Advanced Analysis II: Length of Continuously Differentiable Paths

This lecture covers the concept of the length of a path defined by a function f: [a, b] -> R² that is continuously differentiable on [a, b]. The instructor revisits the definition and properties of such paths, emphasizing the importance of continuity and differentiability. The lecture explores the calculation of path length using integrals and parametrizations, discussing the Euclidean norm and the concept of curve equivalence classes. Various examples and applications are presented to illustrate the theoretical concepts, including the calculation of path length for different types of functions and parametrizations.