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Main Question or Discussion Point
I previously made a derivation of Neumann potential. It can be found in the pdf file below. I originally made it in the ##dx## method. It involved equations like ##dm=I dS##. My maths teacher told that such an expression has no meaning, at least in elementary calculus. However I argued that my physics textbook uses such expressions countless times. Anyway I listened to my maths teacher and changed all ##d## with ##\Delta##. The problem with this was that my final results were not perfect but approximations.
Then I heard about differentials and non standard analysis where expressions like ##dm=I dS## has meaning. However as a graduate student in Physics, I have no understanding in these topics.
I think these differentials and nonstandard analysis strongly suggest that I can go back to my previous ##dx## method.
Right now I have these two methods. Please suggest which of them is more proper and appropriate in my derivation of Neumann potential. Thanks in advance for your advice.
Then I heard about differentials and non standard analysis where expressions like ##dm=I dS## has meaning. However as a graduate student in Physics, I have no understanding in these topics.
I think these differentials and nonstandard analysis strongly suggest that I can go back to my previous ##dx## method.
Right now I have these two methods. Please suggest which of them is more proper and appropriate in my derivation of Neumann potential. Thanks in advance for your advice.
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