Computing and Visualizing Path Integrals of Vector Fields

A few months ago, I posted my path integral functions, which are included in the MATH214 package.  Recently, I came across something I’d been looking for:  a Maxima utility for visualizing vector fields.  Its in the Maxima/Share directory under drawutils.

Written in 2010 by Donald J Bindner, the commands draw_vector_field and draw_vector_field3d do almost everything I was looking for.  The drawback is that I wanted to plot the vector fields along with the integration path.  I modified those two commands slightly into versions called make_vector_field  and make_vector_field3d to produce the lists of vectors for plugging into draw2d and draw3d, so that I could include the vector fields in  bigger graphics calls.  My modifications are available here.

Here’s what the path integral command and the vector field generator look like on an example from chapter 13 of Stewart’s “Calculus Concepts and Contexts”

StewartPathIntegralExample

StewartVectorFieldIntegralPicture

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