## 6527 Reputation

17 years, 112 days
University of British Columbia
Associate Professor Emeritus

## Joining the team...

Maple

I'm happy to announce that, having retired from University of British Columbia, I've joined Maplesoft as a Content Developer.  Some of my work will be appearing in the Application Center from time to time, and I'll announce them here.  If you have any suggestions for topics you'd like to see in the Application Center, I'd be interested in seeing them.

## Application: Kepler 16...

Maple

I have uploaded to the Maplesoft Application Center a worksheet exploring the orbital dynamics of the recently discovered Kepler 16 system, where a planet orbits a double star.

## Maple Math not working in Primes...

Maple

Click Maple Math, enter x^2/(1+x).   The Preview disappears as soon as I press "/", and the result is not pretty-printed.

## Calculus to the Rescue...

This is something I produced for my Calculus students.  It is based on some actual research in Biology by Larry Dill of Simon Fraser University, showing that the escape response of the Zebra Danio, a small tropical fish, is triggered when the rate of change of the visual angle of a potential predator becomes too large (see ugrad.math.ubc.ca/coursedoc/math102/keshet.notes/chapter11Notes.pdf, section 11.2).
Here's my Maple document.

## When Is Runge-Kutta Exact?...

A recent posting of Mario Lemelin showed that Maple's default numerical methods produced wrong results for a certain differential equation.  Further investigation revealed that the problem stemmed from the fact that the fourth and fifth order Runge-Kutta methods used within the rkf45 method both produce the same (exactly correct) result at any step size, causing the adaptive error analysis to go badly wrong.  This leads to the question: when do Runge-Kutta methods produce exact results for arbitrary step sizes and initial conditions?

For a partial answer, see this worksheet:

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