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Math and Physics Educational Platform - Summary

Project Overview

A FastAPI-based backend providing endpoints for mathematical calculations, physics simulations, and data visualizations.

Key Features

  • Complex function visualization
  • Fourier transform analysis
  • Differential equation solver
  • Projectile motion simulation
  • Damped harmonic motion simulation

File Structure Summary

  1. app/main.py

    • Main FastAPI application
    • Sets up CORS middleware
    • Includes routers for math and physics endpoints

  2. app/core/config.py

    • Configuration settings using Pydantic
    • Defines project name, version, and allowed origins

  3. app/api/math_routes.py

    • FastAPI router for math-related endpoints
    • Endpoints:
      • Complex function visualization
      • Fourier transform
      • Differential equation solver

  4. app/api/physics_routes.py

    • FastAPI router for physics-related endpoints
    • Endpoints:
      • Projectile motion
      • Damped harmonic motion

  5. app/services/math_service.py

    • Contains functions for mathematical computations
    • Implements:
      • Complex function plotting
      • Fourier transform calculation
      • Differential equation solving

  6. app/services/physics_service.py

    • Contains functions for physics simulations
    • Implements:
      • Projectile motion calculation
      • Damped harmonic motion simulation

  7. app/utils/plotting.py

    • Utility function to convert Matplotlib figures to base64 encoded strings

  8. requirements.txt

    • Lists all Python dependencies

  9. Dockerfile

    • Instructions for building a Docker image of the application

  10. .env

    • Environment variables for configuration

Key Code Snippets

  1. Complex Function Visualization (math_service.py):

    def generate_complex_function_plot(function_type: str, x_range: tuple, y_range: tuple):
    # Creates contour plots for magnitude and phase of complex functions

  2. Fourier Transform (math_service.py):

    def generate_fourier_transform(signal_type: str, frequency: float, duration: float, sample_rate: float):
    # Generates time-domain signal and its Fourier transform

  3. Differential Equation Solver (math_service.py):

    def solve_differential_equation(equation_type: str, parameters: dict, initial_conditions: list, t_span: list):
    # Solves different types of ODEs using scipy.integrate.odeint

  4. Projectile Motion (physics_service.py):

    def simulate_projectile_motion(initial_velocity, angle_degrees, gravity=9.8):
    # Calculates and plots projectile motion

  5. Damped Harmonic Motion (physics_service.py):

    def simulate_damped_harmonic_motion(mass: float, spring_constant: float, damping_coefficient: float, initial_displacement: float, initial_velocity: float, duration: float):
    # Simulates damped harmonic oscillator using odeint

API Endpoints Summary

  1. POST /api/math/complex_function

    • Visualizes complex functions

  2. POST /api/math/fourier_transform

    • Performs Fourier transform on various signal types

  3. POST /api/math/differential_equation

    • Solves and plots solutions for different types of ODEs

  4. POST /api/physics/projectile_motion

    • Simulates projectile motion

  5. POST /api/physics/damped_harmonic_motion

    • Simulates damped harmonic motion

Setup and Running

  1. Install dependencies: pip install -r requirements.txt
  2. Run server: uvicorn app.main:app --reload
  3. Access API at http://localhost:8000

Docker Support

  • Build: docker build -t math-physics-platform .
  • Run: docker run -p 8000:8000 math-physics-platform