Integration and ODEs: Implementation and Applications (in memory of Albert Rich)

Organizers:

David Jeffrey, Western University, Canada
David Stoutemyer, University of Hawaii, USA
Michael Wester, University of New Mexico, USA
Michel Beaudin, ETS, Canada

Overview:

Although indefinite integration is a well-studied area, new techniques are still being developed. In addition, these new techniques allow new applications. For example, the correct integration of piecewise defined functions and discontinuous functions allows us to solve differential equations containing discontinuous effects. This session will offer a venue for developers and users to discuss principles, techniques (for example, rule-based solutions) and examples. We also wish to consider implementation and applications of ODEs, especially when aided by computer algebra in ways like the above.

One main hope for this session is to create a forum for participants in the late Albert Rich's "Rubi" integration project. This project has shown that great improvements in the performance of integration systems are still possible. The developers have been interacting through email and on-line discussions until now. We hope to get them together in one room to discuss progress. We are also hopeful to hear personal reminiscences of Albert Rich and the Soft Warehouse, and the contributions he inspired and demonstrated.

There are other groups working on integration. Some relevant work by Sam Blake on pseudo-elliptic integrals has been performed recently. Another example is Victor Moll's book "Irresistible integrals". If we can attract more interest, then an interesting session will result. There will be an overlap with the educational session because problems such as a parachutist falling and then opening a parachute are examples of educational problems that have been discussed in previous ACA meetings. Also, if computer algebra systems were not developed with the primary intention of being used in teaching, it must be admitted that they have become essential today in many mathematics and science courses. Despite this fact, many calculus textbooks still ignore the contribution that these systems have had; integration is such an example and Rubi has contributed in this direction.

Other topics to be considered:

• How to implement comprehensive continuous antiderivatives of integrands containing parameters.
• The choice of a specific antiderivative will have an effect on the result the "dsolve" command of a CAS will yield. For example, use Maple to solve the following ODE: y'(x) = 1/(a^2-x^2) with the initial condition y(x0) = yo. Sometimes, you will get an arctanh, sometimes logs, sometimes the imaginary unit will appear on the screen. Al of this can confuse the (young) user.

If you are interested in proposing a talk, please send an abstract to Michel Beaudin who will then restribute it to the other organizers. Please use this LaTeX template for your abstract and send both the LaTeX source and a compiled PDF version.

Talks

1. Albert Rich 1949-2023
   (David J. Jeffrey and David Stoutemyer, Canada and USA)
2. Do like Rubi : don't be afraid of using arctanh !
   (Michel Beaudin, Canada)
3. A future for Rubi?
   (A. C. Norman and David J. Jeffrey, UK and Canada)
4. Rubi : Solving Integrals, One Rule at a Time
   (Patrick Scheibe, Germany via Michel Beaudin, Canada)

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ACA'2024 Conferences on Applications of Computer Algebra main page