1st  Top partial differential equation topics 
Question 1: ________  

Question 2: Although ________ is said by some not to be the originator of these equations, he nevertheless derived them independently in conjunction with his molecular vortex model of Faraday's "lines of force".  

Question 3: It is only in this averaged sense that one can define quantities such as the ________ and permeability of a material.  

Question 4: This formulation allows a natural description of the ________.  

Question 5: ________  

Question 6: Maxwell's equations are generally applied to macroscopic averages of the fields, which vary wildly on a microscopic scale in the vicinity of individual atoms (where they undergo ________ effects as well).  

Question 7: There is no known magnetic analog of an electron, however recently scientists have described behavior in a crystalline state of matter known as spinice which have macroscopic behavior like ________.  

Question 8: A small computation that uses the symmetry of the ________ (i.e., the torsionfreeness of the Levi Civita connection) and the covariant constantness of the Hodge star operator then shows that in this coordinate neighborhood we have:  

Question 9: (Note: The "Faraday's law" that occurs in Maxwell's equations is a bit different than the version originally written by ________.  

Question 10: This fact was then later confirmed experimentally by ________ in 1887.  

