Numerical Methods Repository

Package developed for Universidad del Norte, focused on the Engineering Division. Supervised by professors Augusto Salazar and Marlon Piñeres.

Check out the official repositor: https://github.com/LCCastillo03/NumericalMethods/tree/main

Team: NRC 2381

• Lena Carolina Castillo De la Espriella
• Gabriela De Jesús Bula Pavia
• Edgar Andrés Garcia Davila

Table of Contents

• Summary and Justification
• Repository Contents
• Repository Structure
• Dependencies
• Installation and Usage Instructions
• License

Summary and Justification

This repository contains implementations of numerical methods in Python. The included methods are useful for solving mathematical problems using computational techniques. They are used to build the marlonpy Python package, which aims to help Systems Engineering students at Universidad del Norte, especially in their Computational Solutions to Engineering Problems course.

Repository Contents

This repository currently includes implementations of the following methods:

• Number Conversions: Binary to Decimal, IEEE 754.
• Root-Finding Methods: Includes Bisection, Fixed Point, Newton-Raphson, Regula Falsi, and Secant methods.
• Linear Regression: Techniques for modeling relationships between variables.
• Numerical Differentiation: Methods for approximating derivatives.
• Numerical Integration: Techniques such as the Trapezoidal Rule, Gauss-Legendre, and Simpson's rule.
• Differential Equation Solvers: Includes methods like Runge-Kutta.

Repository Structure

The repository is structured as follows:

1. Conversions:

   • /ConversionBinary.py
   • /ConversionIEEE754.py

2. Differential Equations:

   • /RungeKutta4th.py

3. Linear Regression:

   • /LinearRegression.py

4. Numerical Derivation:

   • /Derivative.py

5. Numerical Integration:

   • /GaussLegendre.py
   • /Simpson38.py
   • /TrapezoidalRule.py

6. Roots:

   • /BisectionMethod.py
   • /FixedPoint.py
   • /NewtonRaphson.py
   • /RegulaFalsi.py
   • /SecantMethod.py

7. System Equations:

   • /Crout.py
   • /DDM.py
   • /Doolittle.py
   • /GaussSeidel.py
   • /Jacobi.py

8. Taylor Series:

   • /TaylorSeries.py

Each directory contains specific implementations of the mentioned methods.

Dependencies

• NumPy: the fundamental package for scientific computing in Python.
• SymPy: a Python library for symbolic mathematics.
• tabulate: Pretty-print tabular data in Python.

Installation and Usage Instructions

Latest version of Python 3.12.3

pip install marlonpy

If the command pip does not work in your computer, please try:

py -m pip install marlonpy

Now, you can use the library.

import marlonpy as mp

Examples

• IEEE 754 Conversion:

>>> from marlonpy.Conversions import ConversionIeee
>>> num = '01000010101010100100000000000000'
>>> print('El equivalente de num en decimal es', ConversionIeee.ieee754(num))
El equivalente de num en decimal es 85.125

• Regula Falsi:

>>> from marlonpy.Roots import RegulaFalsi
>>> import sympy as sp
>>> x = sp.Symbol('x')
>>> f = sp.sec(sp.exp(sp.sqrt(x + 1))) - 3
>>> a = 3
>>> b = 3.1
>>> print('La raíz aproximada es', RegulaFalsi.regula_falsi(f, a, b))
La raíz aproximada es 3.06741643635292

License

This repository is licensed under the MIT License.