Explore transformations and automatic differentiation in this comprehensive lecture from MIT's Computational Thinking Spring 2021 series. Delve into general linear transformations, shear transformations, non-linear warping, rotations, and composite transformations. Learn about linear combinations of images and various function representations in mathematics and Julia programming. Discover automatic differentiation techniques for univariate and multivariate functions, and their applications in machine learning. Investigate vector-valued multivariate functions and their role in transformations. Gain insights into the significance of determinants in scaling and access additional resources for mastering automatic differentiation with Julia in just 10 minutes.