Search results for “integrals”

9 results

Vector calculus. Surface integrals of the second kind. Flux

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.

380

Vector calculus. Line integrals of the first kind

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

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. Surface integrals of the first kind

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

IMO 1989

2026Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

380

IMO 2016

2026Problem sheet

57th International Mathematical Olympiad. Hong Kong, 2016.

440

Sean Cotner

@sean_cotner

NSF Research Fellow and postdoc at the University of Bonn. Previously an NSF Research Fellow and Postdoctoral Assistant Professor at the University of Michigan, and before that a graduate student at Stanford, advised by Brian Conrad. Interested in arithmetic geometry, algebraic groups (broadly construed), and integral questions connected to the local Langlands program.

IMO 1988

2026Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

180

IMO 1994

2026Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

410