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We're finally at one of the core theorems of vector calculus: Stokes' Theorem. We've seen the 2D version of this theorem before when we studied Green's Theorem which compared the circulation around a 2D curve to integrating the circulation density along the region. In contrast, Stokes Theorem is the three-dimensional generational to compare the circulation of a 3D curve in some vector field to the integral over the region of the curl of the vector field (note: the kth component of curl is what we used to call the circulation density). In this video we build up the geometric conceptual understanding of why the curl of a vector field would relate to the line integral along it's boundary, and then finally state the theorem. 0:00 The Geometric Picture 3:30 Recalling Green's Theorem 5:55 Stating Stokes' Theorem 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