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Vector calculus. Problem sheets

SergeyOctober 3, 2026

Six sheets: line integrals of the first and second kind, Green's theorem, surface integrals of the first and second kind, Stokes' theorem. Each sheet opens with the theory its problems need; every solution has a SymPy check.

MathematicsMathematical Analysis
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  1. 1

    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=∣r′(t)∣ dtds = |\mathbf{r}'(t)|\,dt, arc length, curves in polar coordinates, the mass and centre of mass of a wire, symmetry instead of computation.

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    530
  3. 3

    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.
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    260