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2024-10-07
@ -3,7 +3,6 @@
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\ger{Analysis}
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]{cal}
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\Subsection[
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\eng{Convolution}
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\ger{Faltung / Konvolution}
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@ -64,7 +63,7 @@
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\end{formula}
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\Eng[real]{real}
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\Ger[real]{reellwertig}
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\begin{formula}{coefficient-complex}
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\begin{formula}{coefficient}
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\desc{Fourier coefficients}{Complex representation}{}
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\desc[german]{Fourierkoeffizienten}{Komplexe Darstellung}{}
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\eq{
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@ -113,69 +112,14 @@
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\end{enumerate}
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\Subsection[
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\eng{Misc}
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\ger{Verschiedenes}
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]{misc}
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\begin{formula}{stirling-approx}
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\desc{Stirling approximation}{}{}
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\desc[german]{Stirlingformel}{}{}
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\eq{\ln (N!) \approx N \ln(N) - N + \Order(\ln(N))}
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\end{formula}
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\begin{formula}{error-function}
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\desc{Error function}{\erf: \C \to \C}{}
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\desc[german]{Fehlerfunktion}{Error function: \erf: \C \to \C}{}
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\eq{
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\erf(x) &= \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \d t \\
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\erfc(x) &= 1 - \erf(x)\\
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&= \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2} \d t
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}
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\end{formula}
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\Section[
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\eng{Logarithm}
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\ger{Logarithmus}
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]{log}
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\begin{formula}{identities}
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\desc{Logarithm identities}{}{}
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\desc[german]{Logarithmus Identitäten}{Logarithmus Rechenregeln}{}
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\eq{
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\log(xy) &= \log(x) + \log(y) \\
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\log \left(\frac{x}{y}\right) &= \log(x) - \log(y) \\
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\log \left(x^d\right) &= d\log(x) \\
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\log \left(\sqrt[y]{x}\right) &= \frac{\log(x)}{y} \\
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x^{\log(y)} &= y^{\log(x)}
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}
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\end{formula}
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\Section[
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\eng{List of common integrals}
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\ger{Liste nützlicher Integrale}
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]{integrals}
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\begin{formula}{spherical-coordinates}
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\desc{Spherical coordinates}{}{}
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\desc[german]{Kugelkoordinaten}{}{}
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\eq{
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x &= r \sin\phi,\cos\theta \\
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y &= r \cos\phi,\cos\theta \\
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z &= r \sin\theta
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}
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\end{formula}
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\begin{formula}{spheical-coordinates-int}
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\desc{Integration in spherical coordinates}{}{}
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\desc[german]{Integration in Kugelkoordinaten}{}{}
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\eq{\iiint\d x \d y \d z= \int_0^{\infty} \!\! \int_0^{2\pi} \!\! \int_0^\pi \d r \d\phi\d\theta \, r^2\sin\theta}
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\end{formula}
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\begin{formula}{riemann_zeta}
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\desc{Riemann Zeta Function}{}{}
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\desc[german]{Riemannsche Zeta-Funktion}{}{}
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\eq{\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \frac{1}{(1-2^{(1-s)})\Gamma(s)} \int_0^\infty \d\eta \frac{\eta^{(s-1)}}{\e^\eta + 1}}
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\end{formula}
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@ -28,7 +28,7 @@
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\end{formula}
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\begin{formula}{wave_function}
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\desc{Wave function}{}{$R_{nl}(r)$ \fqEqRef{qm:h:radial}, $Y_{lm}$ \fqEqRef{qm:spherical_harmonics}}
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\desc{Wave function}{}{}
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\desc[german]{Wellenfunktion}{}{}
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\eq{\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta,\phi)}
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\end{formula}
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55
src/calculus.tex
Normal file
55
src/calculus.tex
Normal file
@ -0,0 +1,55 @@
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\Part[
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\eng{Analysis}
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\ger{Analysis}
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]{ana}
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\Subsection[
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\eng{Convolution}
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\ger{Faltung / Konvolution}
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]{conv}
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\begin{ttext}
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\eng{Convolution is \textbf{commutative}, \textbf{associative} and \textbf{distributive}.}
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\ger{Die Faltung ist \textbf{kommutativ}, \textbf{assoziativ} und \textbf{distributiv}}
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\end{ttext}
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\begin{formula}{def}
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\desc{Definition}{}{}
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\desc[german]{Definition}{}{}
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\eq{(f*g)(t) = f(t) * g(t) = int_{-\infty}^\infty f(\tau) g(t-\tau) \d \tau}
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\end{formula}
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\begin{formula}{notation}
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\desc{Notation}{}{}
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\desc[german]{Notation}{}{}
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\eq{
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f(t) * g(t-t_0) &= (f*g)(t-t_0) \\
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f(t-t_0) * g(t-t_0) &= (f*g)(t-2t_0)
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}
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\end{formula}
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\begin{formula}{commutativity}
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\desc{Commutativity}{}{}
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\desc[german]{Kommutativität}{}{}
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\eq{f * g = g * f}
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\end{formula}
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\begin{formula}{associativity}
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\desc{Associativity}{}{}
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\desc[german]{Assoziativität]}{}{}
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\eq{(f*g)*h = f*(g*h)}
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\end{formula}
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\begin{formula}{distributivity}
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\desc{Distributivity}{}{}
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\desc[german]{Distributivität}{}{}
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\eq{f * (g + h) = f*g + f*h}
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\end{formula}
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\begin{formula}{complex_conjugate}
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\desc{Complex conjugate}{}{}
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\desc[german]{Komplexe konjugation}{}{}
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\eq{(f*g)^* = f^* * g^*}
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\end{formula}
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\Subsection[
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\eng{Fourier analysis}
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\ger{Fourieranalyse}
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]{fourier}
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@ -2,7 +2,6 @@
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\eng{Condensed matter physics}
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\ger{Festkörperphysik}
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]{cm}
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\TODO{Bonds, hybridized orbitals, tight binding}
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\Section[
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\eng{Bravais lattice}
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\ger{Bravais-Gitter}
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@ -85,17 +84,6 @@
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\end{tabularx}
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\end{adjustbox}
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\end{table}
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family of plane that are equivalent due to crystal symmetry
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\begin{formula}{miller}
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\desc{Miller index}{}{}
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\desc[german]{Millersche Indizes}{}{}
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\eq{
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(hkl) & \text{\GT{plane}}\\
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[hkl] & \text{\GT{direction}}\\
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\{hkl\} & \text{\GT{millerFamily}}
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}
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\end{formula}
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\Section[
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@ -407,50 +395,3 @@ family of plane that are equivalent due to crystal symmetry
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\centering
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\includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
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\end{minipage}
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\Section[
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\eng{Superconductivity}
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\ger{Supraleitung}
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]{sc}
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\begin{ttext}
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\eng{
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Materials for which the electric resistance jumps to 0 under a critical temperature.
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\\\textbf{Type I}: Has a single critical magnetic field at which the superconuctor becomes a normal conductor.
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\\\textbf{Type II}: Has two critical
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}
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\ger{Materialien, bei denen der elektrische Widerstand beim unterschreiten einer kritischen Temperatur auf 0 springt.}
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\end{ttext}
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\begin{formula}{meissner_effect}
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\desc{Meißner-Ochsenfeld effect}{Perfect diamagnetism}{}
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\desc[german]{Meißner-Ochsenfeld Effekt}{Perfekter Diamagnetismus}{}
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\ttxt{
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\eng{Blabla }
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\ger{Blubb blubb }
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}
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\end{formula}
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\Subsection[
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\eng{London equation}
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\ger{London-Gleichungen}
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]{london}
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\begin{formula}{first}
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% \vec{j} = \frac{nq\hbar}{m}\Grad S - \frac{nq^2}{m}\vec{A}
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\desc{First London Equation}{}{$\vec{j}$ current density, $n$, $m$, $q$ density, mass and charge of superconduticng particles}
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\desc[german]{Erste London-Gleichung}{}{$\vec{j}$ Stromdichte, $n$, $m$, $q$ Dichte, Masse und Ladung der supraleitenden Teilchen}
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\eq{
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\partical_t \vec{j} = \frac{nq^2}{m}\vec{E}
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}
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\end{formula}
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\begin{formula}{second}
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\desc{Second London Equation}{}{$\vec{j}$ current density, $n$, $m$, $q$ density, mass and charge of superconduticng particles}
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\desc[german]{Zweite London-Gleichung}{}{$\vec{j}$ Stromdichte, $n$, $m$, $q$ Dichte, Masse und Ladung der supraleitenden Teilchen}
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\eq{
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\Rot \vec{j} = -\frac{nq^2}{m} \vec{B}
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}
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\end{formula}
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\begin{formula}{penetration_depth}
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\desc{London penetration depth}{}{}
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\desc[german]{London Eindringtiefe}{}{}
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\eq{\lambda_\textrm{L} = \sqrt{\frac{m}{\mu_0 nq^2}}}
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\end{formula}
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@ -32,7 +32,6 @@
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\Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
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}
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\end{formula}
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\TODO{Polarization, Magnetisation}
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\Section[
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\eng{Fields}
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15
src/main.tex
Executable file → Normal file
15
src/main.tex
Executable file → Normal file
@ -145,10 +145,13 @@
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\input{util/translations.tex}
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\input{maths/linalg.tex}
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\input{maths/geometry.tex}
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\input{maths/analysis.tex}
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\input{maths/probability_theory.tex}
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\input{linalg.tex}
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||||
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\input{geometry.tex}
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||||
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\input{analysis.tex}
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\input{probability_theory.tex}
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||||
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\input{mechanics.tex}
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@ -161,9 +164,9 @@
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\input{condensed_matter.tex}
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\input{topo.tex}
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% \input{topo.tex}
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\input{quantum_computing.tex}
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% \input{quantum_computing.tex}
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% \input{many-body-simulations.tex}
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||||
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@ -4,27 +4,21 @@
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]{pt}
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\begin{formula}{mean}
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\desc{Mean}{Expectation value}{}
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||||
\desc[german]{Mittelwert}{Erwartungswert}{}
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\desc{Mean}{}{}
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\desc[german]{Mittelwert}{}{}
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\eq{\braket{x} = \int w(x)\, x\, \d x}
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\end{formula}
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\begin{formula}{variance}
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\desc{Variance}{Square of the \fqEqRef{pt:std-deviation}}{}
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\desc[german]{Varianz}{Quadrat der\fqEqRef{pt:std-deviation}}{}
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\eq{\sigma^2 = (\Delta \hat{x})^2 = \Braket{\hat{x}^2} - \braket{\hat{x}}^2 = \braket{(x - \braket{x})^2}}
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\end{formula}
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\begin{formula}{covariance}
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\desc{Covariance}{}{}
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\desc[german]{Kovarianz}{}{}
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\eq{\cov(x,y) = \sigma(x,y) = \sigma_{XY} = \Braket{(x-\braket{x})\,(y-\braket{y})}}
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\desc{Variance}{}{}
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\desc[german]{Varianz}{}{}
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\eq{\sigma^2 = (\Delta \hat{x})^2 = \braket{\hat{x}^2} - \braket{\hat{x}}^2 = \braket{(x - \braket{x})^2}}
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||||
\end{formula}
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\begin{formula}{std-deviation}
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\begin{formula}{std_deviation}
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\desc{Standard deviation}{}{}
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\desc[german]{Standardabweichung}{}{}
|
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\eq{\sigma = \sqrt{\sigma^2} = \sqrt{(\Delta x)^2}}
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\eq{\sigma = \sqrt{(\Delta x)^2}}
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\end{formula}
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\begin{formula}{median}
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@ -198,38 +192,3 @@
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||||
}
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||||
\end{ttext}
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\Section[
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||||
\eng{Propagation of uncertainty / error}
|
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\ger{Fehlerfortpflanzung}
|
||||
]{error}
|
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\begin{formula}{generalised}
|
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\desc{Generalized error propagation}{}{$V$ \fqEqRef{pt:covariance} matrix, $J$ \fqEqRef{ana:jacobi-matrix}}
|
||||
\desc[german]{Generalisiertes Fehlerfortpflanzungsgesetz}{$V$ \fqEqRef{pt:covariance} Matrix, $J$ \fqEqRef{ana:jacobi-matrix}}{}
|
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\eq{V_y = J(x) \cdot V_x \cdot J^{\T} (x)}
|
||||
\end{formula}
|
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|
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\begin{formula}{uncorrelated}
|
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\desc{Propagation of uncorrelated errors}{Linear approximation}{}
|
||||
\desc[german]{Fortpflanzung unabhängiger fehlerbehaftete Größen}{Lineare Näherung}{}
|
||||
\eq{u_y = \sqrt{ \sum_{i} \left(\pdv{y}{x_i}\cdot u_i\right)^2}}
|
||||
\end{formula}
|
||||
|
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\begin{formula}{weight}
|
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\desc{Weight}{Variance is a possible choice for a weight}{$\sigma$ \fqEqRef{pt:variance}}
|
||||
\desc[german]{Gewicht}{Varianz ist eine mögliche Wahl für ein Gewicht}{}
|
||||
\eq{w_i = \frac{1}{\sigma_i^2}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{weighted-mean}
|
||||
\desc{Weighted mean}{}{$w_i$ \fqEqRef{pt:error:weight}}
|
||||
\desc[german]{Gewichteter Mittelwert}{}{}
|
||||
\eq{\overline{x} = \frac{\sum_{i} (x_i w_i)}{\sum_i w_i}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{weighted-mean-error}
|
||||
\desc{Variance of weighted mean}{}{$w_i$ \fqEqRef{pt:error:weight}}
|
||||
\desc[german]{Varianz des gewichteten Mittelwertes}{}{}
|
||||
\eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}}
|
||||
\end{formula}
|
||||
|
||||
|
||||
@ -379,12 +379,6 @@
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{c_a_matrices}
|
||||
\desc{Matrix forms}{}{}
|
||||
\desc[german]{Matrix-Form}{}{}
|
||||
\eq{\TODO{TODO}}
|
||||
\end{formula}
|
||||
|
||||
\Subsubsection[
|
||||
\eng{Harmonischer Oszillator}
|
||||
\ger{Harmonic Oscillator}
|
||||
|
||||
@ -20,18 +20,10 @@ The `<partname>:...:<lowest section name>` will be defined as `fqname` (fully qu
|
||||
- figure: `fig`
|
||||
- parts, (sub)sections: `sec`
|
||||
|
||||
### Reference functions
|
||||
Functions that create a hyperlink (and use the translation of the target element as link name):
|
||||
- `\fqSecRef{}`
|
||||
- `\fqEqRef{}`
|
||||
|
||||
|
||||
## Multilanguage
|
||||
All text should be defined as a translation (`translations` package, see `util/translation.tex`) and then used using the `gt` or `GT` macros.
|
||||
The english translation of any key must be defined, because it will also be used as fallback.
|
||||
|
||||
Lower case macros are relative to the current `fqname`, while upper case macros are absolute.
|
||||
|
||||
Never make a macro that would have to be changed if a new language was added, eg dont do
|
||||
```tex
|
||||
% 1: key, 2: english version, 3: german version
|
||||
|
||||
@ -332,7 +332,7 @@
|
||||
\desc[german]{Entropiedichte}{}{$s = \frac{S}{N}$}
|
||||
\eq{
|
||||
\lim_{T\to 0} s(T) &= 0 \\
|
||||
\shortintertext{\GT{and_therefore_also}}
|
||||
\shortintertext{\GT{and_therefore_also}} \\
|
||||
\lim_{T\to 0} c_V &= 0
|
||||
}
|
||||
\end{formula}
|
||||
@ -376,21 +376,21 @@
|
||||
\desc[german]{Innere Energie}{}{}
|
||||
\eq{\d U(S,V,N) = T\d S -p\d V + \mu\d N}
|
||||
\end{formula}
|
||||
\begin{formula}{free_energy}
|
||||
\desc{Free energy / Helmholtz energy }{}{}
|
||||
\desc[german]{Freie Energie / Helmholtz Energie}{}{}
|
||||
\eq{\d F(T,V,N) = -S\d T -p\d V + \mu\d N}
|
||||
\end{formula}
|
||||
\begin{formula}{enthalpy}
|
||||
\desc{Enthalpy}{}{}
|
||||
\desc[german]{Enthalpie}{}{}
|
||||
\eq{\d H(S,p,N) = T\d S +V\d p + \mu\d N}
|
||||
\end{formula}
|
||||
\begin{formula}{gibbs_energy}
|
||||
\desc{Free enthalpy / Gibbs energy}{}{}
|
||||
\desc[german]{Freie Entahlpie / Gibbs-Energie}{}{}
|
||||
\desc{Gibbs energy}{}{}
|
||||
\desc[german]{Gibbsche Energie}{}{}
|
||||
\eq{\d G(T,p,N) = -S\d T + V\d p + \mu\d N}
|
||||
\end{formula}
|
||||
\begin{formula}{free_energy}
|
||||
\desc{Free energy / Helmholtz energy }{}{}
|
||||
\desc[german]{Freie Energie / Helmholtz Energie}{}{}
|
||||
\eq{\d F(T,V,N) = -S\d T -p\d V + \mu\d N}
|
||||
\end{formula}
|
||||
\begin{formula}{grand_canon_pot}
|
||||
\desc{Grand canonical potential}{}{}
|
||||
\desc[german]{Großkanonisches Potential}{}{}
|
||||
@ -398,27 +398,6 @@
|
||||
\end{formula}
|
||||
|
||||
\TODO{Maxwell Relationen, TD Quadrat}
|
||||
\begin{formula}{td-square}
|
||||
\desc{Thermodynamic squre}{}{}
|
||||
\desc[german]{Themodynamisches Quadrat}{Guggenheim Quadrat}{}
|
||||
\content{
|
||||
\begin{tikzpicture}
|
||||
\draw[thick] (0,0) grid (3,3);
|
||||
\node at (0.5, 2.5) {$-S$};
|
||||
\node at (1.5, 2.5) {\color{blue}$U$};
|
||||
\node at (2.5, 2.5) {$V$};
|
||||
\node at (0.5, 1.5) {\color{blue}$H$};
|
||||
\node at (2.5, 1.5) {\color{blue}$F$};
|
||||
\node at (0.5, 0.5) {$-p$};
|
||||
\node at (1.5, 0.5) {\color{blue}$G$};
|
||||
\node at (2.5, 0.5) {$T$};
|
||||
\end{tikzpicture}
|
||||
\begin{ttext}
|
||||
\eng{The corners opposite from the potential are the coefficients and each coefficients differential is opposite to it.}
|
||||
\ger{Die Ecken gegenüber des Potentials sind die Koeffizienten, das Differential eines Koeffizienten ist in der Ecke gegenüber.}
|
||||
\end{ttext}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Section[
|
||||
\eng{Ideal gas}
|
||||
@ -558,8 +537,8 @@
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{lennard_jones}
|
||||
\desc{Lennard-Jones potential}{Potential between two molecules. Attractive for $r > \sigma$, repulsive for $r < \sigma$.\\ In condensed matter: Attraction due to Landau Dispersion \TODO{verify} and repulsion due to Pauli exclusion principle.}{}
|
||||
\desc[german]{Lennard-Jones-Potential}{Potential zwischen zwei Molekülen. Attraktiv für $r > \sigma$, repulsiv für $r < \sigma$.\\ In Festkörpern: Anziehung durch Landau Dispesion und Abstoßung durch Pauli-Prinzip.}{}
|
||||
\desc{Lennard-Jones potential}{Potential between two molecules. Attractive for $r > \sigma$, repulsive for $r < \sigma$}{}
|
||||
\desc[german]{Lennard-Jones-Potential}{Potential zwischen zwei Molekülen. Attraktiv für $r > \sigma$, repulsiv für $r < \sigma$}{}
|
||||
\figeq{img/potential_lennard_jones.pdf}{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
|
||||
\end{formula}
|
||||
|
||||
@ -679,7 +658,7 @@
|
||||
\eng{Bosons}
|
||||
\ger{Bosonen}
|
||||
]{bos}
|
||||
\begin{formula}{partition-sum}
|
||||
\begin{formula}{partition_sum}
|
||||
\desc{Partition sum}{}{$p \in\N_0$}
|
||||
\desc[german]{Zustandssumme}{}{$p \in\N_0$}
|
||||
\eq{Z_\text{g} = \prod_{p} \frac{1}{1-\e^{-\beta(\epsilon_p - \mu)}}}
|
||||
|
||||
0
src/svgs/convertToPdf.sh
Normal file → Executable file
0
src/svgs/convertToPdf.sh
Normal file → Executable file
@ -15,13 +15,6 @@
|
||||
\def\descwidth{0.3\textwidth}
|
||||
\def\eqwidth{0.6\textwidth}
|
||||
|
||||
|
||||
%
|
||||
% FORMULA ENVIRONMENT
|
||||
% The following commands are meant to be used with the formula environment
|
||||
%
|
||||
|
||||
% Name in black and below description in gray
|
||||
% [1]: minipage width
|
||||
% 2: fqname of name
|
||||
% 3: fqname of a translation that holds the explanation
|
||||
@ -140,54 +133,32 @@
|
||||
|
||||
}
|
||||
|
||||
% 1: key
|
||||
\newenvironment{formula}[1]{
|
||||
% [1]: language
|
||||
% 2: name
|
||||
% 3: description
|
||||
% 4: definitions/links
|
||||
% key
|
||||
\newcommand{\desc}[4][english]{
|
||||
% language, name, description, definitions
|
||||
\dt[#1]{##1}{##2}
|
||||
\ifblank{##3}{}{\dt[#1_desc]{##1}{##3}}
|
||||
\ifblank{##4}{}{\dt[#1_defs]{##1}{##4}}
|
||||
}
|
||||
% 1: equation for align environment
|
||||
\newcommand{\eq}[1]{
|
||||
\insertEquation{#1}{##1}
|
||||
}
|
||||
% 1: equation for alignat environment
|
||||
\newcommand{\eqAlignedAt}[2]{
|
||||
\insertAlignedAt{#1}{##1}{##2}
|
||||
}
|
||||
% 1: equation for flalign environment
|
||||
\newcommand{\eqFLAlign}[1]{
|
||||
\insertFLAlign{#1}{##1}
|
||||
}
|
||||
% 1: file path
|
||||
% 2: equation
|
||||
\newcommand{\figeq}[2]{
|
||||
\insertEquationWithFigure{#1}{##1}{##2}
|
||||
}
|
||||
% 1: any content
|
||||
\newcommand{\content}[1]{
|
||||
\NameLeftContentRight{#1}{##1}
|
||||
}
|
||||
% 1: content for the ttext environment
|
||||
\newcommand{\ttxt}[1]{
|
||||
\NameLeftContentRight{#1}{
|
||||
\begin{ttext}[#1:desc]
|
||||
##1
|
||||
\end{ttext}
|
||||
}
|
||||
}
|
||||
|
||||
}{\ignorespacesafterend}
|
||||
|
||||
|
||||
%
|
||||
% QUANTITY
|
||||
%
|
||||
\newenvironment{quantity}[5]{
|
||||
% key, symbol, si unit, si base units, comment (key to translation)
|
||||
\newcommand{\desc}[3][english]{
|
||||
@ -195,6 +166,15 @@
|
||||
\DT[qty:#1]{}{##1}{##2}
|
||||
\ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}}
|
||||
}
|
||||
\newcommand{\eq}[1]{
|
||||
\insertEquation{#1}{##1}
|
||||
}
|
||||
\newcommand{\eqAlignedAt}[2]{
|
||||
\insertAlignedAt{#1}{##1}{##2}
|
||||
}
|
||||
\newcommand{\eqFLAlign}[1]{
|
||||
\insertFLAlign{#1}{##1}
|
||||
}
|
||||
|
||||
\edef\qtyname{#1}
|
||||
\edef\qtysign{#2}
|
||||
@ -210,9 +190,6 @@
|
||||
|
||||
|
||||
|
||||
%
|
||||
% DISTRIBUTION
|
||||
%
|
||||
\def\distrightwidth{0.45\textwidth}
|
||||
\def\distleftwidth{0.45\textwidth}
|
||||
|
||||
|
||||
@ -37,8 +37,6 @@
|
||||
\DeclareMathOperator{\tr}{tr}
|
||||
\DeclareMathOperator{\const}{const}
|
||||
\DeclareMathOperator{\erf}{erf}
|
||||
\DeclareMathOperator{\erfc}{erfc}
|
||||
\DeclareMathOperator{\cov}{cov}
|
||||
% diff, for integrals and stuff
|
||||
% \DeclareMathOperator{\dd}{d}
|
||||
\renewcommand*\d{\mathop{}\!\mathrm{d}}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user