The Gradient Operator in Vector Calculus: Directions of Fastest Change & the Directional Derivative

This video introduces the gradient operator from vector calculus, which takes a scalar field (like the temperature distribution in a room) and returns a vector field with the direction of fastest change in the temperature at every point. The gradient is a fundamental building block in vector calculus and it is also used more broadly in optimization and machine learning algorithms, for example in gradient descent and stochastic gradient descent. We also discuss the directional derivative.

@eigensteve on Twitter
eigensteve.com
databookuw.com

This video was produced at the University of Washington

%%% CHAPTERS %%%
0:00 Introduction & Overview
5:02 Example: Temperature Gradient
7:30 The Directional Derivative
10:09 Example: Gravitational Potential Field