Explore the concept of divergence in vector calculus through this 21-minute video lecture. Learn how the divergence operator transforms a vector field into a scalar field, quantifying local expansion or contraction at every point. Understand the fundamental role of divergence in vector calculus, its properties as a linear operator, and examine examples of positive, negative, and zero divergence. Discover how vector fields relate to differential equations and grasp the connection between divergence, gradient, and the Laplacian operator. Gain insights into this essential building block of vector calculus, presented by Steve Brunton.
Overview
Syllabus
Introduction & Overview
The Divergence is a Linear Operator
Example of Positive Divergence
Example of Negative Divergence
Example of Zero Divergence
Vector Field is a Differential Equation
Recap
Divergence of a Gradient is the Laplacian
Taught by
Steve Brunton
