Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus
Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus Transcript and Lesson Notes
This video contains a pair of examples where we compute the Circulation (or Flow) of a vector field around a closed curve, and then again for the Flux. But we don't do it using line integrals, we use Green's Theorem part
Quick Summary
This video contains a pair of examples where we compute the Circulation (or Flow) of a vector field around a closed curve, and then again for the Flux. But we don't do it using line integrals, we use Green's Theorem part
Key Takeaways
- Review the core idea: This video contains a pair of examples where we compute the Circulation (or Flow) of a vector field around a closed curve, and then again for the Flux. But we don't do it using line integrals, we use Green's Theorem part
- Understand how Example fits into Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus.
- Understand how math fits into Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus.
- Understand how Solution fits into Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus.
- Understand how Vector Calculus fits into Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus.
Key Concepts
Full Transcript
This video contains a pair of examples where we compute the Circulation (or Flow) of a vector field around a closed curve, and then again for the Flux. But we don't do it using line integrals, we use Green's Theorem parts I and II respectively to do the computation. This let's us compute a double integral over a region of either the circulation density (aka curl) or flux density (aka divergence) respectively. In the case of a square which is relatively easy to compute the double integral for, this is a significant advantage. Check out the previous videos in the vector calculus playlist for the geometric motivation of Green's Theorem. 0:00 Green's Theorem 1:28 Circulation Example 3:49 TYPO! Should substract partial M wrt y, not x. 4:00 Example continued 5:50 Flux Example MY VECTOR CALCULUS PLAYLIST: ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER 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 ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography
Lesson FAQs
What is Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus about?
This video contains a pair of examples where we compute the Circulation (or Flow) of a vector field around a closed curve, and then again for the Flux. But we don't do it using line integrals, we use Green's Theorem part
What key concepts are covered in this lesson?
The lesson covers Example, math, Solution, Vector Calculus, Vector Field.
What should I learn before Example: Using Green's Theorem to Compute Circulation & Flux // 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: Example, math, Solution, Vector Calculus.
Does this lesson include a transcript?
Yes. The full transcript is visible on this page in indexable HTML sections.
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