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

Published: 14 December 2020
on channel: Dr. Trefor Bazett
132,520
3.2k

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 In...  

OTHER COURSE PLAYLISTS:
►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...  
►LINEAR ALGEBRA:    • Linear Algebra (Full Course)  
►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...  
► CALCULUS II:    • Calculus II (Integration Methods, Ser...  
►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...  
►DIFFERENTIAL EQUATIONS:    • How to solve ODEs with infinite serie...  

OTHER PLAYLISTS:
► Learning Math Series
   • 5 Tips To Make Math Practice Problems...  
►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  


Watch video The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus online without registration, duration hours minute second in high quality. This video was added by user Dr. Trefor Bazett 14 December 2020, don't forget to share it with your friends and acquaintances, it has been viewed on our site 132,520 once and liked it 3.2 thousand people.