Creating Dynamic Documents with R and Python as a Computational and Visualization Tool for Teaching Differential Equations

Abstract

The goal of this paper is to promote the use of R and Python as high-level, free, open-source programming environments that can be used as a computational and visualization tool for teaching differential equations. Both R and Python also allow for creating reproducible dynamic documents using Markdown, which combines live code, plain text, and expressions to generate different formats (pdf, html, Word), including the numerical and graphical output from the code, along with the code itself, properly formatted with minimum effort. This technology can be used for creating interactive teaching documents, randomized exams, homework and project reports, and even publication quality papers. We illustrate this technology with several examples implemented in R and Python. This approach has been classroom-tested, with some promising results. This article has online supplemental material posted on the PRIMUS website.

Keywords:

• ODE system
• R, Python
• dynamic documents
• fitting models
• linear
• nonlinear
• least squares

Acknowledgements

We thank the Referees, the Associate Editors, and the Editor-in-Chief for their constructive criticism and suggestions for enhancing the paper.

Additional information

Notes on contributors

Boyan Kostadinov

Boyan Kostadinov is an associate professor of mathematics at NYC College of Technology (CUNY) in Brooklyn, NY. Prior to academia, he held positions at Credit Suisse Securities as a quant analyst in the Global Modeling and Analytics Group, in London and New York. Before completing a Master's in Finance from Princeton University, he was an Adjunct Assistant Professor of Mathematics at UCLA, where he completed his Ph.D. in mathematics, under the supervision of V. S. Varadarajan. His main research interests are in computational problem solving at any level.

Johann Thiel

Johann Thiel is an assistant professor of mathematics at NYC College of Technology (CUNY) in Brooklyn, NY. He completed his Ph.D. in 2011 at the University of Illinois at Urbana-Champaign under the supervision of A. J. Hildebrand. Before coming to NYCCT, he worked at the United States Military Academy in West Point, NY. His main research interests are in number theory and its applications.

Satyanand Singh

Satyanand Singh is an assistant professor in the Department of Mathematics at NYC College of Technology (CUNY) in Brooklyn, NY. His areas of expertise are Number Theory, Statistics and Analysis. He teaches all levels of Mathematics Courses and is a mentor to several students in Mathematics and Interdisciplinary fields.