I have been studying lagrangian and hamiltonian mechanics, and I found some resources online that are very rigorous and formal. I don't understand how to read the definitions.
http://www.ks.uiuc.edu/Services/Clas...m_PDF/chp1.pdf
You can see in the document that they start by defining a functional, and then they define differentiability of a functional, and so on. I just don't understand all of the notation. Are there any online sources that I can turn to? Where can I learn this notation?