Operator Del and Gradient of Function, Study notes of Mathematics

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Module No, 3 The Operator Del and Gradient of Function The Del Operator The ‘Yector differential Operator del, symbolize as V, is defined by a. 0.4 eal taltgh The symbol V called del or nabla is used to symbolize del operatgr. It is only applied as defined derivative on one-dimensional function, and for more dimensions it may be applied as partial derivative on the function, The del operator is not a particular Operator but when we applied it on 4 scalar point function or 4 Vector point function; this may be known as the gradient, the divergence, and the curl, Gradient: grad (=p Curl: curlA= yx 4 —_—- — Divergence: diy (A) = y.4 . We will discuss here the first application of del operator as gradient, Gradient Function Let g(x, y,z) be a scalar point function defined on a specific region on R and also differentiable on the same domain, The we can apply del Operator ony in order to obtain gradient of scalar function p of grad( g) written as Vg is defined by é nod Q veel’ 26 b be mid Mat vp gis Cola yrel, Mo vero ¥ ond any d