Stokes' Theorem on Manifolds
Stokes' Theorem is the crown jewel of differential geometry. It extends the fundamental theorem of Calculus to manifolds in n-dimensional space. --- This video aims to give an intuitive discussion of Stokes' Theorem, without the complicated equations and formalism. For those interested in the details, here's a thorough treatment of the topic: https://arxiv.org/abs/1604.07862 (Be warned, this rabbit hole goes very deep!) --- Follow me! Twitter: https://twitter.com/00aleph00 Instagram: https://www.instagram.com/00aleph00 Facebook: https://www.facebook.com/00aleph00 __ Pictures: Boundary and Green's Theorem - "Calculus: Early Transcendentals - 8th Edition" by James Stewart Exterior Derivative - "A Geometric Approach to Differential Forms" by David Bachman Music: Relaxing Guitar Music - Acoustic - Calming Music for Stress Relief, Studying
Stokes' Theorem is the crown jewel of differential geometry. It extends the fundamental theorem of Calculus to manifolds in n-dimensional space. --- This video aims to give an intuitive discussion of Stokes' Theorem, without the complicated equations and formalism. For those interested in the details, here's a thorough treatment of the topic: https://arxiv.org/abs/1604.07862 (Be warned, this rabbit hole goes very deep!) --- Follow me! Twitter: https://twitter.com/00aleph00 Instagram: https://www.instagram.com/00aleph00 Facebook: https://www.facebook.com/00aleph00 __ Pictures: Boundary and Green's Theorem - "Calculus: Early Transcendentals - 8th Edition" by James Stewart Exterior Derivative - "A Geometric Approach to Differential Forms" by David Bachman Music: Relaxing Guitar Music - Acoustic - Calming Music for Stress Relief, Studying