Q 1 Notation: Describe the meanings ... [FREE SOLUTION]

Chapter 14: Q 1 (page 1153)

Notation: Describe the meanings of each of the following mathematical expressions.
$鈭�$

Short Answer

Expert verified

The description about mathematical expression $鈭�$ 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 :-

$鈭� F = [\begin{matrix} \frac{鈭� F}{鈭� x_{1}} \\ \frac{鈭� F}{鈭� x_{2}} \\ \frac{鈭� F}{鈭� x_{3}} \\ 路 \\ 路 \\ 路 \\ \frac{鈭� F}{鈭� x_{n}} \end{matrix}]$

Step by step solution

Step 1. Given Information

We have given the following mathematical expression :-

$鈭�$ .

We have to describe the meaning of this expression.

Step 2. Description

We have given the following symbol :-

$鈭�$

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 bynabla role="math" localid="1651155107117" $(鈭�)$ .

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 :-

$鈭� F = [\begin{matrix} \frac{鈭� F}{鈭� x_{1}} \\ \frac{鈭� F}{鈭� x_{2}} \\ \frac{鈭� F}{鈭� x_{3}} \\ 路 \\ 路 \\ 路 \\ \frac{鈭� F}{鈭� x_{n}} \end{matrix}]$

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91影视

Notation: Describe the meanings of each of the following mathematical expressions.
$鈭�$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Description

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91影视

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Description

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Notation: Describe the meanings of each of the following mathematical expressions.
$鈭�$