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复数与微积分交互式学习范例

复数与微积分交互式学习范例
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2020-02-15 21:45
微积分复数几何作图
①本范例通过交互式演示复数与微积分的结合应用，展示函数图像与复数运算的动态关系；②涉及核心数学概念包括复数、微积分、等腰三角形、中值定理等；③构造过程中运用了Random, RandomElement, Sequence, If, Min, Length, Solutions, Element, TableText, SurdText等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解复数运算与微积分在几何问题中的应用。

GeoGebra 命令及参数

  1. Random(1, 2) → a1
  2. RandomElement({3, 4}) → b
  3. Random(1, 3) → a2
  4. Sequence(x(Element[l2, i]), i, 1, Length[l2]) → l4
  5. Sequence(x(Element[l1, i]), i, 1, Length[l1]) → l3
  6. If(d ≟ 1, l3, l4) → l5
  7. Min(l5) → c1
  8. Sequence(SurdText[x(Element[l1, i]), {sqrt(2), sqrt(3), sqrt(5)}], i, 1, Length[l1]) → l6
  9. Sequence(SurdText[x(Element[l2, i]), {sqrt(2), sqrt(3), sqrt(5)}], i, 1, Length[l2]) → l7
  10. If(d ≟ 1, l6, l7) → l8
  11. Length(l8) → e
  12. Solutions(h = h1) → l10
  13. Solutions(h(x) > l) → l9
  14. Element(l9, 1) → i
  15. If(d ≟ 1, "real", "imaginary") → text4
  16. Length(l5) → a
  17. If(a ≟ 4, Element[l5, 2], 0) → c2
  18. Sequence(a1 + ((a2 * Element[l5, i]) * ί), i, 1, a) → l11
  19. Sequence(SurdText[Element[l11, i]], i, 1, a) → l12
  20. TableText(l8, "c") → text7
  21. TableText(l12, "c") → text2
  22. Sequence(Sequence[Element[l8, j], i, 1, 1], j, 1, e) → l13
  23. TableText(l13, "c{") → text8
  24. Sequence(Sequence[Element[l12, j], i, 1, 1], j, 1, e) → l14
  25. TableText(l14, "c{") → text9
  26. SurdText(arg(z1^(j)), {π}) → α
  27. SurdText(k, {sqrt(2), sqrt(3)}) → text11
  28. RandomElement({3, 4}) → b_1