Deriving the expression of the Lorentz force using the language of a mathematician
This is a continuation of my previous “complaining” post on the language difference of mathematician vs physicists regarding the same thing.
Recent Posts
Random notes about physicists’ obsession with Einstein notations
I took a quantum physics class on Coursera this year and I found that the Mathematical language spoken by the two communities, math vs physics, are quite dif...
Several explicit constructions of the Helmholtz decomposition
Here we present two approaches to construct Helmholtz decompositions.
An identity for the continuous integral solution of the conservation law
This is an exercise in Evans, Partial Differential Equations (1st edition), page 164, problem 13.
Kernels of a bounded operator’s extension
This is a post recording my answer to a question on Math StackExchange1 with some references in L. Tartar’s book2. https://math.stackexchange...
Proof of the coercivity for Robin boundary problem
This is an exercise for finite element method most likely. Our question is:
How to impose boundary condition for 2-dimensional curl-curl weak problem
First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...
An example on the limiting case of Sobolev embedding
Sobolev embedding When $p=n$
Use a reverse method of characteristics to get the trajectories equation
This is an exercise in Evans, Partial Differential Equations (2nd edition), Chapter 10 Conservation laws.