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微分方程的斜率场 by Martin Flashman

微分方程的斜率场 by Martin Flashman
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2014-11-19 03:04
向量函数微积分导数函数图像
①本范例演示了微分方程 dy/dx = P(x,y) 的斜率场图形；②涉及的核心数学概念包括微分方程、斜率场、向量场；③作图要点提炼自构造摘要，使用了 Sequence, Textfield, Vector, Element, PolyLine, SlopeField, SolveODE, ImplicitCurve, NSolveODE 等GeoGebra命令和对象；④适合大学数学、物理等专业的学生学习和研究微分方程的几何意义。

GeoGebra 命令及参数

  1. Sequence((0, a + (k * (b - a) / N)), k, 0, N) → list3
  2. Sequence(Cell[2, k], k, 2, N + 2) → euler
  3. Sequence((1, Element[euler, k]), k, 1, N + 1) → eulerpts
  4. Sequence(Vector[Element[list3, k], Element[eulerpts, k]], k, 1, N + 1) → eulerarrow
  5. Textfield(a) → inputBox2
  6. Textfield(b) → inputBox3
  7. Vector(Element[list3, N + 1], Element[eulerpts, N + 1]) → f_{arrowb}
  8. Element(eulerpts, N + 1) → f_b
  9. Sequence((a + ((k - 1) * (b - a) / N), Element[euler, k]), k, 1, N + 1) → eulerptsR2
  10. Textfield(f_q) → inputBox1_2
  11. PolyLine(eulerptsR2) → c
  12. Element(eulerptsR2, N + 1) → A
  13. SlopeField(f_q, N + 5, 3) → slopefield1
  14. SolveODE(f_q, B) → f
  15. ImplicitCurve(f_q(x, y) - f_q(x(C), y(C))) → h
  16. NSolveODE({f_q}, x(B), {y(B)}, x(B) + 5) → numericalIntegral1
  17. NSolveODE({f_q}, x(B), {y(B)}, x(B) - 5) → numericalIntegral2