This video reflects my answers to the questions: What are differential forms, what arithmetic do they admit, what is an exterior derivative of a form, and how are the answers to these questions illuminated by known results in vector calculus?
The questions started from a desire to understand Geometric Algebra with its multiplication of vectors, its exterior derivative, and its claim to encompass all of vector calculus and a whole lot more. But the exterior derivative was unfamiliar. Ah, a differential form admits an exterior derivative, so perhaps by knowing something about the differential form and its exterior derivative, light could be shed on the ultimate target of Geometric Algebra.
For this, one wants an implementation of Clifford algebras, something available in Maple's DifferentialGeometry package where an implementation of the differential form, its arithmetic, and its exterior derivative can also be found. Thus, this webinar will demonstrate both how to access differential forms and their manipulations in Maple, and with by-hand calculation. As we do with our students, we rely on examples to clarify and to "drive home."
This is but a first step along a way that might prove to have considerable reach.
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