Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus
We're finally at one of the core theorems of vector calculus: Stokes' Theorem. We've seen the 2D version of this theorem before when we studied Green's Theorem which compared the circulation around a 2D curve to integrating the circulation density along the region. In contrast, Stokes Theorem is the three-dimensional generational to compare the circulation of a 3D curve in some vector field to the integral over the region of the curl of the vector field (note: the kth component of curl is what we used to call the circulation density). In this video we build up the geometric conceptual understanding of why the curl of a vector field would relate to the line integral along it's boundary, and then finally state the theorem.
0:00 The Geometric Picture
3:30 Recalling Green's Theorem
5:55 Stating Stokes' Theorem
MY VECTOR CALCULUS PLAYLIST:
►VECTOR CALCULUS (Calc IV) • Calculus IV: Vector Calculus (Line In...
OTHER COURSE PLAYLISTS:
►DISCRETE MATH: • Discrete Math (Full Course: Sets, Log...
►LINEAR ALGEBRA: • Linear Algebra (Full Course)
►CALCULUS I: • Calculus I (Limits, Derivative, Integ...
► CALCULUS II: • Calculus II (Integration Methods, Ser...
►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivariable Calculus ...
►DIFFERENTIAL EQUATIONS: • How to solve ODEs with infinite serie...
OTHER PLAYLISTS:
► Learning Math Series
• 5 Tips To Make Math Practice Problems...
►Cool Math Series:
• Cool Math Series
BECOME A MEMBER:
►Join: / @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): / treforbazett
►Instagram (photography based): / treforphotography
Смотрите видео Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus онлайн без регистрации, длительностью часов минут секунд в хорошем качестве. Это видео добавил пользователь Dr. Trefor Bazett 11 Декабрь 2020, не забудьте поделиться им ссылкой с друзьями и знакомыми, на нашем сайте его посмотрели 176,857 раз и оно понравилось 4.8 тысяч людям.