Divergence, Flux, and Green's Theorem // Vector Calculus
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
Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus
The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus
Curl, Circulation, and Green's Theorem // Vector Calculus
Best Explanation of Gradient, Divergence and Curl
Stokes' Theorem and Green's Theorem
The most beautiful formula not enough people understand
Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus
Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus
How Maxwell's Equations Were Discovered
Finding the scalar potential function for a conservative vector field // Vector Calculus
William Dunham, A tribute to Euler
The Divergence Theorem, a visual explanation
This is 0 Elo Chess
Terry Tao, Ph.D. Small and Large Gaps Between the Primes
Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007
Green's Theorem, explained visually
