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Q 1

Expert-verifiedFound in: Page 1153

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Notation: Describe the meanings of each of the following mathematical expressions.

$\nabla $

The description about mathematical expression $\nabla $ is as following :-

This symbol is called nabla. This is used to represent gradient where gradient is a collection of all partial derivatives.

If a function $F$ has $n$ variables, then its gradient is :-

$\nabla F=\left[\begin{array}{c}\frac{\partial F}{\partial {x}_{1}}\\ \frac{\partial F}{\partial {x}_{2}}\\ \frac{\partial F}{\partial {x}_{3}}\\ \xb7\\ \xb7\\ \xb7\\ \frac{\partial F}{\partial {x}_{n}}\end{array}\right]$

We have given the following mathematical expression :-

$\nabla $.

We have to describe the meaning of this expression.

We have given the following symbol :-

$\nabla $

In mathematics this symbol is known as **nabla.** This is upside down triangle delta symbol.

This symbol is used is vector derivative.

The symbol of nabla is used for **gradient**. That is the gradient of a vector is denoted by** nabla** role="math" localid="1651155107117" $(\nabla )$.

Gradient is the collection of all partial derivatives of a multivariate function.

if a function $F$ has $n$ variables, then the gradient is defined and denoted as following :-

$\nabla F=\left[\begin{array}{c}\frac{\partial F}{\partial {x}_{1}}\\ \frac{\partial F}{\partial {x}_{2}}\\ \frac{\partial F}{\partial {x}_{3}}\\ \xb7\\ \xb7\\ \xb7\\ \frac{\partial F}{\partial {x}_{n}}\end{array}\right]$

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