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Directional Derivatives, Level Curves, and Gradient

Directional Derivatives, Level Curves, and Gradient
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2017-10-30 17:12
VectorCalculusDerivative
This example illustrates the concepts of directional derivatives, level curves, and gradient. Key mathematical concepts include directional derivatives, level curves, and gradient. Using GeoGebra commands such as Sequence, Derivative, Point, Line, and Vector, these mathematical concepts are visually represented. Suitable for university-level calculus courses.

GeoGebra Commands & Parameters

  1. Sequence(CurveCartesian[t, i, f(t, i), t, -5, 5], i, -5, 5, 1) → lista1
  2. Sequence(CurveCartesian[i, t, f(i, t), t, -5, 5], i, -5, 5, 1) → lista2
  3. Derivative(f, x) → fx
  4. Derivative(f, y) → fy
  5. Point(lista2) → A
  6. Line(P, vt_x) → rx
  7. Line(P, vt_y) → ry
  8. Vector(P, P + (x(vt_x), y(vt_x), z(vt_x))) → vtxp
  9. Vector(P, P + (x(vt_y), y(vt_y), z(vt_y))) → vtyp
  10. Surface(t, s, p(t, s), t, a - 1, a + 1, s, b - 1, b + 1) → c
  11. Vector(P, P + (x(n), y(n), z(n))) → vnp
  12. Vector(P, P + (x(vd_θ), y(vd_θ), z(vd_θ))) → vdp_ θ
  13. Surface(a + t, b, f(a, b) + s, t, -3, 3, s, -3, 3) → d
  14. Surface(a, b + t, f(a, b) + s, t, -3, 3, s, -3, 3) → e
  15. Circle((a, b), 1) → g
  16. Line(P, vd_θ) → h
  17. ImplicitCurve(f(x, y)) → i
  18. Sequence(ImplicitCurve[f(x, y) - k], k, -4, 4) → lista3