MathPlotAI Logo MathPlotAI

Heat Equation Visualization Tool

Heat Equation Visualization Tool
Loading the math board and drawing, please wait…
2016-09-19 10:16
FunctionCalculusSlider Animation
This example visualizes the heat equation. Key mathematical concepts include partial differential equations and heat conduction theory. Using GeoGebra commands such as Sequence, Max, Min, Textfield, etc., it dynamically shows temperature changes over time and space. Suitable for university mathematics and physics courses.

GeoGebra Commands & Parameters

  1. Sequence(g(i), i, 0, L, 0.1) → list1
  2. Max(list1) → maxlist1
  3. Min(list1) → minlist1
  4. Textfield(f) → InputBox1
  5. Vector(A, B) → u
  6. Vector(A, C) → v
  7. OrthogonalLine(C, yAxis) → h
  8. OrthogonalLine(B, yAxis) → i
  9. If(y(v) > 0, 0, 1) → condy
  10. If(y(u) < 0, 0, 1) → condx
  11. If(ymin ≟ 0, (ymax * (-0.1)), ymin) → condy2
  12. If(ymax ≟ 0, (ymin * (-0.1)), ymax) → condx2
  13. Textfield(L) → InputBox2
  14. Textfield(c) → InputBox3
  15. Textfield(n) → InputBox4
  16. Sequence((2 / L * Integral[(f(x) * sin(((i * π) * x / L))), 0, L]), i, 1, n) → AlphaN
  17. Sequence(((Element[AlphaN, i] * ℯ^(((((-i^(1)) * π^(2)) * c^(2)) * t / L^(2)))) * sin(((i * π) * x / L))), i, 1, n) → uxtn
  18. Sum(uxtn) → p
  19. Textfield(steptime) → InputBox5
  20. Textfield(t) → InputBox6