latex 常用数学符号(数值函数、根式、微分与导数、模运算、极限、范围与预测)

目录

数值函数

符号latex
exp ⁡ a b = a b \exp_a b = a^bexpa​b=ab\exp_a b = a^b
exp ⁡ b = e b \exp b = e^bexpb=eb\exp b = e^b
1 0 m 10^m10m10^m
ln ⁡ c \ln clnc\ln c
lg ⁡ d = log ⁡ e \lg d = \log elgd=loge\lg d = \log e
log ⁡ 10 f \log_{10} flog10​f\log_{10} f
sin ⁡ a \sin asina\sin a
cos ⁡ b \cos bcosb\cos b
tan ⁡ c \tan ctanc\tan c
cot ⁡ d \cot dcotd\cot d
sec ⁡ e \sec esece\sec e
csc ⁡ f \csc fcscf\csc f
arcsin ⁡ a \arcsin aarcsina\arcsin a
arccos ⁡ b \arccos barccosb\arccos b
arctan ⁡ c \arctan carctanc\arctan c
arccot ⁡ d \operatorname{arccot} darccotd\operatorname{arccot} d
arcsec ⁡ d \operatorname{arcsec} darcsecd\operatorname{arcsec} d
arccsc ⁡ d \operatorname{arccsc} darccscd\operatorname{arccsc} d
sinh ⁡ a \sinh asinha\sinh a
cosh ⁡ a \cosh acosha\cosh a
tanh ⁡ a \tanh atanha\tanh a
coth ⁡ a \coth acotha\coth a
sh ⁡ d \operatorname{sh} dshd\operatorname{sh} d
ch ⁡ d \operatorname{ch} dchd\operatorname{ch} d
th ⁡ d \operatorname{th} dthd\operatorname{th} d
coth ⁡ d \operatorname{coth} dcothd\operatorname{coth} d
argsh ⁡ d \operatorname{argsh} dargshd\operatorname{argsh} d
argch ⁡ d \operatorname{argch} dargchd\operatorname{argch} d
argth ⁡ d \operatorname{argth} dargthd\operatorname{argth} d
sgn ⁡ d \operatorname{sgn} dsgnd\operatorname{sgn} d
∣ s ∣ \left\vert s \right\vert∣s∣\left\vert s \right\vert
min ⁡ ( x , y ) \min(x,y)min(x,y)\min(x,y)
max ⁡ ( x , y ) \max(x,y)max(x,y)\max(x,y)

根式

符号latex
√ \surd√\surd
3 \sqrt{3}3​\sqrt{3}
3 n \sqrt[n]{3}n3​\sqrt[n]{3}
x 3 + y 3 2 3 \sqrt[3]{\frac{x^3+y^3}{2}}32x3+y3​​\sqrt[3]{\frac{x^3+y^3}{2}}

微分与导数

符号latex
d t dtdtdt
d t \mathrm{d}tdt\mathrm{d}t
∂ t \partial t∂t\partial t
∇ ψ \nabla\psi∇ψ\nabla\psi
d y / d x , d y / d x dy/dx, \mathrm{d}y/\mathrm{d}xdy/dx,dy/dxdy/dx, \mathrm{d}y/\mathrm{d}x
d y d x , d y d x \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}dxdy​,dxdy​\frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}
∂ 2 ∂ x 1 ∂ x 2 y \frac{\partial^2}{\partial x_1\partial x_2}y∂x1​∂x2​∂2​y\frac{\partial^2}{\partial x_1\partial x_2}y
′ , ‵ \prime, \backprime′,‵\prime, \backprime
f ′ , f ′ , f ′ ′ , f ( 3 ) f^\prime, f', f'', f^{(3)}f′,f′,f′′,f(3)f^\prime, f’, f’', f^{(3)}
y ˙ , y ¨ \dot y, \ddot yy˙​,y¨​\dot y, \ddot y

模运算

符号latex
s k ≡ 0 ( m o d m ) s_k \equiv 0 \pmod{m}sk​≡0(modm)s_k \equiv 0 \pmod{m}
a m o d b a \bmod bamodba \bmod b
gcd ⁡ ( m , n ) \gcd(m, n)gcd(m,n)\gcd(m, n)
lcm ⁡ ( m , n ) \operatorname{lcm}(m, n)lcm(m,n)\operatorname{lcm}(m, n)
∣ , ∤ , ∣ , ∤ \mid, \nmid, \shortmid, \nshortmid∣,∤,∣,\mid, \nmid, \shortmid, \nshortmid

极限

符号latex
lim ⁡ n → ∞ x n \lim_{n \to \infty}x_nlimn→∞​xn​\lim_{n \to \infty}x_n
lim ⁡ n → ∞ x n \textstyle \lim_{n \to \infty}x_nlimn→∞​xn​\textstyle \lim_{n \to \infty}x_n

范围与预测

符号latex
min ⁡ x , max ⁡ y , inf ⁡ s , sup ⁡ t \min x, \max y, \inf s, \sup tminx,maxy,infs,supt\min x, \max y, \inf s, \sup t
lim ⁡ u , lim inf ⁡ v , lim sup ⁡ w \lim u, \liminf v, \limsup wlimu,liminfv,limsupw\lim u, \liminf v, \limsup w
dim ⁡ p , deg ⁡ q , det ⁡ m , ker ⁡ ϕ \dim p, \deg q, \det m, \ker\phidimp,degq,detm,kerϕ\dim p, \deg q, \det m, \ker\phi
Pr ⁡ j , hom ⁡ l , ∥ z ∥ , arg ⁡ z \Pr j, \hom l, \lVert z \rVert, \arg zPrj,homl,∥z∥,argz\Pr j, \hom l, \lVert z \rVert, \arg z
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