The derivative isn't what you think it is.
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange answerers and askers point to it as an intuition-building overview of how differential forms, cohomology and the generalized Stokes' Theorem connect.
Recommended by 2 people across 2 different months, 2023 to 2026.
What it is
A short explainer by Aleph 0 that presents the derivative as the exterior derivative, tied to the boundary operator through homology and cohomology. It gives a quick introduction to differential forms and de Rham's theorem, with a reading list for rigorous follow-up.
Cited in 1 Wikipedia article, including Exterior derivative.
What people said
Recommends isaac · 2023-06 · Mathematics Stack Exchange · on “How are Green's Theorem, Stokes' Theorem, etc all connected together”
This is an old post, somewhat too general, but no other post gives an overview of how these theorems generalize, and this topic is worth the elaboration beyond naming the generalized Stokes' Theorem or naming a textbook on complex analysis. While Grant Sanderson gives intuitive explanations of each of these theorems in his Multivariable Calculus [LINK] series on YouTube, I thank Prof. Rick Presman for his exposition of the Generalized Stokes’ Theorem [LINK] , and also Prof. Oliver Knill for his exposition via Calculus in four dimensions [LINK] . And, Aleph Naught’s videos: Stokes' Theorem on Manifolds [LINK] and The derivative isn't what you think it is [this video] give intuition as to the Gener
Recommends cows · 2023-11 · Mathematics Stack Exchange · on “How is de Rham cohomology useful?”
Solutions of the equation of motion for a topological gauge field theory are given by closed form modulo exact form(the gauge symmetry). This is precisely the de Rham cohomology. Please see 4.3 (page 20) and 4.4 (pages 20-21 ) of this reference: [LINK] This particular reference then goes further to show you the full story. It will enable you to give answers to physics problems without even lifting a finger to do a complicated calculation. POWER! Extended commentary. You might want to read part B first Part A There are three concepts here. Homology groups, Cohomology groups, and Equations of motion for say a Chern-Simons theory. A Chern-Simons theory is a name given to an object called an act
Cites SBF · 2026-03 · Mathematics Stack Exchange · on “Visual path to generalized Stokes theorem”
My background is more on measure theory and probability side, with analysis mostly on the undergrad level ( $\Bbb R^n$ , PDEs etc), I also have a decent knowledge of general topology (but only initial of algebraic topology). Now I want to self study part of differential geometry that leads to generalized Stokes theorem in as visual and intuitive way as possible. I am familiar with the definition of a smooth manifold via the atlas of local charts and I'm quite comfortable with it, However, already when thinking about $T_pM$ or $T^*_pM$ I feel I need an aid of some online lectures or a book that helps developing the visual/geometric intution about what's going on there. Ideally, it satisfies t