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Euler's Method Demonstration by Terry Lee Lindenmuth

Euler's Method Demonstration by Terry Lee Lindenmuth
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2015-06-12 22:53
VectorFunctionCalculusDerivativeGeometric Construction
In collections Calculus C06_Differential Equations, Eulers Method
This example dynamically visualizes the geometric meaning of Euler's method for approximating solutions to differential equations. It involves core math concepts like calculus, derivatives, numerical methods, and vector operations. The construction uses points (A1-A24) and segments (B4-B13) to illustrate the iterative numerical process, making it suitable for high school and above students learning numerical solutions and geometric intuition of differential equations.

GeoGebra Commands & Parameters

  1. Numeric A2(0.1)
  2. Numeric B2(0.0)
  3. Numeric C2(1.0)
  4. Numeric A4(0.0)
  5. A4 + 1
  6. A5 + 1
  7. A6 + 1
  8. A7 + 1
  9. A8 + 1
  10. A9 + 1
  11. A10 + 1
  12. A11 + 1
  13. A12 + 1
  14. A13 + 1
  15. A14 + 1
  16. A15 + 1
  17. A16 + 1
  18. A17 + 1
  19. A18 + 1
  20. A19 + 1
  21. A20 + 1
  22. A21 + 1
  23. A22 + 1
  24. A23 + 1
  25. B2
  26. B4 + $A$2
  27. B5 + $A$2
  28. B6 + $A$2
  29. B7 + $A$2
  30. B8 + $A$2
  31. B9 + $A$2
  32. B10 + $A$2
  33. B11 + $A$2
  34. B12 + $A$2
  35. B13 + $A$2
  36. B14 + $A$2
  37. B15 + $A$2
  38. B16 + $A$2
  39. B17 + $A$2
  40. B18 + $A$2
  41. B19 + $A$2
  42. B20 + $A$2
  43. B21 + $A$2
  44. B22 + $A$2
  45. B23 + $A$2
  46. C2
  47. C4 + ($A$2 * (B4 - C4))
  48. C5 + ($A$2 * (B5 - C5))
  49. C6 + ($A$2 * (B6 - C6))
  50. C7 + ($A$2 * (B7 - C7))
  51. C8 + ($A$2 * (B8 - C8))
  52. C9 + ($A$2 * (B9 - C9))
  53. C10 + ($A$2 * (B10 - C10))
  54. C11 + ($A$2 * (B11 - C11))
  55. C12 + ($A$2 * (B12 - C12))
  56. C13 + ($A$2 * (B13 - C13))
  57. C14 + ($A$2 * (B14 - C14))
  58. C15 + ($A$2 * (B15 - C15))
  59. C16 + ($A$2 * (B16 - C16))
  60. C17 + ($A$2 * (B17 - C17))