Sergey

@aethereal

Math and CS

1 follower39 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

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

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.

180

280

Integrals of Trigonometric Functions and Monomials

Aug 13, 2026ReferenceSergey

Reference table of indefinite integrals of products of powers of x with sine and cosine.

290

Integrals of Trigonometric Functions and Exponentials

Aug 13, 2026ReferenceSergey

Reference table of indefinite integrals of products of exponentials with sine and cosine.

290

Sergey

Vector calculus. Surface integrals of the first kind

Vector calculus. Stokes' theorem. Circulation

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

Vector calculus. Line integrals of the first kind

Vector calculus. Green's theorem

Vector calculus. Surface integrals of the second kind. Flux

Linear algebra and analytic geometry. Vector algebra

Суффиксы в Английском Языке

Префиксы в Английском Языке

Integrals with Trigonometric Functions

Integrals of Trigonometric Functions and Monomials

Integrals of Trigonometric Functions and Exponentials

Vector calculus. Surface integrals of the first kind

Vector calculus. Stokes' theorem. Circulation

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

Vector calculus. Line integrals of the first kind

Vector calculus. Green's theorem

Vector calculus. Surface integrals of the second kind. Flux

Linear algebra and analytic geometry. Vector algebra

Суффиксы в Английском Языке

Префиксы в Английском Языке

Integrals with Trigonometric Functions

Integrals of Trigonometric Functions and Monomials

Integrals of Trigonometric Functions and Exponentials