Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Stokes' Theorem Example // Verifying both Sides // Vector Calculus
Stokes' Theorem Example // Verifying both Sides // Vector Calculus Transcript and Lesson Notes
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 calcu
Quick Summary
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 calcu
Key Takeaways
- Review the core idea: 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 calcu
- Understand how Solution fits into Stokes' Theorem Example // Verifying both Sides // Vector Calculus.
- Understand how Example fits into Stokes' Theorem Example // Verifying both Sides // Vector Calculus.
- Understand how math fits into Stokes' Theorem Example // Verifying both Sides // Vector Calculus.
- Understand how Stokes' Theorem fits into Stokes' Theorem Example // Verifying both Sides // Vector Calculus.
Key Concepts
Full Transcript
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. ♡♡♡SUPPORT THE CHANNEL♡♡♡ ►Support on PATREON: https://patreon.com/DrTrefor ►MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett ►CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes 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 COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ►CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw ►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX OTHER PLAYLISTS: ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho ►Learning Math Series: https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►LaTeX: https://www.youtube.com/watch?v=-HvRvBjBAvg&list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73&index=2&ab_channel=Dr.TreforBazett SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok: http://tiktok.com/@drtrefor ►Instagram (photography based): http://instagram.com/treforphotography
Lesson FAQs
What is Stokes' Theorem Example // Verifying both Sides // Vector Calculus about?
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 calcu
What key concepts are covered in this lesson?
The lesson covers Solution, Example, math, Stokes' Theorem, Stokes Theorem.
What should I learn before Stokes' Theorem Example // Verifying both Sides // Vector Calculus?
Review the previous lessons in Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course**, then use the transcript and key concepts on this page to fill any gaps.
How can I practice after this lesson?
Practice by applying the main concepts: Solution, Example, math, Stokes' Theorem.
Does this lesson include a transcript?
Yes. The full transcript is visible on this page in indexable HTML sections.
Is this lesson free?
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