Sergey

@aethereal

Math and CS

1 follower39 works

Personal Information

Researcher Info

Interests

Mathematics Computer Science Physics Philosophy

Matrices

Jul 24, 2026TheorySergey

A matrix, its notation, and the main types: row, column, echelon, square, diagonal, identity, symmetric - defined and shown with worked examples.

570

Linear Dependence and Independence of Rows

Jul 24, 2026TheorySergey

Linear dependence and independence of the rows of a matrix, the criterion via a linear combination, and the connection to rank.

560

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

Recent works

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