Technical Reports
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Technical Reports

This page contains the technical reports written by the students who participated in the 2002 Summer Institute in Mathematics for Undergraduates (SIMU) at the University of Puerto Rico – Humacao.  SIMU, the largest National Science Foundation (NSF) Research Experience for Undergraduate (REU) in mathematics, is a six-week research program currently in its fifth year.

The twenty-four students who participated in SIMU 2002 came from universities in Arkansas, California, Illinois, Louisiana, Massachusetts, Nebraska, New York, Oregon, Pennsylvania, Puerto Rico, Texas, Utah, and Washington.  They worked in groups of three on undergraduate research projects in two exciting areas in the mathematical sciences.  The projects in the area of Computational Mathematics Applied to Fluid Motion were directed by Professor Ricardo Cortez from Tulane University.  Professor Cortez was assisted by Angela Gallegos and Alexander Villacorta, graduate students at the University of California, Davis and the University of California, Santa Barbara respectively.  The projects in the area of Integrals: An Introduction to Research in Mathematics were directed by Professor Víctor H. Moll from Tulane University.  Professor Moll was assisted by Christopher Duncan and Dante V. Manna, graduate students at Tulane University.  The reports contained herein are the culmination of hundreds of hours of work by the SIMU 2002 students and staff during the six weeks of the program.  Because the quantity of work produced by these students during the program is so great and because of other time constraints, these technical reports perhaps best can be classified as “not-fully edited”.  

SIMU’s primary target population is Latino and Native American students from the United States and Puerto Rico.  The goal of SIMU is simple: to increase the number of Chicanos/Latinos and Native American earning Master’s, Ph.D’s, and pursuing research careers in the mathematical sciences.  We believe that one way to try to achieve this goal is by bringing together a group of talented students and challenging them to engage in quality mathematical research in an intense, supportive and collaborative environment.  

The 2002 SIMU was funded by grants from the National Security Agency (NSA Grant MDA904-02-1-0006) and the National Science Foundation (NSF Grant DMS-9987901).  Other support was provided by (of course) the University of Puerto Rico – Humacao and the National Aeronautics and Space Administration (NASA).  A program like SIMU could not take place without the generous support of many individuals.  We take this opportunity to thank Barbara Deuink, National Security Agency; Lloyd Douglas, National Science Foundation; Manuel Gómez, Vice President for Research and Academic Affairs, University of Puerto Rico; Pablo V. Negrón, Professor and Chair of Mathematics (and SIMU Co-Founder), University of Puerto Rico – Humacao; and James Schatz, Chief of Mathematics Research, National Security Agency.

Herbert A. Medina and Ivelisse Rubio
2002 SIMU Co-Directors
Humacao, PR, August 2002

Note on Format: All the reports can be downloaded in Adobe Portable Document Format (PDF) format.*  Each report contains an abstract.  Two of the reports contain bitmap (BMP) graphics that did not convert to PDF; the graphics also can be downloaded below. 

If you would like a paper copy of any of the reports, please send your request to

* Adobe Acrobat Reader is freeware that allows you to view and print PDF files; it can be downloaded from the Adobe website

High-Order Blobs and Particle Methods for Dispersive Partial Differential Equations

Jamie A. Burke, University of California, Los Angeles
Christopher N. Gallo, University of Chicago
Alejandro Pérez, University of California, Santa Barbara


Comparison of Numerical Methods for Solving the Convection-Diffusion Equation in 2D

Edgar Lobaton, Seattle University
Ubaldo Rodríguez Bernier, University of Puerto Rico - Cayey
Leah Shilling, Slippery Rock University


A Computational Model of Caudal Fin Undulations Using Impulse Methods

Jamie N. Bailey, Westminster College, Salt Lake City
Apolinar Gallardo, Los Angeles Valley College
Tiffany Psemeneki, Boston University

   Report       Figures 4, 5.

A Computational Model of the Flagella

Oscar Del Valle, Cosumnes River College
Heather Flores, University of Nebraska - Lincoln
Stefan Mendez-Diez, University of Chicago

   Report        Figure 5 left and 5 right

A Symbolic Evaluation of Integrals of Rational Functions

Danielle Brooker, Keuka College
Aaron Cardona, Ouchita Baptist University
José G. Miranda, University of Puerto Rico - Cayey


Asymptotics of a Transformation on the Space of Rational Functions

M. Sage Briscoe, Tulane University
Laura Jiménez, California State University, Fullerton
Luis A. Medina Rivera, University of Puerto Rico - Humacao


Coefficients and Roots of a Family of Polynomials: Divisibility and Asymptotics

Danielle Heckman, Keuka College
María Osorio, Mount Holyoke College
Juan Carlos Trujillo, Cosumnes River College


Dynamic Properties of a Rational Landen Transformation

Benjamín Alemán, University of Oregon
Angela Gallegos, University of California, Irvine
Sandra Moncada, Texas A&M International University



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