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Elementary Vector Analysis

Definition (Scalar and vector)

Vector is a directed quantity, one with

both magnitude and direction.

For instance acceleration, velocity, force

Scalar is a quantity that has magnitude

but not direction.

For instance mass, volume, distance

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PHYSICAL INTERPRETATION

In mathematics, the directional derivative ofa multivariate differentiable function along a given

vector v at a given point x intuitively represents theinstantaneous rate of change of the function,moving through x with a velocity specified by v. Ittherefore generalizes the notion of a partial

derivative, in which the rate of change is takenalong one of the coordinate curves, all othercoordinates being constant.

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PHYSICAL INTERPRETATION

The physical significance of the divergence ofa vector field is the rate at which "density" exits a

given region of space.

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PHYSICAL INTERPRETATION

The physical significance of the curl of avector field is the amount of "rotation" or angular

momentum of the contents of given region of space.It arises in fluid mechanics and elasticity theory.

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THEEND