W2_L6: Multivariate calculus: linear approximation & applications

Описание: Welcome to Week 2 Lecture 6 of the course "Machine Learning Foundations" by Profs. Harish Guruprasad Ramaswamy, Arun Rajkumar, and Prashanth LA.
Full Course: https://study.iitm.ac.in/ds/course_pa...

Video Overview
In this lecture, we deepen our understanding of gradients by focusing on their geometric and intuitive interpretations. Building on the computational definitions from the previous class, we explore gradients through linear approximations, tangent planes, and contour sets.We then move into directional derivatives and the Cauchy-Schwarz inequality, highlighting how the gradient identifies the direction of steepest ascent. The lecture also introduces descent directions, higher-order approximations, and critical points, setting the stage for optimization methods widely used in machine learning. By the end, you’ll gain a stronger geometric intuition for gradient-based optimization techniques.

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