Dr. Trefor Bazett Curl, Circulation, and Green’s Theorem // Vector Calculus

🎯 Загружено автоматически через бота: 🚫 Оригинал видео: 📺 Данное видео принадлежит каналу «Dr. Trefor Bazett» (@DrTrefor). Оно представлено в нашем сообществе исключительно в информационных, научных, образовательных или культурных целях. Наше сообщество не утверждает никаких прав на данное видео. Пожалуйста, поддержите автора, посетив его оригинальный канал. ✉️ Если у вас есть претензии к авторским правам на данное видео, пожалуйста, свяжитесь с нами по почте support@, и мы немедленно удалим его. 📃 Оригинальное описание: his video is all about Green’s Theorem, or at least the first of two Green’s Theorem sometimes called the curl, circulation, or tangential form. Consider a smooth, simple, closed curve that encloses a region in the 2D plane, together with a Vector Field. One thing we could do is compute the circulation along that curve, which would be a large-scale or global property. Separately, at any point in the enclosed region we could compute the circulation density or curl at that point, which is a small-scale or local property. The power of Green’s Theorem is that it relates these two concepts. The circulation or line integral along the curve (i.e. which only depends thus on the boundary of the region) is equal to the double integral over the entire region of the circulation density. Amazing! MY VECTOR CALCULUS PLAYLIST: ►VECTOR CALCULUS (Calc IV) Curl vs Circulation Derivation Green’s Theorem OTHER COURSE PLAYLISTS: ►DISCRETE MATH: ►LINEAR ALGEBRA: ►CALCULUS I: ► CALCULUS II: ►MULTIVARIABLE CALCULUS (Calc III): ►DIFFERENTIAL EQUATIONS: OTHER PLAYLISTS: ► Learning Math Series ►Cool Math Series: BECOME A MEMBER: ►Join: MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: SOCIALS: ►Twitter (math based): ►Instagram (photography based):