[Reprinted] [latex] latex formula editing Overview

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• Mathematical symbols

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Common special symbolic links: http://hepg.sdu.edu.cn/Service/tips/latex/doc2/MathSymb.html

 

Latex

The most powerful function is to display beautiful mathematical formulas. Let's look at how these formulas are implemented.

1. Add $ or/(and/) before and after the mathematical formula, for example, $ f (x) = 3X + 7 $ and/(f (x) = 3X + 7 /) the results are the same;
If/[and/] is used, or $ and $ are used, the formula occupies only one row;
If/begin {equation} And/end {equation} are used, the sequence number is automatically added in addition to the exclusive row of the formula. use/begin {equation *} And/end {equation *} if the formula does not require serial numbers *}.

2. Characters
Ordinary characters have the same meaning in mathematical formulas,
# $ % &~ _ ^ /{}
To represent these symbols # $ % & _ {} in a mathematical environment, you need to represent them as/#/$/%/&/_/{/}, respectively /&/_/{/}, that is, add/before the characters /.

3. superscript and subscript
Use ^ to represent the superscript, and use _ to represent the subscript. Let's look at a simple example:

$/SUM _ {I = 1} ^ n a_ I = 0 $
$ F (x) = x ^ {x ^ x} $

Effect:

Here there are more
The settings of the top-and bottom-up latex objects.

4. Greek letters

For more information, see
Here

 

5. mathematical functions

6. Insert text into the formula
You can add text in the formula through/mbox {text}, for example:

/Documentclass {Article}
/Usepackage {CJK}
/Begin {CJK *} {GBK} {SONG}
/Begin {document}
$/Mbox {for any $ x> 0 $},/mbox {has} f (x)> 0. $
/End {CJK *}
/End {document}

Effect:

7. Scores and operators
/frac{

Numerator
}{

Denominator
}


/sqrt{

Expression
} Indicates square open,
/sqrt[n]{

Expression
} Indicates the power of Npower.


8. ellipsis (3 points)
/Ldots indicates the ellipsis alignment with the text bottom line;/cdots indicates the ellipsis alignment with the text midline,

For example:




,

Indicates
$ F (x_1, x_x,/ldots, X_n) = X_1 ^ 2 + x_2 ^ 2 +/cdots + x_n ^ 2 $



9. Brackets and delimiters
() And [] and | correspond to yourself; {} corresponds to/{/}; | corresponds to/|.
To display large parentheses or delimiters, apply/left and/right, for example:

/[F (x, y, z) = 3Y ^ 2 Z/left (3 +/frac {7X + 5} {1 + y ^ 2}/right)./]

Corresponds

/left.

And/right.

Only matching is used and is not displayed. For example, to output:

Use
$/Left./frac {du} {DX}/right | _ {x = 0}. $

10. multi-row mathematical formula

It can be expressed:

/Begin {eqnarray *}
/Cos 2/Theta & = &/COS ^ 2/theta-/sin ^ 2/Theta //
& = & 2/COS ^ 2/theta-1.
/End {eqnarray *}

 

& Indicates that the vertices are aligned here.
* Disable latex from automatically displaying the sequence number. If you want latex to automatically mark the sequence number, remove *.

11. Matrix




Indicates:
The/emph {characteristic polynomial} $/CHI (/Lambda) $ OF
$3/times 3 $ ~ Matrix
/[/Left (/begin {array} {CCC}
A & B & C //
D & E & f //
G & H & I/end {array}/right)/]
Is given by the formula
/[/CHI (/Lambda) =/left |/begin {array} {CCC}
/Lambda-A &-B &-C //
-D &/Lambda-E &-f //
-G &-H &/Lambda-I/end {array}/right |./]

C Indicates the center alignment, L indicates the left alignment, and r indicates the right alignment.



12. derivative, limit, sum, and integral

The expressions

Are obtained in latex by typing/frac{du}{dt}
And/frac{d^2 u}{dx^2}
Respectively. The mathematical
Symbol

Is produced using/partial
. Thus the Heat Equation

Is obtained in latex by typing

/[ /frac{/partial u}{/partial t}
   = h^2 /left( /frac{/partial^2 u}{/partial x^2}
      + /frac{/partial^2 u}{/partial y^2}
      + /frac{/partial^2 u}{/partial z^2} /right) /]

To obtain mathematical expressions such

In displayed equations we type/lim_{x /to +/infty}
,
/inf_{x > s}
And/sup_K
Respectively. Thus to obtain

(In Latex) We type

/[ /lim_{x /to 0} /frac{3x^2 +7x^3}{x^2 +5x^4} = 3./] 

To obtain a summation sign such

We type/sum_{i=1}^{2n}
. Thus

Is obtained by typing

/[ /sum_{k=1}^n k^2 = /frac{1}{2} n (n+1)./] 

We now discuss how to obtainIntegrals
In mathematical
Events. A typical integral is the following:

This is typeset using

/[ /int_a^b f(x)/,dx./] 

The integral sign

Is typeset using the control sequence
/int
, AndLimits of Integration
(In this caseA
AndB
Are treated as
Subscript and a superscript on the integral sign.

Most integrals occurring in mathematical documents begin
An integral sign and contain one or more instancesD
Followed by another (Latin or Greek) letter, as in
DX
,Dy
AndDT
.
To obtain the correct appearance one shocould put
Extra space beforeD
,
Using/,
. Thus

And

Are obtained by typing

/[ /int_0^{+/infty} x^n e^{-x} /,dx = n!./] 

/[ /int /cos /theta /,d/theta = /sin /theta./] 

/[ /int_{x^2 + y^2 /leq R^2} f(x,y)/,dx/,dy
   = /int_{/theta=0}^{2/pi} /int_{r=0}^R
      f(r/cos/theta,r/sin/theta) r/,dr/,d/theta./] 

And

/[ /int_0^R /frac{2x/,dx}{1+x^2} = /log(1+R^2)./] 

Respectively.

In some multiple integrals (I. e., integrals containing more
One integral sign) one finds that latex puts too much space
Between the integral signs. The way to improve the appearance
Of the integral is to use the control sequence/!
To
Remove a thin strip of unwanted space. Thus, for example,
Multiple Integral

Is obtained by typing

/[ /int_0^1 /! /int_0^1 x^2 y^2/,dx/,dy./] 

Had we typed

/[ /int_0^1 /int_0^1 x^2 y^2/,dx/,dy./] 

We wowould have obtained

A participant ly noteworthy example comes when we are
Typesetting a Multiple Integral such

Here we use/!
Three times to obtain suitable spacing
Between the integral signs. we typeset this integral using

/[ /int /!/!/! /int_D f(x,y)/,dx/,dy./] 

Had we typed

/[ /int /int_D f(x,y)/,dx/,dy./] 

We wowould have obtained

The following (reasonably complicated) passage exhibits
Number of the features which we have been discussing:

One wowould typeset this in latex by typing

In non-relativistic wave mechanic, the wave function

$/PSI (/mathbf {r}, T) $ of a particle satisfies

/Emph {Schr/"{o} Dinger wave equation}

/[I/hbar/frac {/partial/PSI} {/partial t}

=/Frac {-/hbar ^ 2} {2 m}/left (

/Frac {/partial ^ 2} {/partial x ^ 2}

+/Frac {/partial ^ 2} {/partial y ^ 2}

+/Frac {/partial ^ 2} {/partial Z ^ 2}

/Right)/PSI + V/psi./]

It is customary to normalize the wave equation

Demaning that

/[/INT /! /! /! /INT /! /! /! /INT _ {/textbf {r} ^ 3}

/Left |/PSI (/mathbf {r}, 0)/right | ^ 2/, dx/, dy/, DZ = 1./]

A simple calculation using the SCHR/"{o} Dinger Wave

Equation shows that

/[/Frac {d} {DT}/INT /! /! /! /INT /! /! /! /INT _ {/textbf {r} ^ 3}

/Left |/PSI (/mathbf {r}, T)/right | ^ 2/, dx/, dy/, DZ = 0,/]

And hence

/[/INT /! /! /! /INT /! /! /! /INT _ {/textbf {r} ^ 3}

/Left |/PSI (/mathbf {r}, T)/right | ^ 2/, dx/, dy/, DZ = 1/]

For all times ~ $ T $. If we normalize the wave function in this

Way then, for any (measurable) subset ~ $ V $ of $/textbf {r} ^ 3 $

And time ~ $ T $,

/[/INT /! /! /! /INT /! /! /! /Int_v

/Left |/PSI (/mathbf {r}, T)/right | ^ 2/, dx/, dy/, DZ/]

Represents the probability that the particle is to be found

Within the region ~ $ V $ at time ~ $ T $.


Special symbol input:

Mathematical symbols

There are numerous mathematical symbols that can be used in
Mathematics mode. These are obtained by typing an appropriate
Control sequence.

Miscellaneous symbols:

''Large'' operators:

Binary operations:

Relations:

Negated relations:

Arrows:

Openings:

Closings:

Alternative names: