Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus

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

4.0 (0)

9 learners

What you'll learn

This course includes

5.3 hours of video
Certificate of completion
Access on mobile and TV

Summary

Keywords

Example math Solution Vector Calculus Vector Field curl divergence flux circulation circulation density flux density Green's Theorem

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