Differentiable Functions in R²

This lecture covers the concept of differentiable functions in R², focusing on the representation of vector fields and local copies of R². It also discusses the transformation of coordinates and the derivative of the reciprocal function. The instructor explains the definition of functions in R² and their bijective properties, emphasizing the importance of class C¹ functions. The lecture concludes with a detailed explanation of the derivative of the reciprocal function and the concept of homeomorphism. Various examples and demonstrations are provided throughout the lecture.