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Stokes' Theorem Example // Verifying both Sides // Vector Calculus

In this video we verify Stokes' Theorem by computing out both sides for an explicit example of a hemisphere together with a particular vector field. Stokes Theorem was introduced in the previous video in the vector calculus playlist (see below) and equated the line integral giving the circulation around the boundary curve with the surface integral of the proportion of the curl of the vector field in the normal direction. We finish with a really cool trick, where the old surface can be replaced with an entirely new one that is actually easier to computer. 0:00 Recalling Stoke's Theorem 2:40 Computing Circulation 5:02 Computing Surface Integral 10:40 Replacing the old surface with a new one 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