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Gradient Vector Field by Tatsuyoshi Hamada

Gradient Vector Field by Tatsuyoshi Hamada
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2012-12-04 21:24
VectorFunctionCalculusDerivativeGraphing
This example demonstrates the gradient vector field of a function. It involves core mathematical concepts like vector fields, gradients, derivatives, and function graphs. Construction highlights include using GeoGebra commands/objects such as Point, Derivative, Vector, Sequence, and SolveODE. Suitable for high school and above students learning calculus and vector analysis.

GeoGebra Commands & Parameters

  1. Point(g) → A
  2. Derivative(f, x) → f_x
  3. Derivative(f, y) → f_y
  4. Vector(A, A + (f_x(a, b), f_y(a, b))) → gradient
  5. Sequence(f(x, y) - k = 0, k, -4, 4, 0.5) → list1
  6. SolveODE(f_y(x, y), f_x(x, y), a, b, 4, 0.1) → numericalIntegral1