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.
0
340
Works to read here on Mathematics added this month
7 results
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.
0
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.
0
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 , arc length, curves in polar coordinates, the mass and centre of mass of a wire, symmetry instead of computation.
0
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.
0
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.
0
390
Linear algebra and analytic geometry. Vector algebra
Oct 3, 2026Problem sheetSergey
Vectors in coordinates: dividing a segment, midpoints of sides, the angle between vectors, the cross product and the scalar triple product.
0
180