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location Bethlehem, Pennsylvania
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visits member for 1 year, 1 month
seen Aug 3 at 16:17

I'm a graduate student in the mathematics department at Lehigh University.

My interests are in differential geometry, geometric analysis, and recently various aspects of physics.


Aug
18
awarded  Yearling
Jul
9
awarded  Scholar
Jul
9
accepted Rigorous underpinnings of infinitesimals in physics
Jul
9
awarded  Nice Question
Jul
9
comment Rigorous underpinnings of infinitesimals in physics
By text I had meant The Theoretical Minimum, where my issue first cropped up; I greatly enjoyed reading your entire answer. I speak the language of Lie groups, manifolds, tensors, Hilbert spaces, etc. etc. quite well, it's just that physicists can say simple things in a language I'm not totally comfortable with and I get all backwards!
Jul
8
awarded  Supporter
Jul
8
comment Rigorous underpinnings of infinitesimals in physics
This answer was great. If only the text said "infinitesimals=linear approximation" I would have been fine! As a technical point, where you first define $\hat{T}_{\epsilon}$, the right hand side demands that these transformations occur on a space with an additive structure, so in general manifolds and topological spaces don't seem to support such a concept as stated. Also, the space of transformations where $\epsilon$ takes values would have to have a smooth structure. But none of this has bearing on the particular case I was interested in.
Jul
8
comment Rigorous underpinnings of infinitesimals in physics
I was really hoping there was some way the argument could be phrased in terms of standard calculus. Is it the case that arguments with infinitesimals like this always go outside the realm of ordinary calculus?
Jul
8
awarded  Student
Jul
8
asked Rigorous underpinnings of infinitesimals in physics