Gradient
How long after swallowing a pill does it takes for a drug to enter your bloodstream? How long does it take for hot molten glass to cool? In this video, we'll see how the gradient helps us model molecular and thermal diffusion. This video is part of the Differential Equations video series. Laws that govern a system's properties can be modeled using differential equations. Hi, my name is Tom Peacock, and I'm a Professor of Mechanical Engineering here at MIT. Today I'd like to talk to you a little bit about the gradient. Partial differential equations describe the world around us. And partial differential equations often contain grad, div, and/or curl terms. In order to use these operations to describe physical phenomena, the first step is to understand what each mathematical process means geometrically and how it behaves in different examples. The gradient is an operation that takes in a scalar function and outputs a vector field. Many scalar quantities such...