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Section 2.2 Gradient Vector Field

One important example of a vector field is that generated by the gradient of a scalar function, i.e. \(\nabla f\) . We studied this object a lot back in multivariable calculus and it has many nice properties such as point in the direction of maximal increase of the function \(f\text{.}\)
Learning Objectives:
  1. Describe the gradient vector field

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1.

Recall back to multivariable calculus. How was the gradient vector connected to the notion of directional derivatives?