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. ♡♡♡SUPPORT THE CHANNEL♡♡♡ ►Support on PATREON: / 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 The Geometric Picture 3:30 Recalling Green's Theorem 5:55 Stating Stokes' Theorem COURSE PLAYLISTS: ►DISCRETE MATH: • Discrete Math (Full Course: Sets, Logic, P... ►LINEAR ALGEBRA: • Linear Algebra (Full Course) ►CALCULUS I: • Calculus I (Limits, Derivative, Integrals)... ►CALCULUS II: • Calculus II (Integration Methods, Series, ... ►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivariable Calculus (Vect... ►VECTOR CALCULUS (Calc IV): • Calculus IV: Vector Calculus (Line Integra... ►DIFFERENTIAL EQUATIONS: • Ordinary Differential Equations (ODEs) ►LAPLACE TRANSFORM: • Laplace Transforms and Solving ODEs ►GAME THEORY: • Game Theory OTHER PLAYLISTS: ►Cool Math Series: • Cool Math Series ►Learning Math Series: • 5 Tips To Make Math Practice Problems Actu... ►LaTeX: • Intro to LaTeX **Full Tutorial** Part II ... SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok: / drtrefor ►Instagram (photography based): / treforphotography
Stokes' Theorem Example // Verifying both Sides // Vector Calculus
The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus
Stokes' Theorem and Green's Theorem
Stokes' theorem intuition | Multivariable Calculus | Khan Academy
The most beautiful formula not enough people understand
What is Stokes theorem? - Formula and examples
Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007
Stokes' Theorem on Manifolds
Gauss's Divergence Theorem
I never intuitively understood Tensors...until now!
Stokes Theorem
A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)
What's The Difference Between Matrices And Tensors?
Stokes' Theorem | MIT 18.02SC Multivariable Calculus, Fall 2010
Something is jamming GPS over Europe. Here's what we found
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Everyone Guesses Wrong About This Race
Stokes' Theorem, Multivariable Calculus
