Integration on manifolds | Duality theories | Differential forms | Theorems in calculus | Theorems in differential geometry | Differential topology
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus. In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, and Stokes' theorem is the case of a surface in . Hence, the theorem is sometimes referred to as the Fundamental Theorem of Multivariate Calculus. Stokes' theorem says that the integral of a differential form over the boundary of some orientable manifold is equal to the integral of its exterior derivative over the whole of , i.e., Stokes' theorem was formulated in its modern form by Élie Cartan in 1945, following earlier work on the generalization of the theorems of vector calculus by Vito Volterra, Édouard Goursat, and Henri Poincaré. This modern form of Stokes' theorem is a vast generalization of a classical result that Lord Kelvin communicated to George Stokes in a letter dated July 2, 1850. Stokes set the theorem as a question on the 1854 Smith's Prize exam, which led to the result bearing his name. It was first published by Hermann Hankel in 1861. This classical case relates the surface integral of the curl of a vector field over a surface (that is, the flux of ) in Euclidean three-space to the line integral of the vector field over the surface boundary (also known as the loop integral). Classical generalizations of the fundamental theorem of calculus like the divergence theorem, and Green's theorem from vector calculus are special cases of the general formulation stated above after making a standard identification of vector fields with differential forms (different for each of the classical theorems). (Wikipedia).
What is Stokes theorem? - Formula and examples
► My Vectors course: https://www.kristakingmath.com/vectors-course Where Green's theorem is a two-dimensional theorem that relates a line integral to the region it surrounds, Stokes theorem is a three-dimensional version relating a line integral to the surface it surrounds. For that reaso
From playlist Vectors
In this video, I present another example of Stokes theorem, this time using it to calculate the line integral of a vector field. It is a very useful theorem that arises a lot in physics, for example in Maxwell's equations. Other Stokes Example: https://youtu.be/-fYbBSiqvUw Yet another Sto
From playlist Vector Calculus
An explanation of Stokes' theorem or Green's theorem in 3-space.
From playlist Advanced Calculus / Multivariable Calculus
Stokes' Theorem and Green's Theorem
Stokes' theorem is an extremely powerful result in mathematical physics. It allows us to quantify how much a vector field is circulating or rotating, based on the integral of the curl. @eigensteve on Twitter eigensteve.com databookuw.com %%% CHAPTERS %%% 0:00 Stoke's Theorem Overview
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
In this video, I present Stokes' Theorem, which is a three-dimensional generalization of Green's theorem. It relates the line integral of a vector field over a curve to the surface integral of the curl of that vector field over the corresponding surface. After presenting an example, I expl
From playlist Multivariable Calculus
From playlist Stokes' theorem
Physics Ch 67.1 Advanced E&M: Review Vectors (67 of 113) Stoke's Theorem
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn that Stoke’s Theorem (The Fundamental Theorem of Curl) means the “bending” or curl of the vector field everywhere on th
From playlist PHYSICS 67.1 ADVANCED E&M VECTORS & FIELDS
The most important theorem about vector fields, Stokes' theorem, which relates the surface integral of the curl with the line integral over the boundary. Here orientation matters, which I'll explain as well. Old Stokes Theorem Video https://youtu.be/bDILtddFKxw Vector Calculus Playlist: h
From playlist Vector Calculus
Worldwide Calculus: Stokes' Theorem
Lecture on 'Stokes' Theorem' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Integration and Vector Fields
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 Theo
Lecture 7: Integration (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
ME564 Lecture 25: Stokes' theorem and conservative vector fields
ME564 Lecture 25 Engineering Mathematics at the University of Washington Stokes' theorem and conservative vector fields Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L25.pdf Course Website: http://faculty.washington.edu/sbrunton/me564/ http://faculty.washington.edu/sbrunton/
From playlist Engineering Mathematics (UW ME564 and ME565)
Intermittency, Cascades and Thin Sets in Three-Dimensional Navier-Stokes Turbulenc by John D. Gibbon
Program Turbulence: Problems at the Interface of Mathematics and Physics (ONLINE) ORGANIZERS: Uriel Frisch (Observatoire de la Côte d'Azur and CNRS, France), Konstantin Khanin (University of Toronto, Canada) and Rahul Pandit (Indian Institute of Science, Bengaluru) DATE: 07 December 202
From playlist Turbulence: Problems at The Interface of Mathematics and Physics (Online)
Converting Maxwells Equations from Differential to Integral Form
In this video I show how to make use of Stokes and Divergence Theorem in order to convert between Differential and Integral form of Maxwell's equations. I also try to explain their connection to fluid dynamics, as well as motivation for each form.
From playlist Math/Derivation Videos
Stokes' theorem from Green's theorem | Lecture 51 | Vector Calculus for Engineers
Obtain Stokes' theorem by generalizing Green's theorem to three dimensions. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/use
From playlist Vector Calculus for Engineers
From playlist Stokes' theorem
Valerio Toledano Laredo - "Stability conditions and Stokes Factors"
Toldano lectures on "Stability conditions and Stokes Factors" at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series