Background
I'm trying to understand a document I found online. The reason I'm reading it is because I need to translate the Nedelec element into code for my research.
Problem
My background is in Food Science, which is mostly biology/chemistry. I do have high interest in math, but my highest math education (classes + online self learning) is only ODE and Calculus 3. I tried reading the document, but I do not understand most of it.
In the following section, I list certain parts of the document I have difficulty with. While a direct answer is appreciated, if you could share with me what topic/book I should study so that I can have a deep understanding and appreciation for the concept involved, you will have my unending gratitude.
Specific examples from the document
- Equation (4.2) : I don't understand the ( , )0, Ω notation. Is this set theory?
- Equation (4.8) : From what I understand, the caret-like symbol (^) is sort of like a cross-product, but it really means a wedge product, which I don't know where to study about it. Is this exterior algebra?
- The proof section just slightly below (4.9) : Why would finding a solution to zh prove that curl(qh) belongs to the Lebesgue space? Also, the first part of the proof involves a combination of integration by parts and Stokes theorem, but how did he suddenly jump into that bloated integrand with lots of wedge products?
Thank you for your time and help!