During my sophomore year at USC, I took MATH 458: Numerical Methods, a class in which we completed a series of projects in Python and Matlab that entailed significant numerical computations, error and data visualization, animations, and post-project write-ups. I've compiled them all here.
In this project, I utilized Python to test different mathematical methods of calculating the roots of a quadratic polynomial and compared them to the quadratic formula. As it turns out, methods such as a inverse-root approach and a Taylor series approximation have both benefits and drawbacks to the quadratic formula.
In this project, I utilized Matlab to implement Newton's method to solve for the solutions to the equation z^4-1=0. By vectorizing the real and complex parts of the solutions, the results led to a variety of beautiful fractals. These fractals highlight interesting properties about the regions near a solution as well as axes that are equidistant from two solutions.
In this project, I utilized Matlab to implement polynomial spline techniques to animate a smiley-face. The technique used is to create three images of an animation and then use polynomial spline to effectively insert frames in-between the sequence of pictures.