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Differential Equation Visualization

Differential Equation Visualization
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2016-03-29 13:51
FunctionCalculusOptimizationGraphing
This example demonstrates the solution and direction field of differential equations through dynamic graphics. Core math concepts include differential equations, direction fields, slope fields, and solution curves. Construction highlights involve commands like Textfield, Point, OrthogonalLine, Intersect, Polygon, SlopeField, SolveODE to create an interactive interface for equation solving and visualization. Suitable for high school students and beginners in calculus learning differential equation theory.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. Point(xAxis) → A
  3. Point(xAxis) → B
  4. Point(yAxis) → C
  5. Point(yAxis) → D
  6. OrthogonalLine(A, xAxis) → a
  7. OrthogonalLine(B, xAxis) → b
  8. OrthogonalLine(C, yAxis) → c
  9. OrthogonalLine(D, yAxis) → d
  10. Intersect(a, d) → E
  11. Intersect(a, c) → F
  12. Intersect(b, c) → G
  13. Intersect(b, d) → H
  14. Polygon(E, F, G, H) → poly1, e, f_1, g, h
  15. SlopeField(f, 30, 0.5, xmin, ymin, xmax, ymax) → slopefield1
  16. SolveODE(f, x0, y0, xmin, step) → yLeft
  17. SolveODE(f, x0, y0, xmax, step) → yRight
  18. Textfield(guess) → InputBox2