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Stokes' Theorem - Line Integrals and Surface Integrals

Stokes' Theorem - Line Integrals and Surface Integrals
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2017-07-19 01:16
VectorCalculusIntegral
This example illustrates Stokes' Theorem, which relates line integrals and surface integrals. Key concepts include vector fields, curl, and integral paths. Using GeoGebra commands such as CornerThreeD, Sequence, and Join, the example dynamically shows line integrals and surface integrals of vector fields. Suitable for university-level calculus and vector analysis courses.

GeoGebra Commands & Parameters

  1. CornerThreeD(-1, 1) → A
  2. CornerThreeD(-1, 7) → B
  3. Sequence(Sequence[Sequence[(x(A) + ((x(B) - x(A)) * i / n), y(A) + ((y(B) - y(A)) * j / n), z(A) + ((z(B) - z(A)) * k / n)), i, 0, n], j, 0, n], k, 0, n) → lista1
  4. Join(lista1) → lista2
  5. Join(lista2) → PUNTOS
  6. Sequence(Vector[Element[PUNTOS, i], Element[PUNTOS, i] + (escala * (p(Element[PUNTOS, i]), q(Element[PUNTOS, i]), r(Element[PUNTOS, i])))], i, 1, (n + 1)^(3)) → VECTORES
  7. Textfield(p) → CasillaDeEntrada1
  8. Textfield(q) → CasillaDeEntrada2
  9. Textfield(r) → CasillaDeEntrada3
  10. CurveCartesian(cos(t), sin(t), sin(t)^(2) - cos(t)^(2), t, 0, (2 * π)) → c