Programming Projects - a collection of the numerically analyzed programs.
Every program is followed by an appendix full of MATLAB or C++ function codes and scripts. I wrote the programs my senior year at UC Davis and they appear below from the most recent to oldest. You will see a progression in my use of graphs and implementation of functions as well as a shift from group reliance to independent work.
Click an image to view the program in a new tab as a PDF.
Computer Problem #1
In this program you will observe round-off and truncation error at its finest.
Interpolation Package
This program calculates the coefficients for interpolating polynomials.
(Group work)
Analysis of Interpolating Polynomials: Spline vs. Hermite
This program will analyze the errors between using cubic spline interpolating polynomials and hermite interpolating polynomials.
(Group work)
Analysis of Composite Simpson’s, Romberg, and Quadrature Methods
This program observes iterative methods error based on a constant step size and shows how to choose a small enough step size based on a given tolerance.
(Group work)
Analyzing Gaussian Elimination to Solve Linear Systems of Equations
Comparing algorithms for solving the linear system Ax = b using the methods of Gaussian Elimination with backward substitution, partial pivoting and scaled partial pivoting.
Analysis of Methods to Compute Solutions to Nonlinear Equations
This program will investigate the use of iterative methods to compute solutions to nonlinear equations. The test function in this program is associated with estimating the surface temperature of a star.
Computing Eigenvalues
obtained by solving finite element problems in two dimensionsAnalyzing the Modified Power Method on special sparse matrices similar to the one in the picture that is .
Analysis of Euler's Method and Modified Euler's Method
This program observes numerical approxiamtions to initial value problems using a method Leonhard Euler created in the 1700s and a modified version of his method that turns out to be extremely accurate.
The Tacoma Narrows Bridge
This project is an example of experimental mathematics. Equipped with reliable ODE solvers, numerical trajectories for various parameter settings can illustrate the types of phenomena available to this model. Differential equation models can predict behavior and shed light on mechanisms in scientific and engineering problems.