To interpret the gradient of a scalar field fxyz f x i f y j f z k note that its component in the i direction is the partial derivative of f with respect to x. You would be interested in T x but how would you calculate that.
The Gradient Vector Multivariable Calculus Article Khan Academy
This is the rate of change of f in the x direction since y and z are kept constant.
. Suppose you wanted to know what the change in temperature along an arbitrary direction. Kept the point fixed and asked how does the temperature change of time you would be interested in Tt. But why restrict ourselves to movements up-down left-right etc.
Example 2 Consider the. In general the component of f in any direction is the rate of change of f in that direction. Is Tx a vector or a scalar.
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The Gradient Vector Multivariable Calculus Article Khan Academy
Linear Algebra Simple Interpretation Of The Direction And Projection Of The Gradient Vector Mathematics Stack Exchange
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