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 function on an interval. The distortion of area and volume is discussed, involving determinant algebra and a proof of the formula. The lecture then delves into the generalization to higher dimensions, explaining the concept through determinant algebra and the distortion of length, area, or volume. The application of the change of variables formula is demonstrated through an example involving a double integral, showcasing the process of choosing a suitable transformation to simplify the domain and calculating the integral in the new coordinate system.