Questions, Comments, or the like? Join us join on Discord: https://discord.gg/GnE7XcVs for live and after lecture chats. For more info on the Julia Programming Language, follow us on Twitter: https://twitter.com/JuliaLanguage Contents 00:00 Introduction by MIT's Prof. Alan Edelman 00:35 Agenda of lecture 01:30 Transformations and automatic differentiation 02:30 General Linear Transformation 02:46 Shear Transformation 04:48 Non-Linear Transformation (Warp) 06:12 Rotation 06:25 Compose Transformation(Rotate followed by Warp) 07:28 More Transformations(xy, rθ) 08:01 Linear and Non-Linear Transformations 09:15 Linear combinations of Images 09:45 Functions in Maths and in Julia (short form, anonymous and long form) 14:52 Automatic Differentiation of Univariates 21:16 Scalar Valued Multivariate Functions 27:10 Automatic Differentiation: Scalar valued and Multivariate Functions 30:20 Minimizing "loss function" in Machine Learning 31:35 Transformations: Vector Valued Multivariate Functions 39:42 Automatic Differentiation of Transformations 14:24 But what is a transformation, really? 49:50 Significance of Determinants in Scaling 53:03 Resource for Automatic Differentiation in 10 minutes with Julia S/O to https://github.com/r2cp for the video timestamps! Want to help add timestamps to our YouTube videos to help with discoverability? Find out more here: https://github.com/JuliaCommunity/YouTubeVideoTimestamps Interested in improving the auto generated captions? Get involved here: https://github.com/JuliaCommunity/YouTubeVideoSubtitles