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复数微分的映射图可视化

复数微分的映射图可视化
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2015-12-10 06:01
函数微积分复数
该范例通过映射图展示了复数微分的概念。它涉及复数函数的导数，通过动态调整参数来观察函数图像的变化。主要使用了Sequence, CurveCartesian, Vector, Textfield, Intersect, Derivative等命令。适合大学数学课程中的复分析学习。

GeoGebra 命令及参数

  1. Sequence((r * (cos(t) + (sin(t) * ί))), t, -3.141592653589793, 3.141592653589793, 0.5235987755982988) → z_*
  2. Sequence((x(Element[fz_*, k]), y(Element[fz_*, k]), height_{image}), k, 1, 12) → fpoint_*
  3. Sequence(Vector[Element[z_*, j], Element[fpoint_*, j]], j, 1, 12) → fvec_*
  4. CurveCartesian((r * cos(t)), (r * sin(t)), height_{image}, t, 0, 6.283185307179586) → d
  5. Vector(z_#, f_{(z#).}) → w
  6. CurveCartesian(t, 0, height_{image}, t, -5, 5) → Xh
  7. CurveCartesian(0, t, height_{image}, t, -5, 5) → Yh
  8. Textfield(z_*) → inputBox3
  9. Vector(z_#, z_1) → u
  10. Intersect(xAxis, yAxis) → A
  11. Vector(A, Δz) → v
  12. CurveCartesian((r * cos(t)), (r * sin(t)), t, t_a, t_b) → γ
  13. Textfield(t_a) → inputBox4
  14. Textfield(t_b) → inputBox5
  15. Sequence(t_a + (k / m * (t_b - t_a)), k, 0, m) → t_*
  16. Derivative(f, z) → df
  17. Vector(A, Δw) → h
  18. Vector(f_{(z#).}, f_{z1}) → g
  19. Vector(z_1, f_{z1}) → i
  20. Textfield(F) → InputBox1
  21. Vector(f_{(z#).}, Diff_#) → l