Linear algebra and analytic geometry. Vector algebra
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
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Vector calculus. Line integrals of the first kind
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. 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.
0
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.
0
340
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.
0
380
Vector calculus. Stokes' theorem. Circulation
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