LaTeX Tutorial

文章目录

LaTeX Tutorial
- Greek Alphabet
- Superscript & Subscript
- Fraction & Square Root
- Common Operator
- Advanced Operator
- Common Function
- Vector
- Arrow
- Brackets & Parentheses
- Piecewise Function
- Linear Equations
- Matrix
- Hands-on Projects
- References

Greek Alphabet

\\ \theta \ \lambda \ \epsilon                    \        → a blank space
\\ \theta \; \lambda \; \epsilon                  \;       → a 5/18em blank space
\\ \theta \enspace \lambda \enspace \epsilon      \enspace → a 1/2em blank space
\\ \pi \quad \sigma \quad \omega                              \quad    → a 1em blank space
\\ \phi \qquad \varphi \qquad \Phi \qquad \varPhi \qquad   → a 2em blank space

θ λ ϵ θ λ ϵ θ λ ϵ π σ ω ϕ φ Φ Φ \\ \theta \ \lambda \ \epsilon \\ \theta \; \lambda \; \epsilon \\ \theta \enspace \lambda \enspace \epsilon \\ \pi \quad \sigma \quad \omega \\ \phi \qquad \varphi \qquad \Phi \qquad \varPhi θ λ ϵθλϵθλϵπσωϕφΦΦ

Greek letter	LaTeX Form	Greek letter	LaTeX Form
α A	\alpha A	N	\nu N
β B	\beta B	ξ Ξ	\xi \Xi
γ Γ	\gamma \Gamma	o O	o O
δ Δ	\delta \Delta	π Π	\pi \varpi \Pi
ϵ ε E	\epsilon \varepsilon E	ρ ϱ P	\rho \varrho P
ζ Z	\zeta Z	σ Σ	\sigma \Sigma
η H	\eta H	τ T	\tau T
θ ϑ Θ	\theta \vartheta \Theta	υ Υ	\upsilon \Upsilon
ω Ω	\omega \Omega	ϕ φ Φ	\phi \varphi \Phi
κ K	\kappa K	χ X	\chi X
λ Λ	\lambda \Lambda	ψ Ψ	\psi \Psi
μ M	\mu M	ι	\iota

PS: Upper Greek Letter can become italics by using “var”
Σ → Σ \Sigma \rightarrow \varSigma Σ→Σ

Superscript & Subscript

\\H_2O
\\cm^3
\\x^{y+z}
\\P_{ij}
\\x_i
\\x_{\rm i}

H 2 O c m 3 x y + z P i j x i x i \\H_2O \\cm^3 \\x^{y+z} \\P_{ij} \\x_i \\x_{\rm i} H2Ocm3xy+zPijxixi

Fraction & Square Root

\\ \frac{1}{2}
\\ \frac{x}{y+z}
\\ \frac{\frac{1}{x}}{e+1}  #compare with line4, not recommended
\\ \frac{\dfrac{1}{x}}{e+1} #recommended \\ \sqrt[3]{x+1}
\\ \sqrt{\sqrt{x+1}}
\\ \sqrt{x+\sqrt{x+\sqrt{x+1}}}

1 2 1 2 x y + z 1 x e + 1 1 x e + 1 x + 1 3 x + 1 x + x + x + 1 \\ \frac{1}{2} \\ \frac{1}{2} \\ \frac{x}{y+z} \\ \frac{\frac{1}{x}}{e+1} \\ \frac{\dfrac{1}{x}}{e+1} \\ \sqrt[3]{x+1} \\ \sqrt{\sqrt{x+1}} \\ \sqrt{x+\sqrt{x+\sqrt{x+1}}} 2121y+zxe+1x1e+1x13x+1 x+1 x+x+x+1

Common Operator

\\+-
\\ \times \cdot \div
\\ \pm \ \mp
\\ > < \ge \le \gg \ll
\\  = \ne \approx \equiv
\\ \cap \cup \in \notin \subseteq \subsetneqq \varnothing
\\ \forall \ \exists \ \nexists
\\ \because \ \therefore
\\ \R \ \Q \ \N \ \Z \ \Z_+
\\ \cdot \ \cdots \ \vdots \ \ddots
\\ \infty \ \partial \ \degree

KaTeX parse error: Undefined control sequence: \Q at position 213: …refore \\ \R \ \̲Q̲ ̲\ \N \ \Z \ \Z_…

Advanced Operator

\\ \sum \ \prod
\\ \sum_{i=0}^{n} x_{i} \ \prod_{i=0}^n x_i
\\ \frac {\sum\limits_{i=0}^{n} x_i}{\prod\limits_{i=0}^n x_i}
\\ \int \ \int_a^b \ \iint \ \iiint \ \oint \ \oiint
\\ \int_{-\infty}^{0} f(x)\,\text d x

∑ ∏ ∑ i = 0 n x i ∏ i = 0 n x i ∑ i = 0 n x i ∏ i = 0 n x i ∫ ∫ a b ∬ ∭ ∮ ∯ ∫ − ∞ 0 f ( x ) d x \\ \sum \ \prod \\ \sum_{i=0}^{n} x_{i} \ \prod_{i=0}^n x_i \\ \frac {\sum\limits_{i=0}^{n} x_i}{\prod\limits_{i=0}^n x_i} \\ \int \ \int_a^b \ \iint \ \iiint \ \oint \ \oiint \\ \int_{-\infty}^{0} f(x)\,\text d x ∑ ∏i=0∑nxi i=0∏nxii=0∏nxii=0∑nxi∫ ∫ab ∬ ∭ ∮ ∬ ∫−∞0f(x)dx

Common Function

\\ \sin x \ \cos x \sec x \tan x
\\ \log_2 x \ \ln x \lg x
\\ \lim_{x \to 0} \frac{x}{\sin x}

sin ⁡ x cos ⁡ x sec ⁡ x tan ⁡ x log ⁡ 2 x ln ⁡ x lg ⁡ x lim ⁡ x → 0 x sin ⁡ x \\ \sin x \ \cos x \sec x \tan x \\ \log_2 x \ \ln x \lg x \\ \lim_{x \to 0} \frac{x}{\sin x} sinx cosxsecxtanxlog2x lnxlgxx→0limsinxx

Vector

\\ \vec x \ \vec y \ \vec z
\\ \overrightarrow {ABC}\\ \bar x
\\ \overline {ABC}
\\ \widehat{ABC} \ \widetilde{ABC} \\ \mathbf R\\ \dot{a} \ \ddot{a} \ \mathring{a}
\\ \hat{a} \ \check{a} \ \tilde{a} \ \acute{a}

x ⃗ y ⃗ z ⃗ A B C → x ˉ A B C ‾ A B C ^ A B C ~ R a ˙ a ¨ a ˚ a ^ a ˇ a ~ a ˊ \\ \vec x \ \vec y \ \vec z \\ \overrightarrow {ABC} \\ \bar x \\ \overline {ABC} \\ \widehat{ABC} \ \widetilde{ABC} \\ \mathbf R \\ \dot{a} \ \ddot{a} \ \ \mathring{a} \\ \hat{a} \ \check{a} \ \tilde{a} \ \acute{a} x y z ABC xˉABCABC ABC Ra˙ a¨ a˚a^ aˇ a~ aˊ

Arrow

\\ \gets      \ \to
\\ \leftarrow \ \rightarrow \ \leftrightarrow
\\ \Leftarrow \ \Rightarrow \ \Leftrightarrow
\\ \longleftarrow \ \longrightarrow \ \longleftrightarrow
\\ \Longleftarrow \ \Longrightarrow \ \Longleftrightarrow
\\ \mapsto \ \longmapsto
\\ \hookleftarrow \ \hookrightarrow
\\ \leftharpoonup \ \rightharpoonup
\\ \leftharpoondown \ \rightharpoondown
\\ \rightleftharpoons
\\ \uparrow \ \downarrow \ \updownarrow
\\ \Uparrow \ \Downarrow \ \Updownarrow
\\ \nearrow \ \searrow \ \swarrow \ \nwarrow
\\ \leadsto

← → ← → ↔ ⇐ ⇒ ⇔ ⟵ ⟶ ⟷ ⟸ ⟹ ⟺ ↦ ⟼ ↩ ↪ ↼ ⇀ ↽ ⇁ ⇌ ↑ ↓ ↕ ⇑ ⇓ ⇕ ↗ ↘ ↙ ↖ ⇝ \\ \gets \ \to \\ \leftarrow \ \rightarrow \ \leftrightarrow \\ \Leftarrow \ \Rightarrow \ \Leftrightarrow \\ \longleftarrow \ \longrightarrow \ \longleftrightarrow \\ \Longleftarrow \ \Longrightarrow \ \Longleftrightarrow \\ \mapsto \ \longmapsto \\ \hookleftarrow \ \hookrightarrow \\ \leftharpoonup \ \rightharpoonup \\ \leftharpoondown \ \rightharpoondown \\ \rightleftharpoons \\ \uparrow \ \downarrow \ \updownarrow \\ \Uparrow \ \Downarrow \ \Updownarrow \\ \nearrow \ \searrow \ \swarrow \ \nwarrow \\ \leadsto ← →← → ↔⇐ ⇒ ⇔⟵ ⟶ ⟷⟸ ⟹ ⟺↦ ⟼↩ ↪↼ ⇀↽ ⇁⇌↑ ↓ ↕⇑ ⇓ ⇕↗ ↘ ↙ ↖⇝

Brackets & Parentheses

\\( \ )
\\ \{ \ \}
\\ [ \ ]
\\ \lceil \ \rceil \lfloor \ \rfloor
\\ (0,\frac{1}{a}]
\\ \left(0,\frac{1}{a}\right]
\\ \frac{\partial f}{\partial z}|_{x=0}
\\ \left.\frac{\partial f}{\partial z}\right|_{x=0}

( ) { } [ ] ⌈ ⌉ ⌊ ⌋ ( 0 , 1 a ] ( 0 , 1 a ] ∂ f ∂ z ∣ x = 0 ∂ f ∂ z ∣ x = 0 \\( \ ) \\ \{ \ \} \\ [ \ ] \\ \lceil \ \rceil \lfloor \ \rfloor \\ (0,\frac{1}{a}] \\ \left(0,\frac{1}{a}\right] \\ \frac{\partial f}{\partial z}|_{x=0} \\ \left.\frac{\partial f}{\partial z}\right|_{x=0} ( ){ }[ ]⌈ ⌉⌊ ⌋(0,a1](0,a1]∂z∂f∣x=0∂z∂f∣∣∣∣x=0

PS: use “\left. \right” to add adpative attributes

Piecewise Function

f(x)=
\begin{cases}\sin x,&\dfrac{\pi}{2}\le x \le 2π \\0,&\text {else}
\end{cases}

f ( x ) = { sin ⁡ x , π 2 ≤ x ≤ 2 π 0 , else f(x)= \begin{cases} \sin x,&\dfrac{\pi}{2}\le x \le 2π \\ 0,&\text {else} \end{cases} f(x)={sinx,0,2π≤x≤2πelse

Linear Equations

\begin{cases}
3x+2y-z=7\\
2y+7z=8\\
3z=8
\end{cases}

{ 3 x + 2 y − z = 7 2 y + 7 z = 8 3 z = 8 \begin{cases} 3x+2y-z=7\\ 2y+7z=8\\ 3z=8 \end{cases} ⎩⎪⎨⎪⎧3x+2y−z=72y+7z=83z=8

Matrix

\begin{matrix}a & b & \cdots & c \\\vdots & \vdots & \ddots & \vdots\\d & e & \cdots & d
\end{matrix}\begin{pmatrix}a & b & \cdots & c \\\vdots & \vdots & \ddots & \vdots\\d & e & \cdots & d
\end{pmatrix}\begin{bmatrix}a & b & \cdots & c \\\vdots & \vdots & \ddots & \vdots\\d & e & \cdots & d
\end{bmatrix}\begin{vmatrix}a & b & \cdots & c \\\vdots & \vdots & \ddots & \vdots\\d & e & \cdots & d
\end{vmatrix}

a b ⋯ c ⋮ ⋮ ⋱ ⋮ d e ⋯ d ( a b ⋯ c ⋮ ⋮ ⋱ ⋮ d e ⋯ d ) [ a b ⋯ c ⋮ ⋮ ⋱ ⋮ d e ⋯ d ] ∣ a b ⋯ c ⋮ ⋮ ⋱ ⋮ d e ⋯ ∣ \begin{matrix} a & b & \cdots & c \\ \vdots & \vdots & \ddots & \vdots\\ d & e & \cdots & d \end{matrix} \begin{pmatrix} a & b & \cdots & c \\ \vdots & \vdots & \ddots & \vdots\\ d & e & \cdots & d \end{pmatrix} \begin{bmatrix} a & b & \cdots & c \\ \vdots & \vdots & \ddots & \vdots\\ d & e & \cdots & d \end{bmatrix} \begin{vmatrix} a & b & \cdots & c \\ \vdots & \vdots & \ddots & \vdots\\ d & e & \cdots & \end{vmatrix} a⋮db⋮e⋯⋱⋯c⋮d⎝⎜⎛a⋮db⋮e⋯⋱⋯c⋮d⎠⎟⎞⎣⎢⎡a⋮db⋮e⋯⋱⋯c⋮d⎦⎥⎤∣∣∣∣∣∣∣a⋮db⋮e⋯⋱⋯c⋮∣∣∣∣∣∣∣

Hands-on Projects

F ( x , y ) = ∫ − ∞ x ∫ − ∞ y f ( u , v ) d v d u F(x,y) = \int_{-\infty}^x\int_{-\infty}^y f(u,v)\mathrm dv\mathrm du F(x,y)=∫−∞x∫−∞yf(u,v)dvdu

P ( X = k ) = e − λ λ k k ! , k = 0 , 1 , 2 , ⋯ P(X=k)={\mathrm e}^{-\lambda} \frac{\lambda^k}{k!},\quad k=0,1,2,\cdots P(X=k)=e−λk!λk,k=0,1,2,⋯

f ( x ) = 1 2 π σ e ( x − μ ) 2 2 σ 2 f(x)=\frac{1}{\sqrt{2\pi}\sigma}\mathrm{e}^{\frac{(x-\mu)^2}{2\sigma^2}} f(x)=2π σ1e2σ2(x−μ)2

ρ X Y = C o v ( X , Y ) D ( x ) D ( Y ) \rho_{XY}=\frac{Cov(X,Y)}{\sqrt{D(x)}\sqrt{D(Y)}} ρXY=D(x) D(Y) Cov(X,Y)

∮ S E ⃗ ⋅ d S ⃗ = 1 ε 0 ∑ i = 1 n q i \oint_S \vec E \cdot d\vec S = \frac{1}{\varepsilon_0}\sum_{i=1}^n q_i ∮SE ⋅dS =ε01i=1∑nqi

E x = λ 4 π ε 0 r ( cos ⁡ θ 1 − cos ⁡ θ 2 ) E y = λ 4 π ε 0 r ( sin ⁡ θ 2 − sin ⁡ θ 1 ) \begin{aligned} E_x &= \frac{\lambda}{4\pi\varepsilon_0r}(\cos \theta_1 - \cos \theta_2) E_y &= \frac{\lambda}{4\pi\varepsilon_0r}(\sin \theta_2 - \sin \theta_1) \end{aligned} Ex=4πε0rλ(cosθ1−cosθ2)Ey=4πε0rλ(sinθ2−sinθ1)

References

The Great, Big List of LaTeX Symbols

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