KaTeX

KaTeX\KaTeX ​

行内公式 ​

{x∣Ax=b}\{x | Ax = b\}

md
$\{x | Ax = b\}$

Xc∗<1,Xq∗<1\mathcal{X}_{c^*}<1, \mathcal{X}_{q^*}<1

E=mc2E = mc^2

∂∂t\frac{\partial}{\partial t}

latex
$E = mc^2$
$\frac{\partial}{\partial t}$

行间公式 ​

E=mc2E = mc^2

latex
$$ E = mc^2 $$

a⃗=dv⃗dt=d(drdte⃗∗i+rdθdte⃗∗j)dt=d2rdt2e⃗∗i+drdtde⃗∗idt+drdtdθdte⃗∗j+rd2θdt2e⃗∗j+rdθdtde⃗_jdt\vec a=\frac{d\vec v}{dt}=\frac{d(\frac{dr}{dt}\vec e*{i}+r\frac{d\theta}{dt}\vec e*{j})}{dt}=\frac{d^2r}{dt^2}\vec e*{i}+\frac{dr}{dt}\frac{d\vec e*{i}}{dt}+\frac{dr}{dt}\frac{d\theta}{dt}\vec e*{j}+r\frac{d^2\theta}{dt^2}\vec e*{j}+r\frac{d\theta}{dt}\frac{d\vec e\_{j}}{dt}

latex
$$ \vec a=\frac{d\vec v}{dt}=\frac{d(\frac{dr}{dt}\vec e_{i}+r\frac{d\theta}{dt}\vec e_{j})}{dt}=\frac{d^2r}{dt^2}\vec e_{i}+\frac{dr}{dt}\frac{d\vec e_{i}}{dt}+\frac{dr}{dt}\frac{d\theta}{dt}\vec e_{j}+r\frac{d^2\theta}{dt^2}\vec e_{j}+r\frac{d\theta}{dt}\frac{d\vec e_{j}}{dt} $$

mt=gtm_t=g_t

Vt=1V_t=1

latex
$$ m_t=g_t $$
$$ V_t=1 $$

ηt=lr∗mtVt=lr∗gt\eta_t=lr*{\frac {m_t}{\sqrt V_t}}=lr*g_t

w_t+1=wt−ηt=wt−lr∗mtVt=wt−lr∗gtw\_{t+1}=w_t-\eta_t=w_t-lr*{\frac {m_t}{\sqrt V_t}}=w_t-lr*g_t

qs′′=−k∂∂x(T1+T2)∣x=0=−k∂T1∂x∣x=0⏟qs′′−k∂T2∂x∣x=0→0=−k∂T2∂x∣x=0q''_s = -k \left.\frac{\partial }{\partial x} (T_1+T_2) \right|_{x=0} = \underbrace{-k \left.\frac{\partial T_1}{\partial x} \right|_{x=0}}_{q''_s} -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0} \rightarrow \boxed{0 = -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0}}

latex
$$ \eta_t=lr*{\frac {m_t}{\sqrt V_t}}=lr*g_t $$
$$ w_{t+1}=w_t-\eta_t=w_t-lr*{\frac {m_t}{\sqrt V_t}}=w_t-lr*g_t $$

<div text="red">

$$
q''_s = -k \left.\frac{\partial }{\partial x} (T_1+T_2) \right|_{x=0} = \underbrace{-k \left.\frac{\partial T_1}{\partial x} \right|_{x=0}}_{q''_s}  -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0} \rightarrow \boxed{0 = -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0}}
$$

</div>

[abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}

latex
$$
\begin{bmatrix}
  a & b \\
  c & d
\end{bmatrix}
$$

{x=acos⁡θy=bsin⁡θ\begin{equation} \left\{ \begin{aligned} x=a\cos\theta\\ y=b\sin\theta\\ \end{aligned} \right. \end{equation}

latex
$$
\begin{equation}
  \left\{
    \begin{aligned}
      x=a\cos\theta\\
      y=b\sin\theta\\
    end{aligned}
  \right.
\end{equation}
$$
  • 本文作者:云游君
  • 本文链接:https://yun.valaxy.site/posts/katex
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