Question

Obtain an expression for the gradient of a

Scalar function in rectangular coordinates.​

Answer 1

SOLUTION

TO DETERMINE

The expression for gradient of a Scalar function in rectangular coordinates

EVALUATION

Gradient

Let a scalar field be defined by the scalar function f(x, y, z) of coordinates x , y , z which is also defined and differentiable at each point (x , y , z) in some region of space.

Then gradient of the function is defined as

$\displaystyle\nabla f = \bigg(\hat{i} \frac{ \partial}{ \partial x} + \hat{j} \frac{ \partial}{ \partial y} + \hat{k} \frac{ \partial}{ \partial z} \bigg)f$

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