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Physics and Numerical Methods Projects

This repository contains a collection of Jupyter notebooks exploring classical mechanics and numerical methods in physics. Topics covered include calculus-based motion, curve fitting and optimization, Fourier analysis, pendulum dynamics, projectile motion, and Lennard-Jones potential simulations.

Contents

  • Calculus/: notebooks demonstrating Newton-Raphson vs. bisection methods and other calculus techniques.
  • Curve Fitting and Optimization/: implementations of Taylor series, finite difference methods, and optimization algorithms.
  • Fourier Analysis/: signal processing notebooks using real-world signals.
  • Pendulum/: nonlinear pendulum simulations comparing Runge–Kutta vs. trapezoid methods.
  • Projectile motion/: simulations of projectile motion under air resistance.
  • LJ_potential_Xe.ipynb: notebook exploring Lennard–Jones potential.
  • PHYS_451_Final_Paper 2.pdf: final report for PHYS 451.

How to Run

  1. Clone the repository.
  2. (Optional) Create a Python virtual environment and install any required packages (see notebook headers for dependencies).
  3. Launch Jupyter Notebook or JupyterLab and open any of the notebooks in the folders above.
  4. Run the cells sequentially to see outputs and interactive plots.

These notebooks were created as part of coursework and self-study in physics. Feel free to explore, modify, and run the simulations. Contributions and suggestions are welcome.