Works on Mathematical Analysis added this month

6 results

Vector calculus. Surface integrals of the first kind

Oct 3, 2026Problem sheetSergey

Integration with respect to surface area: the area element for an explicit and a parametric surface, pieces of planes, the sphere in spherical coordinates.

340

Vector calculus. Stokes' theorem. Circulation

Oct 3, 2026Problem sheetSergey

Circulation of a field as the flux of its curl: computing the curl, matching the orientation of the contour and the normal, circulation computed two ways.

310

Vector calculus. Line integrals of the second kind. Work of a field

Oct 3, 2026Problem sheetSergey

Integrating a vector field along a directed curve: parametrising a segment and a graph, the work of a force, path dependence, a potential field and its potential, a curl-free field in a domain that is not simply connected.

400

Vector calculus. Line integrals of the first kind

Oct 3, 2026Problem sheetSergey

Integration with respect to arc length: parametrising a curve, the length element $ds = |\mathbf{r}'(t)|\,dt$ , arc length, curves in polar coordinates, the mass and centre of mass of a wire, symmetry instead of computation.

530

Vector calculus. Green's theorem

Oct 3, 2026Problem sheetSergey

A contour integral as a double integral: the hypotheses of Green's theorem, orientation of the contour, area as a contour integral, closing an open arc, an annulus, a singular point inside the contour.

260

Vector calculus. Surface integrals of the second kind. Flux

Oct 3, 2026Problem sheetSergey

The flux of a vector field through an oriented surface: the normal and the choice of side, the explicit and parametric forms, the lateral surface of a cylinder.

390