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 Ca...
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►LINEAR ALGEBRA: • Linear Algebra (Full C...
►CALCULUS I: • Calculus I (Limits, De...
► CALCULUS II: • Calculus II (Integrati...
►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivar...
►DIFFERENTIAL EQUATIONS: • How to solve ODEs with...
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[@DrTrefor]

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[@DrTrefor]

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[@DrTrefor]

So glad you enjoyed it!

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Glad you enjoyed it!

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THank you! And good luck in your exam in feb:)

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You're very welcome!

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[@DrTrefor]

Glad you enjoyed!! I actually just ordered that hoodie myself in the "Large" and I should be getting the first samples very soon. From what I can tell from the distribution folks these fit pretty standard, but I always like going slightly large as will shrink a little bit washes.

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[@DrTrefor]

Glad to hear that!!

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Congrats on making it to the end!

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[@DrTrefor]

Glad it helped!

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Got my Vector Calculus exam next month. This will be my third time sitting it. Your videos have helped my understanding so much, just finished the playlist. Thankyou Dr Bazett!!!

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Thank you so much!

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Great playlist

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You are an awesome teacher. You just visualise vector calculus. Finally i ends this, before this i was struggling so much.

[@DrTrefor]

Congrats on making it to the end!

[@swaroopdewal4626]

Thank you so much !!

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Thank you so much!!

[@davidgillies620]

This was a nice saunter through topics I covered first year of my physics degree 30 years ago. One thing I would like to see as an extension is the form of the differential operators in non-Cartesian coordinate systems (cylindrical, paraboloidal, generalised curvilinear). From a computational standpoint they can be very useful. Plus you get a toe in the door when it comes to tensor calc.