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Slope Fields for dy/dx = P(x,y)

Slope Fields for dy/dx = P(x,y)
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2014-11-19 03:04
VectorFunctionCalculusDerivativeGraphing
This example demonstrates the slope field for the differential equation dy/dx = P(x,y). It involves core mathematical concepts such as differential equations, slope fields, and vector fields. The construction utilizes GeoGebra commands and objects like Sequence, Textfield, Vector, Element, PolyLine, SlopeField, SolveODE, ImplicitCurve, NSolveODE, etc. It is suitable for university students and researchers in mathematics and physics studying the geometric interpretation of differential equations.

GeoGebra Commands & Parameters

  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