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Applied Mathematics

Time Scale Tensor Geometric Grassmann Calculus

Edwin Gary Schasteen
This model keeps track of the formal development of Timescale calculus available at http://mds.marshall.edu/cgi/viewcontent.cgi?article=1036&context=etd&sei-redir=1&referer=http%3A%2F%2Fwww.google.com%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Dtime%2520scale%2520calculus%26source%3Dweb%26cd%3D8%26sqi%3D2%26ved%3D0CFgQFjAH%26url%3Dhttp%253A%252F%252Fmds.marshall.edu%252Fcgi%252Fviewcontent.cgi%253Farticle%253D1036%2526context%253Detd%26ei%3Dd5peUOTkOan2igLrqICoDQ%26usg%3DAFQjCNH3g65pFJ4LV38xiG7FIfRexA9uiA .

The idea is to use infinitesimals to extend Geometric and Grassmann Algebra to better flush out the details of the interpretation of an unbound vector as a "massless point at the point at infinity". Essentially, the Grassmann and Geomeric Algebra is being generalized to admit multiplication of vectors by infinitesimals, not just real numbers. Doing so allows one to define a concept of a point approaching infinity without having to use limits. This is a work in progress, and so some of the ideas in the above description will likely change as more is descovered as the research unfolds.

Mathematics Applied Mathematics Physics

  • 3 years 9 months ago