方向导数演示 by Ku, Yin Bon (Albert)

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2015-10-06 01:20

向量微积分导数

①本范例演示了方向导数的几何意义，通过向量与切线的夹角变化直观展示导数概念；②涉及核心数学概念包括导数、向量、切线斜率及积分；③作图要点使用了Textfield, Segment, Circle, Point, Vector, CurveCartesian, IntegralBetween, Tangent, Slope等GeoGebra命令与对象；④适合大学微积分课程或数学爱好者学习方向导数及其应用。

GeoGebra 命令及参数

Textfield(f) → inputBox1
Segment(P, A) → a
Circle(A, 1) → c
Point(c) → B
Vector(A, B) → u
CurveCartesian(x(A) + (t * x(u)), y(A) + (t * y(u)), f(x(A) + (t * x(u)), y(A) + (t * y(u))), t, -1, 1) → b
Segment(D, B) → d
Segment(E, D) → e
IntegralBetween(f(x(A) + (x * x(u)), y(A) + (x * y(u))), 0, -1, 1) → h
Tangent(0, g) → i
Segment(C, B) → j
Circle(A, B) → k
Slope(i) → duf
Segment(F, G) → l