1 files changed, 132 insertions, 0 deletions
diff --git a/tutorials/module_2/notebook_2/num_methods_1.ipynb b/tutorials/module_2/notebook_2/num_methods_1.ipynb
new file mode 100644
index 0000000..889014a
--- /dev/null
+++ b/tutorials/module_2/notebook_2/num_methods_1.ipynb
@@ -0,0 +1,132 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Solving non-linear equations\n",
+    "\n",
+    "^ca27a3\n",
+    "\n",
+    "## Introduction\n",
+    "\n",
+    "## Prerequisites\n",
+    "\n",
+    "``` python\n",
+    "import numpy\n",
+    "import scipy\n",
+    "import sympy\n",
+    "```\n",
+    "\n",
+    "## fsolve from SciPy\n",
+    "\n",
+    "``` python\n",
+    "from scipy.optimize import fsolve\n",
+    "\n",
+    "def equations(vars):\n",
+    "    x, y = vars\n",
+    "    eq1 = x**2 + y**2 - 25\n",
+    "    eq2 = x**2 - y\n",
+    "    return [eq1, eq2]\n",
+    "\n",
+    "initial_guess = [1, 1]\n",
+    "solution = fsolve(equations, initial_guess)\n",
+    "print(\"Solution:\", solution)\n",
+    "```\n",
+    "\n",
+    "## root from SciPy\n",
+    "\n",
+    "``` python\n",
+    "from scipy.optimize import root\n",
+    "\n",
+    "def equations(vars):\n",
+    "    x, y = vars\n",
+    "    eq1 = x**2 + y**2 - 25\n",
+    "    eq2 = x**2 - y\n",
+    "    return [eq1, eq2]\n",
+    "\n",
+    "initial_guess = [1, 1]\n",
+    "solution = root(equations, initial_guess)\n",
+    "print(\"Solution:\", solution.x)\n",
+    "```\n",
+    "\n",
+    "## minimize from SciPy\n",
+    "\n",
+    "``` python\n",
+    "from scipy.optimize import minimize\n",
+    "\n",
+    "# Define the equations\n",
+    "def equation1(x, y):\n",
+    "    return x**2 + y**2 - 25\n",
+    "\n",
+    "def equation2(x, y):\n",
+    "    return x**2 - y\n",
+    "\n",
+    "# Define the objective function for optimization\n",
+    "def objective(xy):\n",
+    "    x, y = xy\n",
+    "    return equation1(x, y)**2 + equation2(x, y)**2\n",
+    "\n",
+    "# Initial guess\n",
+    "initial_guess = [1, 1]\n",
+    "\n",
+    "# Perform optimization\n",
+    "result = minimize(objective, initial_guess)\n",
+    "solution_optimization = result.x\n",
+    "\n",
+    "print(\"Optimization Method Solution:\", solution_optimization)\n",
+    "```\n",
+    "\n",
+    "## nsolve from SymPy\n",
+    "\n",
+    "``` python\n",
+    "from sympy import symbols, Eq, nsolve\n",
+    "\n",
+    "# Define the variables\n",
+    "x, y = symbols('x y')\n",
+    "\n",
+    "# Define the equations\n",
+    "eq1 = Eq(x**2 + y**2, 25)\n",
+    "eq2 = Eq(x - y, 0)\n",
+    "\n",
+    "# Initial guess for the solution\n",
+    "initial_guess = [1, 1]\n",
+    "\n",
+    "# Use nsolve to find the solution\n",
+    "solution = nsolve([eq1, eq2], [x, y], initial_guess)\n",
+    "print(\"Solution:\", solution)\n",
+    "```\n",
+    "\n",
+    "## newton_method from NumPy\n",
+    "\n",
+    "``` python\n",
+    "import numpy as np\n",
+    "\n",
+    "def equations(vars):\n",
+    "    x, y = vars\n",
+    "    eq1 = x**2 + y**2 - 25\n",
+    "    eq2 = x**2 - y\n",
+    "    return np.array([eq1, eq2])\n",
+    "\n",
+    "def newton_method(initial_guess, tolerance=1e-6, max_iter=100):\n",
+    "    vars = np.array(initial_guess, dtype=float)\n",
+    "    for _ in range(max_iter):\n",
+    "        J = np.array([[2 * vars[0], 2 * vars[1]], [2 * vars[0], -1]])\n",
+    "        F = equations(vars)\n",
+    "        delta = np.linalg.solve(J, -F)\n",
+    "        vars += delta\n",
+    "        if np.linalg.norm(delta) < tolerance:\n",
+    "            return vars\n",
+    "\n",
+    "initial_guess = [1, 1]\n",
+    "solution = newton_method(initial_guess)\n",
+    "print(\"Solution:\", solution)\n",
+    "```"
+   ],
+   "id": "2ba3c111-8a56-4d09-b043-cdd8c5528e00"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}