_{\infty }^{r}-2\alpha \left({\frac {Q}{4\pi \epsilon _{0}}}\right)^{2}{\frac {1}{r^{5}}}dr=-{\frac {\alpha }{2}}\left({\frac {Q}{4\pi \epsilon _{0}}}\right)^{2}{\frac...

and Forward Euler %u_t= \alpha*u_xx %BC= u(0)=0, u(2*pi)=0 %IC=sin(x) clear all; clc; %Grid N = 64; %Number of steps h = 2*pi/N; %step size x = h*(1:N);...

and Forward Euler %u_t= \alpha*u_xx %BC= u(0)=0, u(2*pi)=0 %IC=sin(x) clear all; clc; %Grid N = 64; %Number of steps h = 2*pi/N; %step size x = h*(1:N);...

character name character alpha α iota ι rho ρ beta β kappa κ sigma σ gamma γ lambda λ tau τ delta δ mu μ upsilon υ epsilon ϵ nu ν phi ϕ zeta ζ xi ξ chi...

m − 1 {\displaystyle R_{\infty }={\frac {m_{e}e^{4}}{(4\pi \epsilon _{0})^{2}\hbar ^{3}4\pi c}}=1.0973731568525(73)\cdot 10^{7}\,\mathrm {m} ^{-1}} where...

a(r;\epsilon )={\frac {1}{{\frac {4}{3}}\pi \epsilon ^{3}}}\left\{{\begin{array}{cc}c&(r\leq \epsilon )\\{\frac {(c-1)\epsilon ^{2}}{k(\epsilon )^{2}}}{\frac...

{\displaystyle \alpha \in A} the function π | V α {\displaystyle \pi |_{V_{\alpha }}} is a homeomorphism between V α {\displaystyle V_{\alpha }} and U {\displaystyle...

{\displaystyle q_{trans}=\int \limits _{0}^{\infty }e^{-\alpha x^{2}}\,dx={\frac {1}{2}}{\sqrt {\frac {\pi }{\alpha }}}} Therefore, q t r a n s = ( 1 2 π α ) 3 {\displaystyle...

{Q}{4\pi \epsilon _{0}x}}\right]_{r}^{\infty }=-{\frac {Q}{4\pi \epsilon _{0}\infty }}-\left(-{\frac {Q}{4\pi \epsilon _{0}r}}\right)={\frac {Q}{4\pi \epsilon...

M {\displaystyle M} . We need to show that given ϵ > 0 {\displaystyle \epsilon >0} we can find some c {\displaystyle c} such that ∫ c 1 f ( x ) d x ∈...

{{E_{r}}_{1}}_{x}={\frac {1}{4\pi \epsilon _{0}}}{\frac {+q}{{(y+a)}^{2}+x^{2}}}\sin \alpha ={\frac {1}{4\pi \epsilon _{0}}}{\frac {+q}{{(y+a)}^{2}+x^{2}}}{\frac...

}{\alpha }}\partial _{\varsigma }((-2\pi ix)^{\beta })\partial _{\alpha -\varsigma }(\phi _{l}(x)-\phi (x))} . Let now ϵ > 0 {\displaystyle \epsilon >0}...

z_{n})|\epsilon _{1}-\alpha <|z_{1}|<\epsilon _{1}\wedge \forall j\in \{2,\ldots ,n\}:|z_{j}|<\epsilon _{1}\}\cup \{\}} , where α > 0 {\displaystyle \alpha >0}...

}{\alpha }}\partial _{\varsigma }((-2\pi ix)^{\beta })\partial _{\alpha -\varsigma }(\phi _{l}(x)-\phi (x))} . Let now ϵ > 0 {\displaystyle \epsilon >0}...

\epsilon >1} , this equation defines a hyperbola. If ϵ = 1 {\displaystyle \epsilon =1} , it defines a parabola. If 0 < ϵ < 1 {\displaystyle 0<\epsilon...

{1}{2i\pi }}\int _{\gamma _{1}}o(F(z)){\frac {dz}{z^{n+1}}}\leq \epsilon 2en^{-\alpha -1}(\log n)^{\gamma }(\log \log n)^{\delta }=o(n^{-\alpha -1}(\log...

= 1.44 × 10 − 8  V {\displaystyle V={\frac {Q}{4\pi \epsilon _{0}r}}={\frac {3.2\times 10^{-19}}{4\pi \times 8.85\times 10^{-12}\times 0.2}}=1.44\times...

_{\infty }^{r}-2\alpha \left({\frac {Q}{4\pi \epsilon _{0}}}\right)^{2}{\frac {1}{r^{5}}}dr=-{\frac {\alpha }{2}}\left({\frac {Q}{4\pi \epsilon _{0}}}\right)^{2}{\frac...

literally is Greek to them. alpha α beta β gamma γ delta δ epsilon ε zeta ζ eta η theta θ iota ι kappa κ lambda λ mu μ nu ν xi ξ pi π piv ϖ rho ρ sigma σ sigmaf...

\left|{\frac {1}{2\pi }}\int _{0}^{2\pi }f(z_{M}+\epsilon e^{i\varphi })d\varphi \right|\leq {\frac {1}{2\pi }}\int _{0}^{2\pi }|f(z_{M}+\epsilon e^{i\varphi...