The lesson starts with a discussion on functional analysis, or functional spaces. To be more specific, the discussion is on Hilbert spaces. Many of the terms and phrases like Heaviside function and, the meaning of functions being square-integrable, are explained. Regularity of functions is also explained.
The lesson continues from where the last video ends and show that the displacement field is also square-integrable. Some examples of H1 functions are shown. Even if the function has jumps, it can be squared and integrated; therefore the Heaviside and discontinuous functions can be squared and integrated. This discussion helps to explain bounds for function and notion of regularity for derivatives.