方向导数与梯度演示 by Šárka Voráčová

GeoGebra 命令及参数

1. CurveCartesian(t, y0, a(t, y0), t, -5, 5) → b
2. CurveCartesian(x0, t, a(x0, t), t, -5, 5) → c
3. CurveCartesian((t * cos(α)) + x0, (t * sin(α)) + y0, a((t * cos(α)) + x0, (t * sin(α)) + y0), t, -2, 2) → cut
4. Curvature(A, cut) → k
5. Segment(D, A_1) → d
6. Surface((u * cos(α)) + x0, (u * sin(α)) + y0, v, u, -2, 2, v, -2, 2) → e
7. Vector(A, A + (cos(α), sin(α))) → v1
8. Derivative(cut) → cut'
9. Vector(A, A + B) → v
10. Angle(v1, v) → β
11. Vector(A_1, A_1 + ((k1 * x0), (k2 * y0))) → grad