📊 Numerical Analysis - Python Laboratories

Repository containing Python implementations of the main numerical methods studied in Numerical Analysis, with practical applications and usage examples.

🎯 Overview

This repository contains complete and functional implementations of fundamental numerical algorithms, developed as part of the practical work for the Numerical Analysis course. Each laboratory addresses a specific topic with robust implementations, input validation, and interactive user interfaces.

🚀 Available Laboratories

🔢 Lab 01: Number Base Conversion (2-62)

Conversion between number bases from 2 to 62

• Main file: changeBaseMerged - final.py
• Features:
  • Conversion of real numbers between bases 2 to 62
  • Support for negative numbers and decimals
  • Automatic digit mapping (0-9, A-Z, a-z)
  • Robust input validation
  • Configurable precision (8 decimal places default)

Usage example:

# Convert 853674.07523901 from base 10 to base 16
# Result: D0A2A.133A

🔍 Lab 02: Root Approximation

Iterative methods for finding function zeros

• Main file: Main.py
• Implemented methods:
  • Bisection Method: Guaranteed convergence for continuous functions
  • Newton's Method: Quadratic convergence (requires derivative)
  • Secant Method: Derivative approximation by finite differences

Characteristics:

• Interactive interface for equation input
• Support for trigonometric and exponential functions
• Interval and convergence validation
• Configurable tolerances and maximum iterations

🧮 Lab 03: Linear Equation Systems

Solving linear systems Ax = b

• Main file: Main.py
• Implemented methods:
  • Gauss-Jordan Elimination: Exact solution for square systems
  • Jacobi Method: Iterative method for diagonally dominant systems
  • Gauss-Seidel Method: Jacobi variant with accelerated convergence

Features:

• Matrix input up to 3x3
• Visualization of all iterations
• Convergence analysis
• Intuitive interface for data input

📐 Lab 04: Numerical Integration

Newton-Cotes formulas for numerical integration

• Main file: Main.py
• Closed Formulas:
  • Trapezoidal Rule (degree 1)
  • Simpson's 1/3 Rule (degree 2)
  • Simpson's 3/8 Rule (degree 3)
  • Boole's Rule (degree 4)
• Open Formulas:
  • Midpoint Rule (degree 0)
  • Degree 1 Rule
  • Milne's Rule (degree 2)
  • Degree 3 Rule

Resources:

• Input by function or discrete points
• Configurable integration intervals
• Configurable precision (8 decimal places default)

🌐 Lab 05: Newton's Method for Non-Linear Systems

Extension of Newton's method for multivariate systems

• Main file: Metodo_Newton -ENL.py
• Features:
  • Solving systems of non-linear equations
  • Automatic Jacobian matrix calculation
  • Support for trigonometric, exponential and logarithmic functions
  • Configurable tolerances and stopping criteria

Applications:

• Transcendental equation systems
• Optimization problems
• Electrical circuit analysis
• Physical phenomena modeling

🛠️ Requirements and Installation

Prerequisites

• Python 3.8 or higher
• pip (Python package manager)

Dependencies

pip install numpy sympy

Installation

# Clone the repository
git clone https://github.com/kanekitakitos/analise-numerica.git

# Navigate to the directory
cd analise-numerica

# Run any laboratory
python "lab01 - Mudançã de bases 2-62/changeBaseMerged - final.py"

🔧 Project Structure

analise-numerica/
├── lab01 - Mudançã de bases 2-62/
│   ├── AN_Lab1.pdf
│   ├── changeBaseMerged - final.py
│   └── changeBaseMerged - final abecedario.py
├── lab02 - Aproximacoes de Raizes (funcoes)/
│   ├── AN_Lab2.pdf
│   ├── Main.py
│   ├── Metodo_Bissecao.py
│   ├── Metodo_Newton.py
│   └── Metodo_Secante.py
├── lab03 - Raizes de sistemas de equacoes Lineares/
│   ├── AN_Lab3.pdf
│   ├── Main.py
│   ├── Metodo_de_Elimininação_Gauss_Jordan.py
│   ├── Metodo_de_Gauss_Seidel.py
│   └── Metodo_de_Jacobi.py
├── lab04 - Integracao Numerica/
│   ├── AN_Lab4.pdf
│   ├── Main.py
│   ├── Newton_Cotes_Aberta.py
│   └── Newton_Cotes_Fechada.py
├── lab05 - Metodos de newton/
│   ├── AN_Lab5.pdf
│   └── Metodo_Newton -ENL.py
└── README.md

📚 Documentation

Each laboratory has a PDF file (AN_Lab*.pdf) containing:

• Complete problem statement
• Specific technical requirements
• Evaluation criteria
• Test examples
• Theoretical considerations

🧪 Testing and Validation

All algorithms have been tested with:

• Standard test cases from literature
• Robust input validation
• Comprehensive error handling
• Convergence verification for iterative methods

🎓 Educational Applications

This repository is ideal for:

• Numerical Analysis students
• Scientific Computing courses
• Applied Mathematics laboratories
• Reference for numerical implementations

🤝 Contributions

Contributions are welcome! To contribute:

1. Fork the project
2. Create a feature branch (git checkout -b feature/AmazingFeature)
3. Commit your changes (git commit -m 'Add some AmazingFeature')
4. Push to the branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

📄 License

This project is under the MIT license.

👨‍💻 Author

Developed as part of the practical work for the Numerical Analysis course.

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