maths.numerical_analysis.simpson_rule
=====================================

.. py:module:: maths.numerical_analysis.simpson_rule

.. autoapi-nested-parse::

   Numerical integration or quadrature for a smooth function f with known values at x_i

   This method is the classical approach of summing 'Equally Spaced Abscissas'

   method 2:
   "Simpson Rule"



Functions
---------

.. autoapisummary::

   maths.numerical_analysis.simpson_rule.f
   maths.numerical_analysis.simpson_rule.main
   maths.numerical_analysis.simpson_rule.make_points
   maths.numerical_analysis.simpson_rule.method_2


Module Contents
---------------

.. py:function:: f(x)

.. py:function:: main()

.. py:function:: make_points(a, b, h)

.. py:function:: method_2(boundary: list[int], steps: int) -> float

   Calculate the definite integral of a function using Simpson's Rule.
   :param boundary: A list containing the lower and upper bounds of integration.
   :param steps: The number of steps or resolution for the integration.
   :return: The approximate integral value.

   >>> round(method_2([0, 2, 4], 10), 10)
   2.6666666667
   >>> round(method_2([2, 0], 10), 10)
   -0.2666666667
   >>> round(method_2([-2, -1], 10), 10)
   2.172
   >>> round(method_2([0, 1], 10), 10)
   0.3333333333
   >>> round(method_2([0, 2], 10), 10)
   2.6666666667
   >>> round(method_2([0, 2], 100), 10)
   2.5621226667
   >>> round(method_2([0, 1], 1000), 10)
   0.3320026653
   >>> round(method_2([0, 2], 0), 10)
   Traceback (most recent call last):
       ...
   ZeroDivisionError: Number of steps must be greater than zero
   >>> round(method_2([0, 2], -10), 10)
   Traceback (most recent call last):
       ...
   ZeroDivisionError: Number of steps must be greater than zero