Directional Derivative Visualization

Directional Derivative Visualization
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2020-05-13 21:59
This example dynamically visualizes the directional derivative at a point in space along any arbitrary direction, highlighting the geometric interpretation and calculation involving gradient vectors, unit vectors, and dot products. Key mathematical concepts include directional derivatives, gradient vectors, unit vectors, and vector dot products. GeoGebra commands and objects like NDerivative, UnitVector, Vector, and IntersectPath are utilized to construct the visualization, making it suitable for university-level calculus and linear algebra courses or advanced mathematics enthusiasts.

GeoGebra Commands & Parameters

  1. NDerivative(A, x) → parx
  2. NDerivative(A, y) → pary
  3. UnitVector(Vector[P, (x0 + 1, y0, A(x0, y0) + parx(x0, y0))]) → vx
  4. UnitVector(Vector[P, (x0, y0 + 1, A(x0, y0) + pary(x0, y0))]) → vy
  5. UnitVector(Vector[P, (x0 + cos(theta), y0 + sin(theta), A(x0, y0) + (cos(theta) * parx(x0, y0)) + (sin(theta) * pary(x0, y0)))]) → vu
  6. Vector(P0, (x0 + 1, y0, 0)) → i
  7. Vector(P0, (x0, y0 + 1, 0)) → j
  8. Vector(P0, (x0 + cos(theta), y0 + sin(theta), 0)) → u
  9. IntersectPath(r, A) → eq1