table of Contents
1. root
Square root
\[\sqrt(x)\]
$$\sqrt(x)$$th root of n
\[\sqrt[n](x)\]
$$\sqrt[n](x)$$2. Score formula
Method a: \ frac {molecule} {} denominator
\[\frac{1}{x}\]
$$\frac{1}{x}$$Method two: {molecule} \} over {denominator
\[ {1+y}\over{x}\]
$$ {1+y}\over{x}$$Method three: {\ left {molecule} \ middle / {denominator} \ right..}
Numerator and the denominator is the fractional form, when available, can be avoided fraction too high .
\ ({\ left. {( \ frac {-csc ^ 2x} {1 + cotx})} \ middle / (\ frac {1} {x}) \ right.} \)
${\left. {(\frac{-csc^2x }{1+cotx})} \middle / (\frac{1}{x})\right.}$\[=e^{\lim\limits_{ {x\to 0^+} } {\left. {(\frac{-csc^2x }{1+cotx})} \middle / (\frac{1}{x})\right.} }\]
3. superscript and subscript
Superscript: ^
\[a^x\]
$$a^x$$Subscript: _
\[a_n\]
$$a_n$$\[A_n^m \quad B^m_n\]
$$A_n^m B^m_n$$4. summation
In the form of a
\[\sum_{n=1}^{100}\]
$$\sum_{n=1}^{100}$$In the form of two: plus \ limits
\[\sum\limits_{n=1}^{100}\]
$$\sum\limits_{n=1}^{100}$$5. Limit
\[\lim\limits_{x\rightarrow\infty}\frac{1}{x}\]
$$\lim\limits_{x\to \infty}\frac{1}{x}$$
Explanation: The ultimate symbol Partial + fractional part
- Limit portions
\lim\limits_{x\to\infty}\[\lim\limits_{x\rightarrow\infty}\]
- Fractional part
\frac{1}{x}6. partial derivatives \ partial
\[ \frac {\partial f(x)}{\partial x}\]
$$ \frac {\partial f(x)}{\partial x}$$7. integral symbol \ int
\[\int_a^b f(x) {\rm d}x\]
$$\int_a^b f(x) {\rm d}x$$Curve integral \ oint
\[ \oint\]
$$ \oint$$Typora
\ [\ Oiint \]
$$ \oiint $$Jane book
\ [\ ooint \]
\oointThree curve integral sign associated with formula
- Green formula
- Gauss formula
- Stokes equations
Green formula:
\[ \iint\limits_{\substack { D}} (\frac{ \partial Q}{\partial x}-\frac{ \partial P}{\partial y}) {\rm d}x {\rm d}y =\oint_L P{\rm d}x +Q{\rm d}y\]
$$ \iint\limits_{\substack { D}} (\frac{ \partial Q}
{\partial x}-\frac{ \partial P}{\partial y}) {\rm d}x
{\rm d}y =\oint_L P{\rm d}x +Q{\rm d}y$$Gauss formula:
\[ \iiint\limits_{\substack { \Omega}} (\frac{ \partial Q}{\partial x} + \frac{ \partial P}{\partial y} + \frac{ \partial R}{\partial z}) {\rm d}v = \mathop{\oiint}_{\Sigma} P{\rm d}y{\rm d}z +Q{\rm d}z{\rm d}x+ R{\rm d}x{\rm d}y\]
$$ \iiint\limits_{\substack { \Omega}}
(\frac{ \partial Q}{\partial x} +
\frac{ \partial P}{\partial y} +
\frac{ \partial R}{\partial z}) {\rm d}v
= \mathop{\oiint}_{\Sigma} 注释|在\ooint
用不了\limits，所以改用\mathop
P{\rm d}y{\rm d}z +Q{\rm d}z{\rm d}x+
R{\rm d}x{\rm d}y$$
Stokes equation:
\[ \mathop{\iint}_{\Sigma} \left | \begin{array}{ccc} dydz &dzdx &dxdy \\ \frac{\partial }{\partial x} & \frac{\partial }{\partial y} &\frac{\partial }{\partial z} \\ P &Q &R \end{array}\right| = \oint_{\Gamma} Pdx+Qdy+Rdz\]
1. \ xleftarrow or \ xrightarrow. Same usage of both.
Code:
\ [Latex A = B \ xleftarrow [H] {\ + XI A \ C} F = G Times \]
$$Latex a=b \xleftarrow[H]{\xi+a\times c} f=g$$- Use \ overset
Code:
\ [LaTeX A = B \ overset {} {F. \ Longleftarrow} C = D \]
$$latex a=b \overset{F}{\longleftarrow}c=d$$- Use \ stackre
Code:
\ [LaTeX A = B \ {F. Stackrel {} \} longleftrightarrow C = D \]
$$latex a=b \stackrel{F}{\longleftrightarrow}c=d$$- Use \ mathop
Code:
\ [LaTeX ab & \ mathop {\ SUM \ SUM \ SUM} _ {A = \ FRAC {. 1} {2} \ Times 100000} ^ {B = \ FRAC {. 4} {. 5}} CD \ ]
$$latex ab \mathop{\sum\sum\sum}_{a=\frac{1}
{2}\times 100000}^{b=\frac{4}{5}}cd$$Changed a bit, sometimes using \ mathop unsuccessful, can be changed \ mathop {} \ limits_ {} ^ {}
8. matrix & determinant
Determinant
Where \ left | and \ right | expressed about delimiter
\[ \left |\begin{array}{cccc} 1 &6 & 9 \\ 7 &90 & f(x) \\ 9 & \psi(x) &g(x) \\ \end{array}\right| \]
$$
\left |\begin{array}{cccc}
1 &6 & 9 \\
7 &90 & f(x) \\
9 & \psi(x) &g(x) \\
\end{array}\right|
$$matrix
If we | replace () or [], we get a matrix.
Align Right
\[ \left (\begin{array}{rrrr} 1 &6 & 9 \\ 7 &90 & f(x) \\ 9 & \psi(x) &g(x) \\ \end{array}\right) \]
Left
\[ \left [\begin{array}{llll} 1 &6 & 9 \\ 7 &90 & f(x) \\ 9 & \psi(x) &g(x) \\ \end{array}\right] \]
& Aligned symbols.
left = L
C = Center
R & lt right =
9. operational sign
Dot \ cdot
\ (A \ cdot b \)Cross product \ Times
\ (A \ Times b \)Divide \ div
\ (A \ div b \)In addition to the slash /
\ [A ^ E / B \]Approximate symbol \ SIM
\ [SiNx \ SIM X \]
10. Space
Use spaces are \ quad command in general. But the recent discovery that the space distance too, need smaller spaces. So instead command.
Use \ Command Effect
Use \ quad command effect
| Two quad spaces | a \ qquad b | 