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线性系统临界点分类

线性系统临界点分类
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2016-08-21 13:28
函数解析几何微积分矩阵最值优化
所属专题 UQ-Applied Mathematical Analysis
①本范例演示线性系统临界点的分类及其几何意义；②涉及核心数学概念包括矩阵的行列式、迹、特征值、线性变换等；③构造过程中运用了 GeoGebra 命令如 Determinant（行列式）、SolveODE（解常微分方程）、Segment（线段）、Sequence（序列）、Polygon（多边形）、IntegralBetween（定积分）等对象；④适合大学数学、线性代数课程教学与学习。

GeoGebra 命令及参数

  1. Determinant(JacM) → Det
  2. SolveODE(gx, fx, x(A), y(A), time, step) → numericalIntegral1
  3. SolveODE(gx, fx, x(A), y(A), (-time), step) → numericalIntegral2
  4. Segment(A, B) → f
  5. Segment(C1, D1) → E1
  6. Segment(C2, D2) → E2
  7. Segment(C3, D3) → E3
  8. Segment(C4, D4) → E4
  9. Segment(C5, D5) → E5
  10. Segment(C6, D6) → E6
  11. Segment(C7, D7) → E7
  12. Segment(C8, D8) → E8
  13. Segment(C9, D9) → E9
  14. Segment(C10, D10) → E10
  15. Sequence(SolveODE[gx, fx, x(Element[points1, i]), y(Element[points1, i]), time, step], i, 1, 7) → list2
  16. Sequence(SolveODE[gx, fx, x(Element[points1, i]), y(Element[points1, i]), (-time), step], i, 1, 7) → list3
  17. Polygon(D, E, F, G) → poly1, d_1, e, f_1, g_1
  18. IntegralBetween(Con, Con1, -3, 3) → UnderP
  19. IntegralBetween(Con3, Con, 0, 3) → TopP1
  20. IntegralBetween(Con3, Con, -3, 0) → TopP2