# UGA Undergrad Course Projects

Here are four of the projects I completed during my coursework at UGA.

## Image Compression

For my **Numerical Analysis II** final, I implemented Principal Component Analysis (PCA) to perform mathematical image compression. The class’s algorithms were ranked based on visual image recovery and mine won the 50% compression category. The project report introduces the reader to PCA, discusses an OS X Automator program for improving the compression algorithm, and provides the Mathematica code for compressing any arbitrary image.

## Railgun Simulation

For my **Numerical Analysis II** midterm, I simulated the launch of a railgun projectile from Pearl Harbor, HI to a hostile watercraft 250 miles due west. The project report includes the relevant physical assumptions that were made, the system of ordinary differential equations modeling the projectile’s path, the code to run the simulation, and discussion and visualization of the results.

## Path Minimization

For my **Numerical Analysis I** final, I wrote Mathematica code that implements a minimization algorithm to determine the shortest possible distance over the San Gabriel mountain range in California using topological data provided by National Elevation Dataset. The project report includes a description of the project, relevant code, and plots of the path over the given terrain.

## Numerical Ordinary Differential Equation Solution and Integration Project

For my numerical project in **Mathematical Methods in Physics**, I developed and programmed a forty-sheet Excel workbook to solve for the solutions to a Hydrogen Combustion Model during the “ignition” and “explosive growth” phases. The report includes discussion and analysis of numerical error when computing complex integrals.