A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)
In the final video of my vector calculus playlist (congrats to everyone for making it to the end!!!) I want to do a bit of an overview of the major theorems we have seen in this course - Stokes' Theorem, Divergence Theorem, Green's Theorem - all are part of a unified framework. Loosely, integrating a differential operator such as the curl or divergence along a region equates to a quantity computed just along the boundary. Exactly what quantity (flux vs circulation, say) changes depending on the set-up, but they all obey this principle. Indeed, this principle really goes back to the fundamental theorem of calculus II, which was also the root for the fundamental theorem of line integrals we saw earlier in the course.
Anyways, a HUGE thank you to everyone for following along, and I wish you best of luck in any exams!
MY VECTOR CALCULUS PLAYLIST:
►VECTOR CALCULUS (Calc IV) • Calculus IV: Vector Calculus (Line In...
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►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...
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• 5 Tips To Make Math Practice Problems...
►Cool Math Series:
• Cool Math Series
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