdx = 6*x_0*y_0
+dvdy = 1 + 6*x_0*y_0
+
+# Find determinant
+det = dudx * dvdy - dudy * dvdx
+
+# Values of functions valuated at initial guess
+u_0 = u(x_0,y_0)
+v_0 = v(x_0,y_0)
+
+# Substitute into newton-raphson equation
+x_1 = x_0 - (u_0*dvdy-v_0*dudy) / det
+y_1 = y_0 - (v_0*dudx-v_0*dvdx) / det
+
+print(x_1)
+print(y_1)
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