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P(A|B)=\frac{P(B|A)P(A)}{P(B)}

SE▌W▌▌

\nabla\times\mathbf{B}=\mu_0\mathbf{J}

▌▌

fun▌

E=mc^2

▌▌

\sum_{n=1}^\infty\frac{1}{n^2}=\frac{\pi^2}{6}

▌▌

Зн▌c▌

\Delta x\,\Delta p\geq\frac{\hbar}{2}

▌▌

e^{i\pi}+1=0

▌

st▌

\sin^2\theta+\cos^2\theta=1

▌▌

F=ma

▌▌

\frac{d}{dx}[e^x]=e^x

▌▌▌

\sigma^2=\mathbb{E}[(X-\mu)^2]

▌▌

a▌

\hat{H}|\psi\rangle=E|\psi\rangle

▌▌

\oint\mathbf{E}\cdot d\mathbf{A}=\frac{Q}{\varepsilon_0}

▌▌

\chi^2=\sum\frac{(O-E)^2}{E}

▌

PV=nRT

▌▌

S=k_B\ln\Omega

▌▌▌

\nabla^2 f=0

▌▌

▌

T(n)=2T(n/2)+O(n)

▌▌

\Gamma(n+1)=n!

▌▌

z=\frac{x-\mu}{\sigma}

▌

\eta=1-\frac{T_c}{T_h}

▌▌

O(n\log n)

▌▌▌

e^x=\sum_{n=0}^\infty\frac{x^n}{n!}

▌▌

▌

\phi=\frac{1+\sqrt{5}}{2}

▌▌

\nabla\cdot\mathbf{E}=\frac{\rho}{\varepsilon_0}

▌▌

\lambda=\frac{h}{p}

▌▌▌

\frac{dN}{dt}=-\lambda N

▌▌

▌

\cos x=\sum_{n=0}^\infty(-1)^n\frac{x^{2n}}{(2n)!}

▌▌

\mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B})

▌▌

\zeta(2)=\frac{\pi^2}{6}

▌

r=\frac{\text{Cov}(X,Y)}{\sigma_X\sigma_Y}

▌▌

\frac{\partial^2 u}{\partial t^2}=c^2\nabla^2 u

▌▌▌

(1+x)^n=\sum_{k=0}^n\binom{n}{k}x^k

▌▌

▌

\Delta G=\Delta H-T\Delta S

▌▌

E_n=-\frac{13.6\,\text{eV}}{n^2}

▌▌

\hbar\omega=h\nu

▌

PV^\gamma=\text{const}

▌▌

\ln(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\cdots

▌▌▌

\sum_{i=1}^n i=\frac{n(n+1)}{2}

▌▌

▌

\sqrt[n]{a}=a^{1/n}

▌▌

W=\int\mathbf{F}\cdot d\mathbf{s}

▌▌

\frac{d}{dt}\int_V\rho\,dV=0

▌

\mathbb{P}(X>x)=e^{-\lambda x}

▌▌

\vec{a}\cdot\vec{b}=|a||b|\cos\theta

▌▌▌

\iiint_V dV=\frac{4}{3}\pi r^3

▌▌

▌

\nabla f=\langle f_x, f_y, f_z\rangle

▌▌

\sum_{i=0}^n 2^i=2^{n+1}-1

▌▌

\text{Var}(X)=E[X^2]-(E[X])^2

▌

\oint_C f(z)\,dz=2\pi i\sum\text{Res}

▌▌

\nabla^2\psi+k^2\psi=0

▌▌▌

A^{-1}A=I

▌▌

▌

\text{MSE}=\frac{1}{n}\sum(y_i-\hat{y}_i)^2

▌▌

\prod_{p}\frac{1}{1-p^{-s}}=\zeta(s)

▌▌

\mathcal{L}=T-V

▌

a^2+b^2=c^2

▌▌

▌

\nabla\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}

▌▌

\mu=\frac{1}{n}\sum_{i=1}^n x_i

▌▌

\det(A-\lambda I)=0

▌▌▌

f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}

▌▌

\int_a^b f(x)\,dx=F(b)-F(a)

▌

\sum_{i=1}^n i^2=\frac{n(n+1)(2n+1)}{6}

▌▌

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Why is chlorophyll green?

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What happens to the internal energy of a gas during an adiabatic expansion?

Cell Biology — Unit 3

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In an adiabatic process (Q=0), the gas does work on its surroundings, using its own internal energy. Therefore ΔU = −W.

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