L2-Part2of3 - Preliminary Theory: Vector Spaces, Normed Spaces, Continuity of Functionals
This lecture continues discussing the mathematical preliminaries required to understand the theory of the first variation by introducing the concept of a norm (or size) functional and gives examples of many common normed vector spaces (normed linear spaces) used in mathematics and focuses on specific spaces used to study problems in the calculus of variations.
The concept of a norm or ''size'' functional is crucial to properly defining the notion of the derivative in infinite dimensional spaces. It allows us to properly set up the derivative of a functional.