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Classification of Critical Points in Linear Systems

Classification of Critical Points in Linear Systems
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2016-08-21 13:28
FunctionCoordinate GeometryCalculusMatrixOptimization
In collections UQ-Applied Mathematical Analysis
This example demonstrates the classification of critical points in linear systems, highlighting geometric interpretations. Key mathematical concepts include determinants, traces, eigenvalues, and linear transformations. GeoGebra commands like Determinant, SolveODE, Segment, Sequence, Polygon, and IntegralBetween are utilized in the construction. Suitable for university-level mathematics and linear algebra education.

GeoGebra Commands & Parameters

  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