Question

What is the del operator? What is it used for in vector calculus? What is contour integration?

Answer 1

one of the most important and useful mathematical constructs is the " del operator ". usually it is denoted by the symbol which is known as nabla
this can be regarded as a vector whose components in the three principle direction of a Cartesian coordinate. Of course the partial differentiation by themselves have no definite magnitude until we apply them to some function of the coordinate. 
Contour integration
It is the process of calculating the value a contour integration around
a given contour in a complex plane. As a result of truly amazing property of holomorphic functions , such integrals can be computed easily simply by summing the value of the complex residues inside the contour.