VECTOR CALCULUS : DEL OPRATOR(PART 1)

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1.COORDINATE SYSTEMS

• DEL (∇) is always used to know the spatial variations of any quantity i.e. changing in space.
  
• When operated on any quantity it specifies the rate of change of quantity along with the direction of this change. This is called a directional derivative.

• Above figure explains the different operation of del (∇) operator on the scalar and vector fields.
  
• The spatial variation of any scalar quality results in a vector quantity which is called "Gradient of Scalar”.
  
• The spatial variation of any vector quantity can be analyzed in two ways:

                      A) First is Dot Product i.e. Divergence Of Vector that gives a scalar quantity.

           B) Second is Cross Product i.e. Curl Of a Vector that gives a vector quantity.
VECTOR IDENTITIES

                                               Curl of gradient of any scalar is zero.

                                     Divergence of curl of any vector is zero.

Divergence of gradient is Laplacian of that scalar

The 3 remaining vector derivatives are related by the equation