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3 MathJax HTML \ Y \ Y mathjax.html <html> <head> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax /2.7.0/MathJax.js?config=TeX-AMS_CHTML"></script> <title>mathjax </title> </head> MathJax <br> \(ax+b=0\) \[ x = -\frac{b}{a} \] </html> <head></head> <script type="text/javascript" src="https://cdn.mathjax.o rg/mathjax/latest/mathjax.js?config=tex-ams_chtml"></script> MathJax <br> \( \) \[ \] \frac{}{} HTML MathJax ax + b = 0 x = b a \ 2

\ Y TeX TeX mathjax.html \(ax^{2}+bx+c=0\) \[ x = \frac{-b\pm\sqrt{b^{2}-4ac}}{2a} \tag{1} \] ax 2 + bx + c = 0 x = b ± b 2 4ac 2a (1) ^{} e^{x} \pm ± \sqrt{} n n \sqrt[n]{} \tag{} \tag{*} ( ) \pm a ±a \pma 3

4 1 HTML \[ \sum_{k=1}^{n} a_{k} = a_{1} + a_{2} + \dots + a_{n} \] n a k = a 1 + a 2 + + a n k=1 \sum_{}^{} _{} ^{} _{} \dots 2 HTML \[ \int_{-\infty}^{\infty} e^{-x^{2}} \, dx = \sqrt{\pi} \] e x2 dx = π \int_{}^{} \infty \, \pi π 4

3 HTML \(f(x)\) \[ f (x) = \lim_{\delta x \to 0} \frac{ f(x+\delta x) - f(x) }{\Delta x} \] f(x) \lim_{} \to \Delta f f(x + x) f(x) (x) = lim x 0 x 4 HTML \[ \int \tan\theta \, d\theta = \int \frac{\sin\theta}{\cos\theta} \, d\theta = -\log \cos\theta + C \] tan θ dθ = sin θ dθ = log cos θ + C cos θ \sin, \cos, \tan, \log sin, cos, tan, log sin sin s i n \theta θ 5

5 HTML \begin{align} \cos 2\theta &= \cos^{2} \theta - \sin^{2} \theta \\ &= 2\cos^{2} \theta - 1 \\ &= 1-2\sin^{2} \theta \end{align} cos 2θ = cos 2 θ sin 2 θ = 2 cos 2 θ 1 = 1 2 sin 2 θ \begin{align}\end{align} \\ & 6 HTML \[ x = \begin{cases} x & \text{\(x\ge0\) } \\ -x & \text{\(x<0\) } \end{cases} \] x = { x x x 0 x < 0 \begin{cases}\end{cases} & \\ \text{} \ge \le 6

7 HTML \(n \times n\) \[ A = \begin{pmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \ldots & a_{nn} \end{pmatrix} \] \(A^{-1}\) \(\det A \neq 0\) n n a 11 a 12... a 1n a 21 a 22... a 2n A =...... a n1 a n2... a nn A 1 det A 0 \times \begin{pmatrix}\end{pmatrix} & \\ \ldots, \vdots, \ddots \det det \neq pmatrix ( ) bmatrix [ ] Bmatrix { } vmatrix Vmatrix matrix 7

5 MathJax MathJax config.js mathjax.html config.js window.mathjax = { TeX: { equationnumbers: {autonumber: "AMS"}, Macros: { x: {\\times}, bm: [ {\\boldsymbol{#1}},1], dd: [ {\\frac{\\partial #1}{\\partial #2}},2] } }, CommonHTML: { scale: 110, mtextfontinherit: true } }; equationnumbers \[ \] \begin{equation} \end{equation} Macros x \times \x bm 1 \bm{} \boldsymbol{a} \bm{a} dd 2 \dd{}{} \frac{{\partial A}{\partial B} \dd{a}{b} scale 110% mtextfontinherit false MathJax http://docs.mathjax.org/en/latest/ 8

HTML mathjax.html <html> <head> <script type="text/javascript" src="config.js"></script> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax /2.7.0/MathJax.js?config=TeX-AMS_CHTML"></script> <title>mathjax </title> </head> \(\bm{b}(x,y,z)\) \begin{equation} \bm{b} = \nabla \x \bm{a} \label{a} \end{equation} \begin{equation} \nabla \cdot \bm{b} = \dd{b_{x}}{x} + \dd{b_{y}}{y} + \dd{b_{z}}{z} \end{equation} 0 \eqref{a} \(\bm{a}\) \(\bm{b}\) </html> \nabla \cdot <head></head> MathJax config.js HTML B(x, y, z) B = A (1) B = B x x + B y y + B z z (2) 0 (1) A B \label{} \eqref{} a \eqref{a} \notag 9

6 1 2 3 f(x) = f(x) = e iθ = cos θ + i sin θ n=0 f (n) (a) (x a) n n! ( ) 1 exp (x µ)2 2πσ 2 2σ 2 \pi, \mu, \sigma π, µ, σ \exp exp \left( \right) \left \right () [] \{\} 4 m d2 r dt 2 = F \vec{} \overrightarrow{} AB 5 d dt ( ) L L q q = 0 \partial \mathcal{} \mathcal{l} \dot{} 10

6 ˆf(ξ) = f(x) e 2πix ξ dx R n \hat{} ˆ \xi ξ \mathbb{} \cdot 7 \alpha α \oint f(α) = 1 f(z) 2πi C z α dz 8 A dv = A n ds V V \iint, \iiint, \iiiint,, \nabla \boldsymbol{} 9 iħ ( ) t ψ(r, t) = ħ2 2m 2 + V (r, t) ψ(r, t) \hbar ħ \psi ψ \biggl( \biggr) \bigl, \Bigl, \biggl, \Biggl l r l m 11

10 H 2 (g) + 1 2 O 2(g) = H 2 O(l) + 286 kj \mathrm{} \mathrm{} \, 11 A B = { x x A x B } \{ \} {} {} \cap, \cup, \wedge, \vee,,, \in, \ni, \notin, \subset, \supset,, /,, \emptyset, \forall, \exists, \neg,,, 12 1 Γ (z) = zeγz n=1 ( 1 + z ) e z/n n \gamma, \Gamma, \vargamma γ, Γ, Γ \prod_{}^{} 13 E = ρ ε 0, B = 0, E = B t B = µ 0 i + 1 E c 2 t \rho, \varepsillon, \mu ρ, ε, µ \times \begin{align}\end{align} & & 1 1 3 & 12

A \ \quad \qquad \quad 2 \, \quad 3/18 \: \quad 4/18 \; \quad 5/18 \! \quad 3/18 \alpha \beta \gamma \delta \epsilon \varepsilon α β γ δ ϵ ε \zeta \eta \theta \vartheta \iota \kappa ζ η θ ϑ ι κ \lambda λ \mu µ \nu ν \xi ξ o o \pi π \varpi \rho \varrho \sigma \varsigma \tau ϖ ρ ϱ σ ς τ \upsilon \phi \varphi \chi \psi \omega υ ϕ φ χ ψ ω \Gamma \vargamma \Delta \vardelata \Theta \vartheta Γ Γ Θ Θ \Lambda \varlambda \Xi \varxi \Pi \varpi Λ Λ Ξ Ξ Π Π \Sigma \varsigma \Upsilon \varupsilon \Phi \varphi Σ Σ Υ Υ Φ Φ \Psi \varpsi \Omega \varomega Ψ Ψ Ω Ω (x) [x] \{x\} \langle x \rangle \lfloor x \rfloor \lceil x \rceil (x) [x] {x} x x x x x \ x\ x / / \backslash \ 13

+ + - \pm ± \mp \times \div \ast \star \cdot \bullet \circ \bigcirc \setminus \ \wr \cap \cup \sqcap \sqcup \wedge \vee \oplus \ominus \otimes \oslash \odot \dagger \ddagger \amalg = = \neq \doteq \doteqdot \equiv \sim \backsim \simeq \backsimeq \eqsim \approx \approxeq. = \cong = \propto \varpropto \perp \mid \shortmid \parallel \shortparallel \therefore \because \risingdotseq \fallingdotseq < < > > \ll \gg \lll \ggg \le, \leq \ge, \geq \leqq \geqq \leqslant \geqslant \lesssim \gtrsim \subset \supset \subseteq \supseteq \subseteqq \supseteqq \in \ni \notin / \backepsilon \not \not\equiv \emptyset \varnothing \infty \aleph \complement \partial \digamma \hbar \hslash \imath \jmath ℵ ϝ ħ ħ ı ȷ \Bbbk k \varkappa κ \ell l \Re R \Im I \mho \eth ð \prime \backprime \surd \nabla \triangle \square \blacksquare \bigstar \spadesuit \heartsuit \diamondsuit \clubsuit \angle \measuredangle \sphericalangle \top \bot \diagup \diagdown \forall \exists \nexists \neg, \lnot \sharp \flat \natural 14

\sin sin \cos cos \tan tan \cot cot \sec sec \csc csc \arcsin arcsin \arccos arccos \arctan arctan \sinh sinh \cosh cosh \tanh tanh \coth coth \exp exp \log log \ln ln \lg lg \arg arg \Pr Pr \det det \hom hom \ker ker \dim dim \deg deg \gcd gcd \bmod mod \pmod{n} (mod n) \lim lim \min min \max max \inf inf \sup sup \liminf lim inf \limsup lim sup \sum \prod \coprod \bigcap \bigcup \biguplus \bigsqcup \bigwedge \bigvee \bigoplus \bigotimes \bigodot \int \oint \iint \iiint \iiiint \idotsint _{}^{} \rightarrow, \to \leftarrow, \gets \longrightarrow \longleftarrow \leftrightarrow \longleftrightarrow \mapsto \longmapsto \hookrightarrow \hookleftarrow \rightleftarrows \leftrightarrows \rightrightarrows \leftleftarrows \uparrow \downarrow \updownarrow \upuparrows \downdownarrows \nearrow \searrow \nwarrow \swarrow \Rightarrow \Leftarrow \Longrightarrow = \Longleftarrow = \Leftrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \rightleftharpoons \leftrightharpoons \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright 15

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