Stokes’ Theorem says that boundary circulation equals the total curl through a surface. In this Woody Calculus visual lesson, learn how Stokes’ Theorem connects line integrals, surface integrals, curl, orientation, the right-hand rule, Green’s Theorem, and vector calculus in Calculus 3.
Green’s Theorem turns a boundary line integral into an interior double integral. In this Woody Calculus visual lesson, learn how Green’s Theorem connects circulation, curl, flux, area, line integrals, double integrals, Stokes’ Theorem, and the Divergence Theorem in Calculus 3.
The Jacobian is the hidden scale factor behind every coordinate change in Calculus III. In this Woody Calculus visual lesson, learn how Jacobians explain area and volume scaling, change of variables, polar coordinates, cylindrical coordinates, spherical coordinates, double integrals, triple integrals, and why the mysterious extra factors r and ρ²sinφ appear.
The Möbius strip is one of the clearest examples of why orientation matters in Calculus 3, vector calculus, topology, and surface integrals. Learn how one half-twist creates a one-sided surface with one boundary edge, no global normal vector, and a powerful obstruction to the standard global form of Stokes’ Theorem.
Line integrals are one of the core ideas in Calculus 3 and vector calculus. Learn what line integrals measure, how vector fields interact with paths, why direction matters, and when different paths from the same start to the same end can produce different work.