OrthogonalExpansions - A Great Maple Add-On

The typical undergraduate math course in boundary-value problems (BVPs) solves the heat, wave, and Laplace equations in one and two dimensions, and in Cartesian, polar, cylindrical and spherical coordinates. To do this, the course must treat Fourier series, Fourier-Bessel series, and Fourier-Legendre series. Such series come with extended discussions of orthogonal functions, completeness, and convergence. For the student headed for graduate studies in mathematics, these ideas are essential. But what about the science and engineering students who need exposure to boundary-value problems, but who ultimately solve such problems numerically, not analytically with techniques developed in the 18th and 19th centuries?
Maple is a marvelous tool for implementing and visualizing the solutions arising in the BVP course. It has, at top-level, all the tools needed for these calculations. So, in addition to teaching all the conceptual content of this course, an instructor also needs to bring students up to speed on how to assemble the appropriate Maple commands to make its tools useful.
This video will illustrate the third-party OrthogonalExpansions package, a great Maple add-on. Written by Dr. Sergey Moiseev, this package provides consistent commands for generating all the series needed in a first BVP course, and even goes beyond that need by providing tools for exploring various wavelet expansions. An earlier webinar, (Fourier and Other Orthogonal-Function Expansions in Maple), mentioned three add-on packages that specifically addressed creating and manipulating Fourier series, then detailed one, and introduced Moiseev's package.
This video is devoted entirely to the OrthogonalExpansions package and its utility in teaching, learning, and implementing orthogonal-function expansions one meets in the applications, including the solution of BVPs.
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