The CURL of a 3D vector field // Vector Calculus

One property of a three dimensional vector field is called the CURL, and it measures the degree to which the field induces spinning in some plane. This is a local property, which means there could be a different curl at each point, in contrast to a more global property like the circulation around a larger curve. We've actually seen the "kth component of curl" previously when we were talking about the analogous concept in two dimensions, and then we called it circulation density. In this video we will also look at the del operator which provides a quick way to compute the curl of a vector field. We finally note the curl of a gradient field is zero, and connect this back to the notion of a conservative vector field. 0:00 Definition of Curl 0:55 Geometric Meaning in 2D 2:16 Geometric Meaning in 3D 4:02 del operator formula 5:55 Curl of Gradient 6:43 Test for Conservative MY VECTOR CALCULUS PLAYLIST: ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line Integra...   OTHER COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►DIFFERENTIAL EQUATIONS:    • How to solve ODEs with infinite series | I...   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems Actu...   ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography