Integrating Sage into an Ordinary Differential Equations Course using MathBook XML

Thomas W. Judson

Stephen F. Austin State University

Theron Hitchman

University of Northern Iowa

Some Background

  • Until the 1980s, most undergraduate differential equations courses were largely a collection of techniques or time-consuming numerical approximation and infinite series methods.
  • For the most part, qualitative theory did not make it into the undergraduate classroom.
  • The situation begain to change in the 1980s and 90s with availability of computer algebra systems and good numerical software.
  • Qualitative and quantitative methods became linked, and applications beyond the fields of physics and engineering began to appear in textbooks.
  • It is now hard to imagine teaching an undegraduate ODE course without technology.

Current (and Future) Technology

  • Computer algebra systems such as Maple, Mathematica, and Sage (a steep learning curve and perhaps limited numerical routines).
  • Numerical software such as MatLab (steep learning curve and limited symbolic routines).
  • Menu-driven software and applets such as pplane, dfield, and DE Tools (easy to learn but limited in scope).
  • We believe that the next step is to start removing the boundary between software tools and textbooks and that this is best done with open source materials such as Sage and MathBook XML.

What is Open Source?

  • Definition: A textbook (or software) is open if the copyright holder explicitly allows unlimited copying, and the distribution of modified versions.
  • Open source textbooks can be licensed under Gnu Free Document License (GFDL). Another possible way to go is the Creative Commons license.
  • You have a copyright in everything you create, automatically.
  • A lifetime monopoly, plus seventy years.
  • As copyright holder, you control copies of your work.
  • An open license grants additional rights.

Open Licenses

  • Gnu Free Document License (GFDL) or the Creative Commons license.
  • Unlimited copying, forever.
  • Possibly distribute modified versions.
  • Possibly require attribution in modified versions.
  • Possibly require modified versions to have same license.
  • Do not confuse open source with “free to download.”

Why Open Source?

  • Open textbooks allow a return to a free exchange of ideas.
  • The best book for the course that you are teaching is the one that you wrote.
  • Others may find your book useful.
  • Commercially published textbooks are expensive.
    • Blanchard/Devaney/Hall. Differential Equations, 4th Edition, 4th Edition. $229.95
    • Boyce/DiPrima. Elementary Differential Equations and Boundary Value Problems, 10th Edition. $246.95
  • Print-on-demand makes physical copies of open source textbooks possible at a reasonable price ($25–35).

Open Source Textbooks Can Be Better

  • Open source textbooks can be available in a variety of formats—print, PDF, HTML, EPUB, Jupyter notebooks, Sage worksheets.
  • Open source textbooks can be read on a variety of devices—paper, desktop, laptop, smartphone, tablet, Kindle.
  • The Internet makes physical manufacturing a non-issue and distribution almost a non-issue.
  • Open licenses make digital rights restrictions unnecessary.
  • HTML versions can be enriched with Javascript widgets/applets/tools—GeoGebra (geometry demonstrations), JSXGraph (interactive graphs), WeBWorK, Skulpt (in-browser Python), Sage cells, audio and video players, MathJax.

Ordinary Differential Equations Example

We can even use Sage to solve the initial value problem \begin{align*} \frac{dP}{dt} & = kP\\ P(0) & = 1000. \end{align*}

The Sage Cell Server

What Does the MathBook XML Code Look Like?

        		<input>k, t = var('k, t')
		P = function('P', t)
		de = diff(P, t) == k*P
		solution = desolve(de, P, ivar=t, ics=[0, 1000]) 

The Ordinary Differential Equations Project

  • The Ordinary Differential Equations Project is the working title of what will be an open source ordinary differential equations textbook.
  • Details and sample sections are available at The ODE Project website:
  • This is very much a work in progress.

Learning More about MathBook XML

  • There is an upcoming workshop at the American Institute of Mathematics (April 25–29), Open textbooks in MathBook XML.
  • The conference is organized by Rob Beezer, David Farmer, and Kent Morrison.
  • Stop by the AIM booth for details.

What We are Doing Now

  • Continued development XML tools to be able quickly publish in different formats.
  • Rob Beezer and David Farmer are developing a collaborative authoring tool (CAT).
  • Rob Beezer and Alex Jordan are integrating WeBWorK into MBX:
  • AIM Editorial Board. Stop by the AIM booth at JMM in Seattle.
  • Integration with Sage and SageMathCloud. Stop by the Sage both at JMM in Seattle.


Thanks for Listening

Thomas W. Judson, Associate Professor
Department of Mathematics and Statistics
Stephen F. Austin State University
P.O. Box 13040–3040 SFA Station
Nacogdoches, TX  75962

Theron Hitchman, Associate Professor
Department of Mathematics 0506
University of Nothern Iowa
Cedar Falls, IA 50613–0506