Change of Variables Theorem

This lecture covers the change of variables formula in higher dimensions, starting with a reformulation for one dimension and examining the local effect of a C1 function on area volume. The proof of the change of variable formula is presented, discussing cases of G increasing and decreasing. The lecture delves into determinant algebra and generalizes the concept to higher dimensions, showcasing the distortion of area or volume. The application of the theorem is demonstrated through an example involving the calculation of an integral over a given region using the change of variables technique.