MathPlotAI Logo MathPlotAI

Graphical and Numerical Solution of Nonlinear Systems

Graphical and Numerical Solution of Nonlinear Systems
Loading the math board and drawing, please wait…
2016-07-04 18:53
FunctionTrigonometryCoordinate GeometryOptimizationGraphing
In collections Solution of Systems of nonlinear Equations
This example demonstrates the graphical and numerical solution of a system of two nonlinear equations in two variables, focusing on comparing methods like Roots, RootsByLocus, and ImplicitCurve. It involves core math concepts such as roots, loci, and implicit curves. Constructed using GeoGebra commands like Element, Point, If, Locus, Textfield, Polygon, Sequence, RemoveUndefined, Join, Zip, and ImplicitCurve with objects like i, P5, P4, P3, P2, P1, lP, P_i, a, b, etc. Ideal for high school and advanced learners to explore nonlinear equations and mathematical tools comparison.

GeoGebra Commands & Parameters

  1. Element(lP, i) → P_i
  2. Point(Segment[Px2, Px1]) → Ax
  3. Point(Segment[Py2, Py1]) → Ay
  4. If(Funktion ≟ 1, a(x, y), If[Funktion ≟ 2, b(x, y), (a(x, y) * b(x, y))]) → f00
  5. If((f1(x0 - ε / 2) * f1(x0 + ε / 2)) < 1E-8 ∧ (f2(x0 - ε / 2) * f2(x0 + ε / 2)) < 1E-8, (x0, y0)) → E0x
  6. If((g1(y0 - ε / 2) * g1(y0 + ε / 2)) < 0 ∧ (g2(y0 - ε / 2) * g2(y0 + ε / 2)) < 0, (x0, y0)) → E0y
  7. If((fxx(xi - ε / 2) * fxx(xi + ε / 2)) < 0, (xi, y(Ay))) → Bxx1
  8. If((fyy(yi - ε / 2) * fyy(yi + ε / 2)) < 0, (x(Ax), yi)) → Byy1
  9. Locus(Bxx1, Ay) → locxx1
  10. Locus(Byy1, Ax) → locyy1
  11. Textfield(a) → inputBox1
  12. Textfield(b) → inputBox2
  13. Polygon((x_{max}, y_{max}), (x_{min}, y_{max}), (x_{min}, y_{min}), (x_{max}, y_{min})) → VV, d, e, g, h
  14. Textfield(N_P) → Textfeld1
  15. If(a_1, N_P, 2) → N_1
  16. Sequence(x_{min} + ((x_{max} - x_{min}) / N_1 * i), i, 0, N_1) → xx, {-6, 0, 6}
  17. Sequence(y_{min} + ((y_{max} - y_{min}) / N_1 * i), i, 0, N_1) → yy, {-6, 0, 6}
  18. RemoveUndefined(Join[Zip[Mirror[{Roots[f00(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, xx]]) → Pxxy
  19. Join(Zip[Reverse[{Roots[f00(x, b), x_{min}, x_{max}]}] + (0, b), b, yy]) → Pyyx
  20. Textfield(Funktion) → Textfeld2
  21. Textfield(x_{min}) → Textfeld3
  22. Textfield(y_{min}) → Textfeld4
  23. Textfield(x_{max}) → Textfeld5
  24. Textfield(y_{max}) → Textfeld6
  25. Textfield(N) → Textfeld7
  26. Zip((a(x(pp), y(pp)), b(x(pp), y(pp))), pp, lP) → Liste1
  27. Textfield(ε) → Textfeld8
  28. ImplicitCurve(a) → fa
  29. ImplicitCurve(b) → fb
  30. Textfield(v_{V1}) → InputBox1