Finished off system_of_equations and pde's

1 files changed, 2 insertions, 3 deletions

diff --git a/tutorials/module_3/4_numerical_integration.md b/tutorials/module_3/4_numerical_integration.md
index 78b0328..06cb8b9 100644
--- a/tutorials/module_3/4_numerical_integration.md
+++ b/tutorials/module_3/4_numerical_integration.md
@@ -183,9 +183,6 @@ for n in n_list:
 
 
 ```python
-#!/usr/bin/env python3
-# Gauss Quadrature using Gauss-Legendre method (manual 2-point & 3-point)
-
 import numpy as np
 from scipy.integrate import quad   # for reference "exact" integral
 
@@ -244,6 +241,7 @@ print(f"Error (3-point): {err3:.2e}")
 
 ## Numerical Integration to Compute Work
 
+
 ## Implementing the Composite Trapezoidal Rule
 
 **Objective:** Implement a Python function to approximate integrals using the trapezoidal rule.
@@ -266,6 +264,7 @@ for n in [4, 8, 16, 32]:
 
 Students should compare results for increasing $n$ and observe how the error decreases with $O(h^2$).
 
+---
 ## Gaussian Quadrature
 
 Write a Python function for two-point and three-point Gauss–Legendre quadrature over an arbitrary interval $[a,b]$. Verify exactness for polynomials up to the appropriate degree and compare performance against the trapezoidal rule on oscillatory test functions.