The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus скачать в хорошем качестве

The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus

In this video we get to the last major theorem in our playlist on vector calculus: The Divergence Theorem. We've actually already seen the two-dimensional analog when we studied the Divergence or Flux form of Green's Theorem. Now we upgrade to the three-dimensional situation where we have a closed, smooth surface and a vector field. The question is, to what degree is there outwards flux of the vector field across this surface? The divergence theorem allows this global property to be compared to a triple integral over the enclosed volume of the divergence of the vector field; that is, adding up a local property of the divergence. Much like Stokes' Theorem before it, the divergence theorem is another example where integrating a differential operator along an entire region gives us information (in this case outward flux) on the boundary of that region. 0:00 Divergence of a Field 2:49 Recalling Green's Theorem 4:40 Divergence Theorem 6:20 Conditions 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