Divergence, Flux, and Green's Theorem // Vector Calculus

Описание: In the previous video in our Vector Calculus Playlist (   • Calculus IV: Vector Calculus (Line Integra...  ) we saw Part I of Green's Theorem, which related the local property of Curl (aka circulation density) with the global property of Circulation. Circulation, a line integral over a vector field, was compared to a double integral over the area enclosed of the Flux. In this video we look at Part II of Green's Theorem which now contrasts the local property of Divergence (aka Flux Density) with the global property of outward Flux across the boundary of a region. We are going to introduce the concept of Divergence, come up with a formula for it, and discuss the geometric idea behind why Green's Theorem is true.

0:00 Divergence vs Flux
3:50 Divergence Formula
5:22 Derivation of Green's Theorem
7:56 Statement of Green's Theorem

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